├── CREDITS.md ├── .github └── workflows │ └── github-ci.yml ├── CODEOWNERS ├── .gitignore ├── README.md ├── gmshcfd ├── __init__.py ├── errors.py ├── wake.py ├── gmshcfd.py ├── utils.py ├── domain.py └── wing.py ├── setup.py ├── examples ├── airfoils │ ├── naca_0012.dat │ ├── rae_2822.dat │ ├── lann_5.dat │ ├── lann_6.dat │ ├── lann_7.dat │ ├── lann_4.dat │ ├── lann_3.dat │ ├── lann_0.dat │ ├── lann_1.dat │ ├── lann_2.dat │ └── onera_m6.dat ├── m6.py ├── wing_tail.py └── lann.py ├── run.py └── LICENSE /CREDITS.md: -------------------------------------------------------------------------------- 1 | GmshCFD is Copyright (C) of Adrien Crovato. 2 | 3 | The main author of GmshCFD is Adrien Crovato. 4 | 5 | Direct and indirect contributions have been made to GmshCFD by the following people: 6 | - Romain Boman 7 | -------------------------------------------------------------------------------- /.github/workflows/github-ci.yml: -------------------------------------------------------------------------------- 1 | name: Continuous integration 2 | 3 | on: 4 | push: 5 | pull_request: 6 | 7 | jobs: 8 | build: 9 | runs-on: ubuntu-22.04 10 | container: 11 | image: onelab/ubuntu20.04 12 | options: --user root 13 | steps: 14 | - name: Checkout repo 15 | uses: actions/checkout@v4 16 | - name: Install 17 | run: | 18 | python3 -m pip install . 19 | - name: Test 20 | run: | 21 | mkdir WORKSPACE && cd WORKSPACE 22 | cp -r ../examples/. . 23 | for f in ./*.py; do python3 "$f"; done 24 | -------------------------------------------------------------------------------- /CODEOWNERS: -------------------------------------------------------------------------------- 1 | # This is a comment. 2 | # Each line is a file pattern followed by one or more owners. 3 | 4 | # These owners will be the default owners for everything in 5 | # the repo. Unless a later match takes precedence, they 6 | # will be requested for review when someone opens a pull request. 7 | * @acrovato 8 | 9 | # These owners own a directory and nested subdirectories 10 | #/gmshcfd/ @acrovato 11 | 12 | # You can also use email addresses if you prefer. They'll be 13 | # used to look up users just like we do for commit author 14 | # emails. 15 | #*.go docs@example.com 16 | 17 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | *$py.class 5 | 6 | # C extensions 7 | *.so 8 | 9 | # Distribution / packaging 10 | .Python 11 | build/ 12 | develop-eggs/ 13 | dist/ 14 | downloads/ 15 | eggs/ 16 | .eggs/ 17 | lib/ 18 | lib64/ 19 | parts/ 20 | sdist/ 21 | var/ 22 | wheels/ 23 | share/python-wheels/ 24 | *.egg-info/ 25 | .installed.cfg 26 | *.egg 27 | MANIFEST 28 | 29 | # PEP 582; used by e.g. github.com/David-OConnor/pyflow and github.com/pdm-project/pdm 30 | __pypackages__/ 31 | 32 | # Environments 33 | .env 34 | .venv 35 | env/ 36 | venv/ 37 | ENV/ 38 | 39 | # Misc 40 | core 41 | *.*~ 42 | 43 | # OS 44 | .DS_Store 45 | *.swp 46 | *.bak 47 | 48 | # Workspace 49 | workspace 50 | *.tar.gz 51 | *.tgz 52 | 53 | # build dir 54 | build 55 | 56 | # Gmsh 57 | *.pos 58 | *.msh 59 | 60 | # IDE 61 | .project 62 | .pydevproject 63 | .settings 64 | .vscode 65 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # GmshCFD 2 | Python tool based on [Gmsh](https://gmsh.info/) for creating CFD meshes around lifting surfaces. 3 | Adrien Crovato, 2023. 4 | 5 | [![Python](https://img.shields.io/badge/python-3.8-blue.svg)](https://www.python.org/downloads/release/python-386/) 6 | [![Continuous integration](https://github.com/acrovato/gmshcfd/actions/workflows/github-ci.yml/badge.svg)](https://github.com/acrovato/gmshcfd/actions) 7 | [![License: GPL v3](https://img.shields.io/badge/License-GPLv3-blue.svg)](https://www.gnu.org/licenses/gpl-3.0) 8 | 9 | ## Main features 10 | GmshCFD can create tetrahedral CFD meshes around isolated or multiple lifting surfaces suitable for external aerodynamics (potential, Euler or RANS equations). The lifting surfaces can have a sharp or a blunt trailing edge. 11 | 12 | ## Documentation 13 | Detailed build and use instructions can be found in the [wiki](https://github.com/acrovato/gmshcfd/wiki). 14 | -------------------------------------------------------------------------------- /gmshcfd/__init__.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | 3 | # GmshCFD 4 | # Copyright (C) 2023 Adrien Crovato 5 | # 6 | # This program is free software: you can redistribute it and/or modify 7 | # it under the terms of the GNU General Public License as published by 8 | # the Free Software Foundation, either version 3 of the License, or 9 | # (at your option) any later version. 10 | # This program is distributed in the hope that it will be useful, 11 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | # GNU General Public License for more details. 14 | # You should have received a copy of the GNU General Public License 15 | # along with this program. If not, see . 16 | 17 | __version__ = '1.1.0' 18 | 19 | from .gmshcfd import GmshCFD 20 | from .wing import Wing 21 | from .wake import Wake 22 | from .domain import Box, Sphere 23 | from .utils import * 24 | -------------------------------------------------------------------------------- /gmshcfd/errors.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | 3 | # GmshCFD 4 | # Copyright (C) 2023 Adrien Crovato 5 | # 6 | # This program is free software: you can redistribute it and/or modify 7 | # it under the terms of the GNU General Public License as published by 8 | # the Free Software Foundation, either version 3 of the License, or 9 | # (at your option) any later version. 10 | # This program is distributed in the hope that it will be useful, 11 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | # GNU General Public License for more details. 14 | # You should have received a copy of the GNU General Public License 15 | # along with this program. If not, see . 16 | 17 | class GmshCFDError(RuntimeError): 18 | def __init__(self, message, caller): 19 | message = 'in ' + str(caller.__class__) + ' ' + message 20 | super().__init__(message) 21 | -------------------------------------------------------------------------------- /setup.py: -------------------------------------------------------------------------------- 1 | # GmshCFD 2 | # Copyright (C) 2023 Adrien Crovato 3 | # 4 | # This program is free software: you can redistribute it and/or modify 5 | # it under the terms of the GNU General Public License as published by 6 | # the Free Software Foundation, either version 3 of the License, or 7 | # (at your option) any later version. 8 | # This program is distributed in the hope that it will be useful, 9 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 10 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 11 | # GNU General Public License for more details. 12 | # You should have received a copy of the GNU General Public License 13 | # along with this program. If not, see . 14 | 15 | from setuptools import setup, find_packages 16 | import re 17 | 18 | __version__ = re.findall( 19 | r"""__version__ = ["']+([0-9\.]*)["']+""", 20 | open('gmshcfd/__init__.py').read(), 21 | )[0] 22 | 23 | setup( 24 | name='gmshcfd', 25 | version=__version__, 26 | description='GmshCFD is a tool based on Gmsh for creating CFD meshes around lifting surfaces suitable for external aerodynamic analysis.', 27 | keywords='Gmsh CFD aerodynamic mesh Python', 28 | author='Adrien Crovato', 29 | author_email='', 30 | url='https://github.com/acrovato/gmshcfd', 31 | license='GNU General Public License 3.0', 32 | packages=find_packages(include=['gmshcfd*']), 33 | install_requires=['numpy>=1.22', 'scipy>=1.10', 'gmsh==4.10.5'], 34 | classifiers=['Operating System :: OS Independent', 'Programming Language :: Python'], 35 | ) 36 | -------------------------------------------------------------------------------- /examples/airfoils/naca_0012.dat: -------------------------------------------------------------------------------- 1 | NACA 0012 2 | 1.000000 0.001260 3 | 0.998459 0.001476 4 | 0.993844 0.002120 5 | 0.986185 0.003182 6 | 0.975528 0.004642 7 | 0.961940 0.006478 8 | 0.945503 0.008658 9 | 0.926320 0.011149 10 | 0.904508 0.013914 11 | 0.880203 0.016914 12 | 0.853553 0.020107 13 | 0.824724 0.023452 14 | 0.793893 0.026905 15 | 0.761249 0.030423 16 | 0.726995 0.033962 17 | 0.691342 0.037476 18 | 0.654508 0.040917 19 | 0.616723 0.044237 20 | 0.578217 0.047383 21 | 0.539230 0.050302 22 | 0.500000 0.052940 23 | 0.460770 0.055241 24 | 0.421783 0.057148 25 | 0.383277 0.058609 26 | 0.345492 0.059575 27 | 0.308658 0.060000 28 | 0.273005 0.059848 29 | 0.238751 0.059092 30 | 0.206107 0.057714 31 | 0.175276 0.055709 32 | 0.146447 0.053083 33 | 0.119797 0.049854 34 | 0.095492 0.046049 35 | 0.073680 0.041705 36 | 0.054497 0.036867 37 | 0.038060 0.031580 38 | 0.024472 0.025893 39 | 0.013815 0.019854 40 | 0.006156 0.013503 41 | 0.001541 0.006877 42 | 0.000000 0.000000 43 | 0.001541 -0.006877 44 | 0.006156 -0.013503 45 | 0.013815 -0.019854 46 | 0.024472 -0.025893 47 | 0.038060 -0.031580 48 | 0.054497 -0.036867 49 | 0.073680 -0.041705 50 | 0.095492 -0.046049 51 | 0.119797 -0.049854 52 | 0.146447 -0.053083 53 | 0.175276 -0.055709 54 | 0.206107 -0.057714 55 | 0.238751 -0.059092 56 | 0.273005 -0.059848 57 | 0.308658 -0.060000 58 | 0.345492 -0.059575 59 | 0.383277 -0.058609 60 | 0.421783 -0.057148 61 | 0.460770 -0.055241 62 | 0.500000 -0.052940 63 | 0.539230 -0.050302 64 | 0.578217 -0.047383 65 | 0.616723 -0.044237 66 | 0.654508 -0.040917 67 | 0.691342 -0.037476 68 | 0.726995 -0.033962 69 | 0.761249 -0.030423 70 | 0.793893 -0.026905 71 | 0.824724 -0.023452 72 | 0.853553 -0.020107 73 | 0.880203 -0.016914 74 | 0.904508 -0.013914 75 | 0.926320 -0.011149 76 | 0.945503 -0.008658 77 | 0.961940 -0.006478 78 | 0.975528 -0.004642 79 | 0.986185 -0.003182 80 | 0.993844 -0.002120 81 | 0.998459 -0.001476 82 | 1.000000 -0.001260 -------------------------------------------------------------------------------- /examples/m6.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | 3 | # GmshCFD 4 | # Copyright (C) 2023 Adrien Crovato 5 | # 6 | # This program is free software: you can redistribute it and/or modify 7 | # it under the terms of the GNU General Public License as published by 8 | # the Free Software Foundation, either version 3 of the License, or 9 | # (at your option) any later version. 10 | # This program is distributed in the hope that it will be useful, 11 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | # GNU General Public License for more details. 14 | # You should have received a copy of the GNU General Public License 15 | # along with this program. If not, see . 16 | 17 | # ONERA M6 wing 18 | # Adrien Crovato 19 | 20 | import gmshcfd 21 | 22 | def build_cfg(): 23 | # Build path 24 | import os.path 25 | apath = os.path.abspath(os.path.join(os.path.dirname(__file__), 'airfoils', 'onera_m6.dat')) 26 | airf_path = [apath, apath] 27 | # Compute wing leading edge coordinates and chord lengths 28 | le_coords, chords = gmshcfd.utils.compute_wing_cfg([1.196], [0.56], [30], [0], 0.8059) 29 | le_coords, chords, incidences, airf_path = gmshcfd.utils.add_section(le_coords, chords, [0., 0.], airf_path, y_sec=0.99) 30 | # Compute mesh sizes 31 | sizes = [c / 100 for c in chords] 32 | ff_size = gmshcfd.utils.compute_ff_mesh_size(sizes[0], 20 * chords[0], 1.2) 33 | # Build cfg 34 | cfg = { 35 | 'wings': { 36 | 'wing': { 37 | 'offset': [0., 0.], 38 | 'le_offsets': le_coords, 39 | 'airfoils': airf_path, 40 | 'chords': chords, 41 | 'incidences': incidences 42 | } 43 | }, 44 | 'domain': { 45 | 'type': 'potential', 46 | 'length': 20 * chords[0], 47 | 'merge_wake': 'last' 48 | }, 49 | 'mesh': { 50 | 'wing_sizes': { 51 | 'wing': { 52 | 'te': [s for s in sizes], 53 | 'le': [s for s in sizes] 54 | } 55 | }, 56 | 'domain_size': ff_size 57 | } 58 | } 59 | return cfg 60 | 61 | def main(): 62 | # Generate wing and domain geometry 63 | cfd = gmshcfd.GmshCFD('m6', build_cfg()) 64 | cfd.generate_geometry() 65 | 66 | # Generate mesh 67 | cfd.generate_mesh() 68 | 69 | # Write geometry and mesh 70 | cfd.write_geometry() 71 | cfd.write_mesh('msh2') 72 | 73 | # eof 74 | print('') 75 | 76 | if __name__ == '__main__': 77 | main() 78 | -------------------------------------------------------------------------------- /run.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3 2 | # -*- coding: utf8 -*- 3 | # test encoding: à-é-è-ô-ï-€ 4 | 5 | # GmshCFD 6 | # Copyright (C) 2023 Adrien Crovato 7 | # 8 | # This program is free software: you can redistribute it and/or modify 9 | # it under the terms of the GNU General Public License as published by 10 | # the Free Software Foundation, either version 3 of the License, or 11 | # (at your option) any later version. 12 | # This program is distributed in the hope that it will be useful, 13 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 14 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 15 | # GNU General Public License for more details. 16 | # You should have received a copy of the GNU General Public License 17 | # along with this program. If not, see . 18 | 19 | # Run a script as if the software was installed 20 | 21 | def parse_args(): 22 | """Parse command line arguments 23 | """ 24 | import argparse 25 | parser = argparse.ArgumentParser() 26 | parser.add_argument('--clean', help='clean workspace', action='store_true') 27 | parser.add_argument('file', help='python files') 28 | args = parser.parse_args() 29 | return args 30 | 31 | def setup_workdir(testname, clean, verb=True): 32 | """Create a single directory for the given test 33 | """ 34 | import os, os.path 35 | 36 | # build the name of the workspace folder 37 | dir1 = os.path.dirname(os.path.abspath(os.path.dirname(__file__))) + os.sep 38 | if verb: print(f'Setting workspace for "{testname}"') 39 | common = os.path.commonprefix((testname, dir1)) 40 | resdir = testname[len(common):].replace(os.sep, "_") 41 | resdir = os.path.splitext(resdir)[0] # remove ".py" 42 | wdir = os.path.join('workspace', resdir) 43 | 44 | # create the directory 45 | if not os.path.isdir(wdir): 46 | if verb: print('- creating', wdir) 47 | os.makedirs(wdir) 48 | elif os.path.isdir(wdir) and clean: 49 | if verb: print('- cleaning', wdir) 50 | import shutil 51 | for f in os.listdir(wdir): 52 | fpth = os.path.join(wdir, f) 53 | if os.path.isfile(fpth): 54 | os.remove(fpth) 55 | elif os.path.isdir(fpth): 56 | shutil.rmtree(fpth) 57 | # change dir 58 | if verb: print('- changing to', wdir) 59 | os.chdir(wdir) 60 | 61 | def main(): 62 | import os, time, socket 63 | import gmshcfd 64 | 65 | # prepare run 66 | args = parse_args() 67 | testname = os.path.abspath(args.file) 68 | if not os.path.isfile(testname): 69 | raise Exception(f'File not found: {testname}') 70 | setup_workdir(testname, args.clean) 71 | 72 | # Run 73 | print('Starting test', testname) 74 | print('Time:', time.strftime('%c')) 75 | print('Hostname:', socket.gethostname()) 76 | script = open(testname, 'r', encoding='utf-8').read() 77 | exec(compile(script, testname, 'exec'), {'__file__': testname, '__name__':'__main__'}) 78 | 79 | if __name__ == '__main__': 80 | main() 81 | -------------------------------------------------------------------------------- /examples/wing_tail.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | 3 | # GmshCFD 4 | # Copyright (C) 2023 Adrien Crovato 5 | # 6 | # This program is free software: you can redistribute it and/or modify 7 | # it under the terms of the GNU General Public License as published by 8 | # the Free Software Foundation, either version 3 of the License, or 9 | # (at your option) any later version. 10 | # This program is distributed in the hope that it will be useful, 11 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | # GNU General Public License for more details. 14 | # You should have received a copy of the GNU General Public License 15 | # along with this program. If not, see . 16 | 17 | # Generic wing/tail 18 | # Adrien Crovato 19 | 20 | import gmshcfd 21 | 22 | def build_cfg(): 23 | # Build path 24 | import os.path 25 | wairf_path = os.path.abspath(os.path.join(os.path.dirname(__file__), 'airfoils', 'rae_2822.dat')) 26 | tairf_path = os.path.abspath(os.path.join(os.path.dirname(__file__), 'airfoils', 'naca_0012.dat')) 27 | airf_path = [[wairf_path, wairf_path, wairf_path], [tairf_path, tairf_path]] 28 | # Compute wing and tail leading edge coordinates and chord lengths 29 | wle_coords, wchords = gmshcfd.utils.compute_wing_cfg([0.5, 3.0], [0.82, 0.35], [20., 20.], [1., 3.], 1.0) 30 | tle_coords, tchords = gmshcfd.utils.compute_wing_cfg([1.0], [0.3], [25.], [2.], 0.5) 31 | # Compute mesh sizes 32 | wsizes = [c / 100 for c in wchords] 33 | tsizes = [c / 100 for c in tchords] 34 | ff_size = gmshcfd.utils.compute_ff_mesh_size(wsizes[0], 50 * wchords[0], 1.2) 35 | # Build cfg 36 | cfg = { 37 | 'wings': { 38 | 'wing': { 39 | 'offset': [0., 0.], 40 | 'le_offsets': wle_coords, 41 | 'airfoils': airf_path[0], 42 | 'chords': wchords, 43 | 'incidences': [2., 1., -1.] 44 | }, 45 | 'tail': { 46 | 'offset': [4., 0.5], 47 | 'le_offsets': tle_coords, 48 | 'airfoils': airf_path[1], 49 | 'chords': tchords, 50 | 'incidences': [0., 0.] 51 | } 52 | }, 53 | 'domain': { 54 | 'type': 'euler', 55 | 'length': 50 * wchords[0] 56 | }, 57 | 'mesh': { 58 | 'wing_sizes': { 59 | 'wing': { 60 | 'te': [s for s in wsizes], 61 | 'le': [s for s in wsizes] 62 | }, 63 | 'tail': { 64 | 'te': [s for s in tsizes], 65 | 'le': [s for s in tsizes] 66 | } 67 | }, 68 | 'domain_size': ff_size 69 | } 70 | } 71 | return cfg 72 | 73 | def main(): 74 | # Generate wing and domain geometry 75 | cfd = gmshcfd.GmshCFD('wing_tail', build_cfg()) 76 | cfd.generate_geometry() 77 | 78 | # Generate mesh 79 | cfd.generate_mesh() 80 | 81 | # Write geometry and mesh 82 | cfd.write_geometry() 83 | cfd.write_mesh('msh') 84 | 85 | # eof 86 | print('') 87 | 88 | if __name__ == '__main__': 89 | main() 90 | -------------------------------------------------------------------------------- /examples/lann.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | 3 | # GmshCFD 4 | # Copyright (C) 2023 Adrien Crovato 5 | # 6 | # This program is free software: you can redistribute it and/or modify 7 | # it under the terms of the GNU General Public License as published by 8 | # the Free Software Foundation, either version 3 of the License, or 9 | # (at your option) any later version. 10 | # This program is distributed in the hope that it will be useful, 11 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | # GNU General Public License for more details. 14 | # You should have received a copy of the GNU General Public License 15 | # along with this program. If not, see . 16 | 17 | # LANN wing 18 | # Adrien Crovato 19 | 20 | import gmshcfd 21 | 22 | def build_cfg(): 23 | # Build path 24 | import os.path 25 | airf_path = [] 26 | for i in range(8): 27 | airf_path.append(os.path.abspath(os.path.join(os.path.dirname(__file__), 'airfoils', f'lann_{i}.dat'))) 28 | # Define wing leading edge coordinates and chord lengths 29 | le_coords = [[0.0, 0.0, 0.0], 30 | [0.10408, 0.2, 0.0], 31 | [0.16913, 0.325, 0.0], 32 | [0.24720, 0.475, 0.0], 33 | [0.33827, 0.65, 0.0], 34 | [0.42934, 0.825, 0.0], 35 | [0.49439, 0.95, 0.0], 36 | [0.52041, 1.0, 0.0]] 37 | chords = [0.3606, 0.31765, 0.29071, 0.25806, 0.22029, 0.18235, 0.15534, 0.14445] 38 | # Compute mesh sizes 39 | sizes = [c / 100 for c in chords] 40 | ff_size = gmshcfd.utils.compute_ff_mesh_size(sizes[0], 50 * chords[0], 1.2) 41 | # Build cfg 42 | cfg = { 43 | 'wings': { 44 | 'wing': { 45 | 'offset': [0., 0.], 46 | 'le_offsets': le_coords, 47 | 'airfoils': airf_path, 48 | 'chords': chords, 49 | 'incidences': [0. for _ in chords] 50 | } 51 | }, 52 | 'domain': { 53 | 'type': 'rans', 54 | 'length': 50 * chords[0] 55 | }, 56 | 'mesh': { 57 | 'wing_sizes': { 58 | 'wing': { 59 | 'te': [s for s in sizes], 60 | 'le': [s for s in sizes] 61 | } 62 | #'wing': { 63 | # 'num_cell_chord': 125, 64 | # 'num_cell_span': [50, 30, 40, 40, 40, 30, 10], 65 | # 'prog_chord': 0.25 66 | #} 67 | }, 68 | 'boundary_layer': { 69 | 'wing': { 70 | 'num_layer': 30, 71 | 'growth_ratio': 1.2, 72 | 'hgt_first_layer': 2e-6 73 | }, 74 | 'write_tags': True 75 | }, 76 | 'domain_size': ff_size 77 | } 78 | } 79 | return cfg 80 | 81 | def main(): 82 | # Generate wing and domain geometry 83 | cfd = gmshcfd.GmshCFD('lann', build_cfg()) 84 | cfd.generate_geometry() 85 | 86 | # Generate mesh 87 | cfd.generate_mesh() 88 | 89 | # Write mesh (write geometry not supported for extruded boundary layer) 90 | cfd.write_mesh('msh') 91 | 92 | # eof 93 | print('') 94 | 95 | if __name__ == '__main__': 96 | main() 97 | -------------------------------------------------------------------------------- /examples/airfoils/rae_2822.dat: -------------------------------------------------------------------------------- 1 | RAE 2822 2 | 1.000000 0.000000 3 | 0.999398 0.000128 4 | 0.997592 0.000510 5 | 0.994588 0.001137 6 | 0.990393 0.002001 7 | 0.985016 0.003092 8 | 0.978470 0.004401 9 | 0.970772 0.005915 10 | 0.961940 0.007622 11 | 0.951995 0.009508 12 | 0.940961 0.011562 13 | 0.928864 0.013769 14 | 0.915735 0.016113 15 | 0.901604 0.018580 16 | 0.886505 0.021153 17 | 0.870476 0.023817 18 | 0.853553 0.026554 19 | 0.835779 0.029347 20 | 0.817197 0.032176 21 | 0.797850 0.035017 22 | 0.777785 0.037847 23 | 0.757051 0.040641 24 | 0.735698 0.043377 25 | 0.713778 0.046029 26 | 0.691342 0.048575 27 | 0.668445 0.050993 28 | 0.645142 0.053258 29 | 0.621490 0.055344 30 | 0.597545 0.057218 31 | 0.573365 0.058845 32 | 0.549009 0.060194 33 | 0.524534 0.061254 34 | 0.500000 0.062029 35 | 0.475466 0.062530 36 | 0.450991 0.062774 37 | 0.426635 0.062779 38 | 0.402455 0.062562 39 | 0.378510 0.062133 40 | 0.354858 0.061497 41 | 0.331555 0.060660 42 | 0.308658 0.059629 43 | 0.286222 0.058414 44 | 0.264302 0.057026 45 | 0.242949 0.055470 46 | 0.222215 0.053753 47 | 0.202150 0.051885 48 | 0.182803 0.049874 49 | 0.164221 0.047729 50 | 0.146447 0.045457 51 | 0.129524 0.043071 52 | 0.113495 0.040585 53 | 0.098396 0.038011 54 | 0.084265 0.035360 55 | 0.071136 0.032644 56 | 0.059039 0.029874 57 | 0.048005 0.027062 58 | 0.038060 0.024219 59 | 0.029228 0.021348 60 | 0.021530 0.018441 61 | 0.014984 0.015489 62 | 0.009607 0.012480 63 | 0.005412 0.009416 64 | 0.002408 0.006306 65 | 0.000602 0.003165 66 | 0.000000 0.000000 67 | 0.000602 -0.003160 68 | 0.002408 -0.006308 69 | 0.005412 -0.009443 70 | 0.009607 -0.012559 71 | 0.014984 -0.015649 72 | 0.021530 -0.018707 73 | 0.029228 -0.021722 74 | 0.038060 -0.024685 75 | 0.048005 -0.027586 76 | 0.059039 -0.030416 77 | 0.071136 -0.033170 78 | 0.084265 -0.035843 79 | 0.098396 -0.038431 80 | 0.113495 -0.040929 81 | 0.129524 -0.043326 82 | 0.146447 -0.045610 83 | 0.164221 -0.047773 84 | 0.182803 -0.049805 85 | 0.202150 -0.051694 86 | 0.222215 -0.053427 87 | 0.242949 -0.054994 88 | 0.264302 -0.056376 89 | 0.286222 -0.057547 90 | 0.308658 -0.058459 91 | 0.331555 -0.059046 92 | 0.354858 -0.059236 93 | 0.378510 -0.058974 94 | 0.402455 -0.058224 95 | 0.426635 -0.056979 96 | 0.450991 -0.055257 97 | 0.475466 -0.053099 98 | 0.500000 -0.050563 99 | 0.524534 -0.047719 100 | 0.549009 -0.044642 101 | 0.573365 -0.041397 102 | 0.597545 -0.038043 103 | 0.621490 -0.034631 104 | 0.645142 -0.031207 105 | 0.668445 -0.027814 106 | 0.691342 -0.024495 107 | 0.713778 -0.021289 108 | 0.735698 -0.018232 109 | 0.757051 -0.015357 110 | 0.777785 -0.012690 111 | 0.797850 -0.010244 112 | 0.817197 -0.008027 113 | 0.835779 -0.006048 114 | 0.853553 -0.004314 115 | 0.870476 -0.002829 116 | 0.886505 -0.001592 117 | 0.901604 -0.000600 118 | 0.915735 0.000157 119 | 0.928864 0.000694 120 | 0.940961 0.001033 121 | 0.951995 0.001197 122 | 0.961940 0.001212 123 | 0.970772 0.001112 124 | 0.978470 0.000935 125 | 0.985016 0.000719 126 | 0.990393 0.000497 127 | 0.994588 0.000296 128 | 0.997592 0.000137 129 | 0.999398 0.000035 130 | 1.000000 0.000000 -------------------------------------------------------------------------------- /gmshcfd/wake.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | 3 | # GmshCFD 4 | # Copyright (C) 2023 Adrien Crovato 5 | # 6 | # This program is free software: you can redistribute it and/or modify 7 | # it under the terms of the GNU General Public License as published by 8 | # the Free Software Foundation, either version 3 of the License, or 9 | # (at your option) any later version. 10 | # This program is distributed in the hope that it will be useful, 11 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | # GNU General Public License for more details. 14 | # You should have received a copy of the GNU General Public License 15 | # along with this program. If not, see . 16 | 17 | from .errors import GmshCFDError 18 | import gmsh 19 | 20 | class Wake: 21 | """Wake attached to the trailing edge of a lifting surface 22 | 23 | Parameters: 24 | pte_ids: dict 25 | tag and coordinates of trailing edge points 26 | cte_ids: list 27 | tag of trailing edge curves 28 | name: string 29 | name of the wake 30 | domain_cfg: dict 31 | parameters to configure domain 32 | mesh_size: float 33 | mesh size at farfield boundary 34 | 35 | Attribute: 36 | tags: dict 37 | gmsh tags of remarkable curves/surfaces of the lifting surface 38 | """ 39 | def __init__(self, pte_ids, cte_ids, name, domain_cfg, mesh_size): 40 | # Create Gmsh wake model 41 | wake_length = domain_cfg['length'] 42 | merge = domain_cfg.get('merge_wake') 43 | if merge not in [None, 'all', 'last']: 44 | raise GmshCFDError('merge must be either None, "all" or "last"!\n', self) 45 | self.__create_model(pte_ids, cte_ids, name, wake_length, merge, mesh_size) 46 | 47 | def __create_model(self, pte_ids, cte_ids, name, wake_length, merge, mesh_size): 48 | """Create wake points, curves and surfaces in Gmsh model 49 | """ 50 | # Retain points and curves needed to build wake 51 | if merge == 'all': 52 | pte_tags = [list(pte_ids.keys())[0], list(pte_ids.keys())[-1]] 53 | pte_coords = [list(pte_ids.values())[0], list(pte_ids.values())[-1]] 54 | cte_tags = [[-i for i in cte_ids]] 55 | elif merge == 'last': 56 | pte_tags = [*list(pte_ids.keys())[:-2], list(pte_ids.keys())[-1]] 57 | pte_coords = [*list(pte_ids.values())[:-2], list(pte_ids.values())[-1]] 58 | cte_tags = [*[[-i] for i in cte_ids[:-2]], [-cte_ids[-2], -cte_ids[-1]]] 59 | else: 60 | pte_tags = list(pte_ids.keys()) 61 | pte_coords = list(pte_ids.values()) 62 | cte_tags = [[-i] for i in cte_ids] 63 | 64 | # Create points 65 | ptags = [] 66 | for te_coord in pte_coords: 67 | ptags.append(gmsh.model.geo.add_point(wake_length, te_coord[1], te_coord[2])) 68 | 69 | # Create curves 70 | shed_ctags = [] 71 | for i, te_tag in enumerate(pte_tags): 72 | shed_ctags.append(gmsh.model.geo.add_line(te_tag, ptags[i])) 73 | trail_ctags = [] 74 | for i in range(len(ptags) - 1): 75 | trail_ctags.append(gmsh.model.geo.add_line(ptags[i], ptags[i+1])) 76 | 77 | # Create surfaces 78 | stags = [] 79 | for i in range(len(cte_tags)): 80 | cltag = gmsh.model.geo.add_curve_loop([trail_ctags[i], -shed_ctags[i+1], *cte_tags[i], shed_ctags[i]]) 81 | stags.append(gmsh.model.geo.add_plane_surface([cltag])) 82 | 83 | # Add physical groups 84 | gmsh.model.geo.synchronize() 85 | gmsh.model.add_physical_group(1, [shed_ctags[-1]], name=name+'Tip') 86 | gmsh.model.add_physical_group(2, stags, name=name) 87 | 88 | # Add meshing constraints 89 | for i in range(len(ptags)): 90 | gmsh.model.mesh.set_size([(0, ptags[i])], mesh_size) 91 | 92 | # Create tag dictionary 93 | self.tags = {'symmetry_point': ptags[0], 94 | 'symmetry_curve': shed_ctags[0], 95 | 'trailing_curves': trail_ctags, 96 | 'wake_surfaces': stags} 97 | -------------------------------------------------------------------------------- /gmshcfd/gmshcfd.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | 3 | # GmshCFD 4 | # Copyright (C) 2023 Adrien Crovato 5 | # 6 | # This program is free software: you can redistribute it and/or modify 7 | # it under the terms of the GNU General Public License as published by 8 | # the Free Software Foundation, either version 3 of the License, or 9 | # (at your option) any later version. 10 | # This program is distributed in the hope that it will be useful, 11 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | # GNU General Public License for more details. 14 | # You should have received a copy of the GNU General Public License 15 | # along with this program. If not, see . 16 | 17 | from .wing import Wing 18 | from .domain import Box, Sphere 19 | import gmsh, os 20 | 21 | class GmshCFD: 22 | """Main driver 23 | 24 | Parameters: 25 | name: string 26 | name of the model 27 | cfg: dict 28 | geometrical and mesh parameters 29 | 30 | Attributes: 31 | name: string 32 | name of the model 33 | wing_cfgs: dict 34 | geometrical parameters defining the lifting surfaces 35 | domain_cfg: dict 36 | geometrical parameters defining the domain 37 | mesh_cfg: dict 38 | parameters defining the mesh 39 | wings: list 40 | list of lifting surfaces 41 | domain: gmshcfd.Box or Sphere object 42 | domain 43 | """ 44 | def __init__(self, name, cfg): 45 | # Initialize attributes 46 | self.__name = name 47 | self.__wing_cfgs = cfg['wings'] 48 | self.__domain_cfg = cfg['domain'] 49 | self.__mesh_cfg = cfg['mesh'] 50 | self.__wings = [] 51 | self.__domain = None 52 | # Start Gmsh logger 53 | gmsh.initialize() 54 | gmsh.logger.start() 55 | gmsh.model.add(name) 56 | 57 | def __del__(self): 58 | # Get log and stop Gmsh 59 | log_msgs = gmsh.logger.get() 60 | gmsh.logger.stop() 61 | file = open(f'log_{self.__name}', 'w') 62 | for m in log_msgs: 63 | file.write(m + '\n') 64 | file.close() 65 | gmsh.finalize() 66 | 67 | def generate_geometry(self): 68 | """Generate the wings and the domain using the configurations 69 | """ 70 | # Create wings 71 | for name, cfg in self.__wing_cfgs.items(): 72 | self.__wings.append(Wing(name, cfg, self.__domain_cfg, self.__mesh_cfg)) 73 | # Create domain 74 | if self.__domain_cfg['type'] == 'potential': 75 | self.__domain = Box(self.__wings, self.__domain_cfg, self.__mesh_cfg) 76 | else: 77 | self.__domain = Sphere(self.__wings, self.__domain_cfg, self.__mesh_cfg) 78 | # Synchronize model 79 | gmsh.model.geo.synchronize() 80 | 81 | def generate_mesh(self, algo_2d='delaunay', algo_3d='hxt'): 82 | """Generate mesh 83 | """ 84 | algos_2d = {'delaunay': 5, 'frontal-delaunay': 6} 85 | algos_3d = {'delaunay': 1, 'hxt': 10} 86 | gmsh.option.set_number('Mesh.Algorithm', algos_2d[algo_2d]) 87 | gmsh.option.set_number('Mesh.Algorithm3D', algos_3d[algo_3d]) 88 | gmsh.option.set_number('Mesh.Optimize', 1) 89 | gmsh.option.set_number('Mesh.Smoothing', 10) 90 | gmsh.option.set_number('Mesh.SmoothNormals', 1) 91 | gmsh.option.set_number('General.NumThreads', os.cpu_count()) 92 | try: 93 | gmsh.model.mesh.generate(3) 94 | except Exception as e: 95 | gmsh.write(self.__name + '.msh') 96 | raise Exception(e) 97 | 98 | def write_geometry(self): 99 | """Save geometry to disk and rename using .geo 100 | """ 101 | gmsh.write(self.__name + '.geo_unrolled') 102 | nname = self.__name + '.geo' 103 | if os.path.isfile(nname): 104 | os.remove(nname) 105 | os.rename(self.__name + '.geo_unrolled', nname) 106 | 107 | def write_mesh(self, format): 108 | """Save mesh to disk 109 | """ 110 | if format == 'msh2': 111 | gmsh.option.set_number('Mesh.MshFileVersion', 2.2) 112 | gmsh.write(self.__name + '.msh') 113 | else: 114 | gmsh.write(self.__name + '.' + format) 115 | -------------------------------------------------------------------------------- /examples/airfoils/lann_5.dat: -------------------------------------------------------------------------------- 1 | # LANN Airfoil 6 2 | 1.00000e+00 7.80000e-03 3 | 9.99760e-01 7.87100e-03 4 | 9.99022e-01 8.02500e-03 5 | 9.97788e-01 8.26000e-03 6 | 9.96061e-01 8.57800e-03 7 | 9.93844e-01 8.97900e-03 8 | 9.91141e-01 9.46400e-03 9 | 9.87955e-01 1.00320e-02 10 | 9.84289e-01 1.06840e-02 11 | 9.80146e-01 1.14210e-02 12 | 9.75528e-01 1.22430e-02 13 | 9.70441e-01 1.31500e-02 14 | 9.64888e-01 1.41390e-02 15 | 9.58877e-01 1.52100e-02 16 | 9.52413e-01 1.63600e-02 17 | 9.45503e-01 1.75860e-02 18 | 9.38153e-01 1.88860e-02 19 | 9.30370e-01 2.02560e-02 20 | 9.22163e-01 2.16900e-02 21 | 9.13540e-01 2.31840e-02 22 | 9.04508e-01 2.47310e-02 23 | 8.95077e-01 2.63270e-02 24 | 8.85256e-01 2.79700e-02 25 | 8.75055e-01 2.96540e-02 26 | 8.64484e-01 3.13780e-02 27 | 8.53553e-01 3.31370e-02 28 | 8.42273e-01 3.49270e-02 29 | 8.30655e-01 3.67310e-02 30 | 8.18711e-01 3.85310e-02 31 | 8.06453e-01 4.03080e-02 32 | 7.93893e-01 4.20450e-02 33 | 7.81042e-01 4.37230e-02 34 | 7.67913e-01 4.53360e-02 35 | 7.54520e-01 4.68760e-02 36 | 7.40877e-01 4.83370e-02 37 | 7.26995e-01 4.97100e-02 38 | 7.12890e-01 5.09930e-02 39 | 6.98574e-01 5.21890e-02 40 | 6.84062e-01 5.33030e-02 41 | 6.69369e-01 5.43410e-02 42 | 6.54508e-01 5.53100e-02 43 | 6.39495e-01 5.62150e-02 44 | 6.24345e-01 5.70580e-02 45 | 6.09071e-01 5.78400e-02 46 | 5.93691e-01 5.85630e-02 47 | 5.78217e-01 5.92290e-02 48 | 5.62667e-01 5.98370e-02 49 | 5.47054e-01 6.03840e-02 50 | 5.31395e-01 6.08640e-02 51 | 5.15705e-01 6.12700e-02 52 | 5.00000e-01 6.15980e-02 53 | 4.84295e-01 6.18440e-02 54 | 4.68605e-01 6.20110e-02 55 | 4.52946e-01 6.21070e-02 56 | 4.37333e-01 6.21380e-02 57 | 4.21783e-01 6.21100e-02 58 | 4.06309e-01 6.20280e-02 59 | 3.90929e-01 6.18920e-02 60 | 3.75655e-01 6.16980e-02 61 | 3.60505e-01 6.14450e-02 62 | 3.45492e-01 6.11300e-02 63 | 3.30631e-01 6.07520e-02 64 | 3.15938e-01 6.03100e-02 65 | 3.01426e-01 5.98030e-02 66 | 2.87110e-01 5.92330e-02 67 | 2.73005e-01 5.85980e-02 68 | 2.59123e-01 5.78990e-02 69 | 2.45480e-01 5.71370e-02 70 | 2.32087e-01 5.63100e-02 71 | 2.18958e-01 5.54200e-02 72 | 2.06107e-01 5.44670e-02 73 | 1.93547e-01 5.34500e-02 74 | 1.81288e-01 5.23700e-02 75 | 1.69345e-01 5.12270e-02 76 | 1.57727e-01 5.00190e-02 77 | 1.46447e-01 4.87470e-02 78 | 1.35516e-01 4.74110e-02 79 | 1.24945e-01 4.60140e-02 80 | 1.14744e-01 4.45590e-02 81 | 1.04923e-01 4.30510e-02 82 | 9.54920e-02 4.14930e-02 83 | 8.64600e-02 3.98870e-02 84 | 7.78370e-02 3.82250e-02 85 | 6.96300e-02 3.64980e-02 86 | 6.18470e-02 3.46940e-02 87 | 5.44970e-02 3.28060e-02 88 | 4.75870e-02 3.08230e-02 89 | 4.11230e-02 2.87440e-02 90 | 3.51120e-02 2.65660e-02 91 | 2.95600e-02 2.42880e-02 92 | 2.44720e-02 2.19080e-02 93 | 1.98530e-02 1.94270e-02 94 | 1.57090e-02 1.68470e-02 95 | 1.20420e-02 1.41750e-02 96 | 8.85700e-03 1.14150e-02 97 | 6.15600e-03 8.57200e-03 98 | 3.94300e-03 5.65800e-03 99 | 2.22000e-03 2.71300e-03 100 | 9.87000e-04 -2.18000e-04 101 | 2.47000e-04 -3.08700e-03 102 | 0.00000e+00 -5.85000e-03 103 | 2.47000e-04 -8.46900e-03 104 | 9.87000e-04 -1.09500e-02 105 | 2.22000e-03 -1.33060e-02 106 | 3.94300e-03 -1.55530e-02 107 | 6.15600e-03 -1.77040e-02 108 | 8.85700e-03 -1.97710e-02 109 | 1.20420e-02 -2.17540e-02 110 | 1.57090e-02 -2.36490e-02 111 | 1.98530e-02 -2.54510e-02 112 | 2.44720e-02 -2.71560e-02 113 | 2.95600e-02 -2.87660e-02 114 | 3.51120e-02 -3.02920e-02 115 | 4.11230e-02 -3.17540e-02 116 | 4.75870e-02 -3.31690e-02 117 | 5.44970e-02 -3.45540e-02 118 | 6.18470e-02 -3.59250e-02 119 | 6.96300e-02 -3.72870e-02 120 | 7.78370e-02 -3.86390e-02 121 | 8.64600e-02 -3.99850e-02 122 | 9.54920e-02 -4.13250e-02 123 | 1.04923e-01 -4.26600e-02 124 | 1.14744e-01 -4.39850e-02 125 | 1.24945e-01 -4.52930e-02 126 | 1.35516e-01 -4.65800e-02 127 | 1.46447e-01 -4.78380e-02 128 | 1.57727e-01 -4.90610e-02 129 | 1.69345e-01 -5.02410e-02 130 | 1.81288e-01 -5.13710e-02 131 | 1.93547e-01 -5.24430e-02 132 | 2.06107e-01 -5.34480e-02 133 | 2.18958e-01 -5.43790e-02 134 | 2.32087e-01 -5.52310e-02 135 | 2.45480e-01 -5.59990e-02 136 | 2.59123e-01 -5.66770e-02 137 | 2.73005e-01 -5.72600e-02 138 | 2.87110e-01 -5.77450e-02 139 | 3.01426e-01 -5.81300e-02 140 | 3.15938e-01 -5.84150e-02 141 | 3.30631e-01 -5.85990e-02 142 | 3.45492e-01 -5.86830e-02 143 | 3.60505e-01 -5.86640e-02 144 | 3.75655e-01 -5.85310e-02 145 | 3.90929e-01 -5.82700e-02 146 | 4.06309e-01 -5.78690e-02 147 | 4.21783e-01 -5.73120e-02 148 | 4.37333e-01 -5.65900e-02 149 | 4.52946e-01 -5.56950e-02 150 | 4.68605e-01 -5.46220e-02 151 | 4.84295e-01 -5.33680e-02 152 | 5.00000e-01 -5.19280e-02 153 | 5.15705e-01 -5.02980e-02 154 | 5.31395e-01 -4.84840e-02 155 | 5.47054e-01 -4.64940e-02 156 | 5.62667e-01 -4.43350e-02 157 | 5.78217e-01 -4.20140e-02 158 | 5.93691e-01 -3.95430e-02 159 | 6.09071e-01 -3.69530e-02 160 | 6.24345e-01 -3.42770e-02 161 | 6.39495e-01 -3.15510e-02 162 | 6.54508e-01 -2.88070e-02 163 | 6.69369e-01 -2.60780e-02 164 | 6.84062e-01 -2.33780e-02 165 | 6.98574e-01 -2.07180e-02 166 | 7.12890e-01 -1.81080e-02 167 | 7.26995e-01 -1.55600e-02 168 | 7.40877e-01 -1.30840e-02 169 | 7.54520e-01 -1.06930e-02 170 | 7.67913e-01 -8.39800e-03 171 | 7.81042e-01 -6.21300e-03 172 | 7.93893e-01 -4.15000e-03 173 | 8.06453e-01 -2.21900e-03 174 | 8.18711e-01 -4.29000e-04 175 | 8.30655e-01 1.21200e-03 176 | 8.42273e-01 2.69600e-03 177 | 8.53553e-01 4.01600e-03 178 | 8.64484e-01 5.16700e-03 179 | 8.75055e-01 6.15200e-03 180 | 8.85256e-01 6.97800e-03 181 | 8.95077e-01 7.65200e-03 182 | 9.04508e-01 8.17900e-03 183 | 9.13540e-01 8.56900e-03 184 | 9.22163e-01 8.83200e-03 185 | 9.30370e-01 8.98400e-03 186 | 9.38153e-01 9.03900e-03 187 | 9.45503e-01 9.01100e-03 188 | 9.52413e-01 8.91300e-03 189 | 9.58877e-01 8.75400e-03 190 | 9.64888e-01 8.54300e-03 191 | 9.70441e-01 8.29000e-03 192 | 9.75528e-01 8.00100e-03 193 | 9.80146e-01 7.68700e-03 194 | 9.84289e-01 7.36100e-03 195 | 9.87955e-01 7.03500e-03 196 | 9.91141e-01 6.72200e-03 197 | 9.93844e-01 6.43800e-03 198 | 9.96061e-01 6.19300e-03 199 | 9.97788e-01 6.00300e-03 200 | 9.99022e-01 5.88000e-03 201 | 9.99760e-01 5.83800e-03 202 | 1.00000e+00 5.89000e-03 203 | -------------------------------------------------------------------------------- /examples/airfoils/lann_6.dat: -------------------------------------------------------------------------------- 1 | # LANN Airfoil 7 2 | 1.00000e+00 1.76200e-02 3 | 9.99760e-01 1.77110e-02 4 | 9.99022e-01 1.78850e-02 5 | 9.97788e-01 1.81420e-02 6 | 9.96061e-01 1.84820e-02 7 | 9.93844e-01 1.89050e-02 8 | 9.91141e-01 1.94140e-02 9 | 9.87955e-01 2.00070e-02 10 | 9.84289e-01 2.06860e-02 11 | 9.80146e-01 2.14510e-02 12 | 9.75528e-01 2.23020e-02 13 | 9.70441e-01 2.32400e-02 14 | 9.64888e-01 2.42640e-02 15 | 9.58877e-01 2.53700e-02 16 | 9.52413e-01 2.65590e-02 17 | 9.45503e-01 2.78260e-02 18 | 9.38153e-01 2.91700e-02 19 | 9.30370e-01 3.05860e-02 20 | 9.22163e-01 3.20670e-02 21 | 9.13540e-01 3.36080e-02 22 | 9.04508e-01 3.52020e-02 23 | 8.95077e-01 3.68440e-02 24 | 8.85256e-01 3.85310e-02 25 | 8.75055e-01 4.02600e-02 26 | 8.64484e-01 4.20290e-02 27 | 8.53553e-01 4.38340e-02 28 | 8.42273e-01 4.56690e-02 29 | 8.30655e-01 4.75100e-02 30 | 8.18711e-01 4.93270e-02 31 | 8.06453e-01 5.10940e-02 32 | 7.93893e-01 5.27800e-02 33 | 7.81042e-01 5.43630e-02 34 | 7.67913e-01 5.58390e-02 35 | 7.54520e-01 5.72070e-02 36 | 7.40877e-01 5.84690e-02 37 | 7.26995e-01 5.96250e-02 38 | 7.12890e-01 6.06760e-02 39 | 6.98574e-01 6.16270e-02 40 | 6.84062e-01 6.24820e-02 41 | 6.69369e-01 6.32470e-02 42 | 6.54508e-01 6.39250e-02 43 | 6.39495e-01 6.45210e-02 44 | 6.24345e-01 6.50380e-02 45 | 6.09071e-01 6.54750e-02 46 | 5.93691e-01 6.58340e-02 47 | 5.78217e-01 6.61170e-02 48 | 5.62667e-01 6.63240e-02 49 | 5.47054e-01 6.64590e-02 50 | 5.31395e-01 6.65260e-02 51 | 5.15705e-01 6.65290e-02 52 | 5.00000e-01 6.64700e-02 53 | 4.84295e-01 6.63530e-02 54 | 4.68605e-01 6.61760e-02 55 | 4.52946e-01 6.59360e-02 56 | 4.37333e-01 6.56320e-02 57 | 4.21783e-01 6.52600e-02 58 | 4.06309e-01 6.48200e-02 59 | 3.90929e-01 6.43120e-02 60 | 3.75655e-01 6.37400e-02 61 | 3.60505e-01 6.31060e-02 62 | 3.45492e-01 6.24130e-02 63 | 3.30631e-01 6.16630e-02 64 | 3.15938e-01 6.08540e-02 65 | 3.01426e-01 5.99830e-02 66 | 2.87110e-01 5.90480e-02 67 | 2.73005e-01 5.80450e-02 68 | 2.59123e-01 5.69740e-02 69 | 2.45480e-01 5.58350e-02 70 | 2.32087e-01 5.46290e-02 71 | 2.18958e-01 5.33590e-02 72 | 2.06107e-01 5.20260e-02 73 | 1.93547e-01 5.06330e-02 74 | 1.81288e-01 4.91780e-02 75 | 1.69345e-01 4.76630e-02 76 | 1.57727e-01 4.60880e-02 77 | 1.46447e-01 4.44520e-02 78 | 1.35516e-01 4.27560e-02 79 | 1.24945e-01 4.10000e-02 80 | 1.14744e-01 3.91860e-02 81 | 1.04923e-01 3.73130e-02 82 | 9.54920e-02 3.53810e-02 83 | 8.64600e-02 3.33920e-02 84 | 7.78370e-02 3.13450e-02 85 | 6.96300e-02 2.92380e-02 86 | 6.18470e-02 2.70710e-02 87 | 5.44970e-02 2.48430e-02 88 | 4.75870e-02 2.25510e-02 89 | 4.11230e-02 2.01830e-02 90 | 3.51120e-02 1.77280e-02 91 | 2.95600e-02 1.51720e-02 92 | 2.44720e-02 1.25010e-02 93 | 1.98530e-02 9.71200e-03 94 | 1.57090e-02 6.83800e-03 95 | 1.20420e-02 3.92000e-03 96 | 8.85700e-03 9.99000e-04 97 | 6.15600e-03 -1.88400e-03 98 | 3.94300e-03 -4.69300e-03 99 | 2.22000e-03 -7.42300e-03 100 | 9.87000e-04 -1.00750e-02 101 | 2.47000e-04 -1.26510e-02 102 | 0.00000e+00 -1.51500e-02 103 | 2.47000e-04 -1.75730e-02 104 | 9.87000e-04 -1.99160e-02 105 | 2.22000e-03 -2.21720e-02 106 | 3.94300e-03 -2.43360e-02 107 | 6.15600e-03 -2.64020e-02 108 | 8.85700e-03 -2.83660e-02 109 | 1.20420e-02 -3.02400e-02 110 | 1.57090e-02 -3.20360e-02 111 | 1.98530e-02 -3.37680e-02 112 | 2.44720e-02 -3.54480e-02 113 | 2.95600e-02 -3.70860e-02 114 | 3.51120e-02 -3.86640e-02 115 | 4.11230e-02 -4.01590e-02 116 | 4.75870e-02 -4.15510e-02 117 | 5.44970e-02 -4.28170e-02 118 | 6.18470e-02 -4.39450e-02 119 | 6.96300e-02 -4.49570e-02 120 | 7.78370e-02 -4.58870e-02 121 | 8.64600e-02 -4.67690e-02 122 | 9.54920e-02 -4.76350e-02 123 | 1.04923e-01 -4.85120e-02 124 | 1.14744e-01 -4.93960e-02 125 | 1.24945e-01 -5.02770e-02 126 | 1.35516e-01 -5.11460e-02 127 | 1.46447e-01 -5.19930e-02 128 | 1.57727e-01 -5.28070e-02 129 | 1.69345e-01 -5.35800e-02 130 | 1.81288e-01 -5.43030e-02 131 | 1.93547e-01 -5.49680e-02 132 | 2.06107e-01 -5.55640e-02 133 | 2.18958e-01 -5.60860e-02 134 | 2.32087e-01 -5.65330e-02 135 | 2.45480e-01 -5.69080e-02 136 | 2.59123e-01 -5.72120e-02 137 | 2.73005e-01 -5.74480e-02 138 | 2.87110e-01 -5.76150e-02 139 | 3.01426e-01 -5.77050e-02 140 | 3.15938e-01 -5.77090e-02 141 | 3.30631e-01 -5.76160e-02 142 | 3.45492e-01 -5.74170e-02 143 | 3.60505e-01 -5.71030e-02 144 | 3.75655e-01 -5.66660e-02 145 | 3.90929e-01 -5.61040e-02 146 | 4.06309e-01 -5.54100e-02 147 | 4.21783e-01 -5.45790e-02 148 | 4.37333e-01 -5.36040e-02 149 | 4.52946e-01 -5.24710e-02 150 | 4.68605e-01 -5.11610e-02 151 | 4.84295e-01 -4.96570e-02 152 | 5.00000e-01 -4.79420e-02 153 | 5.15705e-01 -4.60040e-02 154 | 5.31395e-01 -4.38580e-02 155 | 5.47054e-01 -4.15240e-02 156 | 5.62667e-01 -3.90210e-02 157 | 5.78217e-01 -3.63690e-02 158 | 5.93691e-01 -3.35920e-02 159 | 6.09071e-01 -3.07200e-02 160 | 6.24345e-01 -2.77870e-02 161 | 6.39495e-01 -2.48290e-02 162 | 6.54508e-01 -2.18790e-02 163 | 6.69369e-01 -1.89650e-02 164 | 6.84062e-01 -1.60870e-02 165 | 6.98574e-01 -1.32400e-02 166 | 7.12890e-01 -1.04180e-02 167 | 7.26995e-01 -7.61600e-03 168 | 7.40877e-01 -4.83500e-03 169 | 7.54520e-01 -2.11400e-03 170 | 7.67913e-01 5.01000e-04 171 | 7.81042e-01 2.96400e-03 172 | 7.93893e-01 5.22900e-03 173 | 8.06453e-01 7.26100e-03 174 | 8.18711e-01 9.06800e-03 175 | 8.30655e-01 1.06690e-02 176 | 8.42273e-01 1.20850e-02 177 | 8.53553e-01 1.33330e-02 178 | 8.64484e-01 1.44320e-02 179 | 8.75055e-01 1.53840e-02 180 | 8.85256e-01 1.61900e-02 181 | 8.95077e-01 1.68520e-02 182 | 9.04508e-01 1.73680e-02 183 | 9.13540e-01 1.77430e-02 184 | 9.22163e-01 1.79900e-02 185 | 9.30370e-01 1.81230e-02 186 | 9.38153e-01 1.81580e-02 187 | 9.45503e-01 1.81110e-02 188 | 9.52413e-01 1.79950e-02 189 | 9.58877e-01 1.78220e-02 190 | 9.64888e-01 1.76010e-02 191 | 9.70441e-01 1.73420e-02 192 | 9.75528e-01 1.70540e-02 193 | 9.80146e-01 1.67470e-02 194 | 9.84289e-01 1.64330e-02 195 | 9.87955e-01 1.61220e-02 196 | 9.91141e-01 1.58260e-02 197 | 9.93844e-01 1.55550e-02 198 | 9.96061e-01 1.53220e-02 199 | 9.97788e-01 1.51360e-02 200 | 9.99022e-01 1.50100e-02 201 | 9.99760e-01 1.49540e-02 202 | 1.00000e+00 1.49800e-02 203 | -------------------------------------------------------------------------------- /examples/airfoils/lann_7.dat: -------------------------------------------------------------------------------- 1 | # LANN Airfoil 8 2 | 1.00000e+00 2.15500e-02 3 | 9.99760e-01 2.16170e-02 4 | 9.99022e-01 2.17820e-02 5 | 9.97788e-01 2.20410e-02 6 | 9.96061e-01 2.23940e-02 7 | 9.93844e-01 2.28370e-02 8 | 9.91141e-01 2.33700e-02 9 | 9.87955e-01 2.39880e-02 10 | 9.84289e-01 2.46920e-02 11 | 9.80146e-01 2.54780e-02 12 | 9.75528e-01 2.63440e-02 13 | 9.70441e-01 2.72890e-02 14 | 9.64888e-01 2.83140e-02 15 | 9.58877e-01 2.94210e-02 16 | 9.52413e-01 3.06110e-02 17 | 9.45503e-01 3.18870e-02 18 | 9.38153e-01 3.32490e-02 19 | 9.30370e-01 3.46930e-02 20 | 9.22163e-01 3.62130e-02 21 | 9.13540e-01 3.78040e-02 22 | 9.04508e-01 3.94610e-02 23 | 8.95077e-01 4.11770e-02 24 | 8.85256e-01 4.29420e-02 25 | 8.75055e-01 4.47440e-02 26 | 8.64484e-01 4.65720e-02 27 | 8.53553e-01 4.84130e-02 28 | 8.42273e-01 5.02560e-02 29 | 8.30655e-01 5.20780e-02 30 | 8.18711e-01 5.38570e-02 31 | 8.06453e-01 5.55710e-02 32 | 7.93893e-01 5.71960e-02 33 | 7.81042e-01 5.87140e-02 34 | 7.67913e-01 6.01190e-02 35 | 7.54520e-01 6.14110e-02 36 | 7.40877e-01 6.25890e-02 37 | 7.26995e-01 6.36510e-02 38 | 7.12890e-01 6.45970e-02 39 | 6.98574e-01 6.54300e-02 40 | 6.84062e-01 6.61550e-02 41 | 6.69369e-01 6.67760e-02 42 | 6.54508e-01 6.72970e-02 43 | 6.39495e-01 6.77230e-02 44 | 6.24345e-01 6.80590e-02 45 | 6.09071e-01 6.83140e-02 46 | 5.93691e-01 6.84920e-02 47 | 5.78217e-01 6.86020e-02 48 | 5.62667e-01 6.86470e-02 49 | 5.47054e-01 6.86300e-02 50 | 5.31395e-01 6.85500e-02 51 | 5.15705e-01 6.84060e-02 52 | 5.00000e-01 6.81970e-02 53 | 4.84295e-01 6.79240e-02 54 | 4.68605e-01 6.75850e-02 55 | 4.52946e-01 6.71810e-02 56 | 4.37333e-01 6.67110e-02 57 | 4.21783e-01 6.61760e-02 58 | 4.06309e-01 6.55750e-02 59 | 3.90929e-01 6.49080e-02 60 | 3.75655e-01 6.41780e-02 61 | 3.60505e-01 6.33840e-02 62 | 3.45492e-01 6.25280e-02 63 | 3.30631e-01 6.16090e-02 64 | 3.15938e-01 6.06280e-02 65 | 3.01426e-01 5.95810e-02 66 | 2.87110e-01 5.84680e-02 67 | 2.73005e-01 5.72860e-02 68 | 2.59123e-01 5.60330e-02 69 | 2.45480e-01 5.47090e-02 70 | 2.32087e-01 5.33090e-02 71 | 2.18958e-01 5.18330e-02 72 | 2.06107e-01 5.02780e-02 73 | 1.93547e-01 4.86450e-02 74 | 1.81288e-01 4.69480e-02 75 | 1.69345e-01 4.52030e-02 76 | 1.57727e-01 4.34290e-02 77 | 1.46447e-01 4.16410e-02 78 | 1.35516e-01 3.98480e-02 79 | 1.24945e-01 3.80260e-02 80 | 1.14744e-01 3.61390e-02 81 | 1.04923e-01 3.41560e-02 82 | 9.54920e-02 3.20410e-02 83 | 8.64600e-02 2.97740e-02 84 | 7.78370e-02 2.73870e-02 85 | 6.96300e-02 2.49260e-02 86 | 6.18470e-02 2.24360e-02 87 | 5.44970e-02 1.99630e-02 88 | 4.75870e-02 1.75360e-02 89 | 4.11230e-02 1.51270e-02 90 | 3.51120e-02 1.26910e-02 91 | 2.95600e-02 1.01830e-02 92 | 2.44720e-02 7.55800e-03 93 | 1.98530e-02 4.78600e-03 94 | 1.57090e-02 1.88900e-03 95 | 1.20420e-02 -1.10000e-03 96 | 8.85700e-03 -4.14500e-03 97 | 6.15600e-03 -7.21000e-03 98 | 3.94300e-03 -1.02620e-02 99 | 2.22000e-03 -1.32640e-02 100 | 9.87000e-04 -1.61830e-02 101 | 2.47000e-04 -1.89830e-02 102 | 0.00000e+00 -2.16300e-02 103 | 2.47000e-04 -2.40970e-02 104 | 9.87000e-04 -2.63960e-02 105 | 2.22000e-03 -2.85480e-02 106 | 3.94300e-03 -3.05730e-02 107 | 6.15600e-03 -3.24920e-02 108 | 8.85700e-03 -3.43210e-02 109 | 1.20420e-02 -3.60580e-02 110 | 1.57090e-02 -3.76960e-02 111 | 1.98530e-02 -3.92300e-02 112 | 2.44720e-02 -4.06510e-02 113 | 2.95600e-02 -4.19590e-02 114 | 3.51120e-02 -4.31620e-02 115 | 4.11230e-02 -4.42760e-02 116 | 4.75870e-02 -4.53120e-02 117 | 5.44970e-02 -4.62860e-02 118 | 6.18470e-02 -4.72100e-02 119 | 6.96300e-02 -4.80900e-02 120 | 7.78370e-02 -4.89320e-02 121 | 8.64600e-02 -4.97410e-02 122 | 9.54920e-02 -5.05240e-02 123 | 1.04923e-01 -5.12840e-02 124 | 1.14744e-01 -5.20190e-02 125 | 1.24945e-01 -5.27270e-02 126 | 1.35516e-01 -5.34040e-02 127 | 1.46447e-01 -5.40490e-02 128 | 1.57727e-01 -5.46570e-02 129 | 1.69345e-01 -5.52200e-02 130 | 1.81288e-01 -5.57330e-02 131 | 1.93547e-01 -5.61850e-02 132 | 2.06107e-01 -5.65700e-02 133 | 2.18958e-01 -5.68820e-02 134 | 2.32087e-01 -5.71220e-02 135 | 2.45480e-01 -5.72940e-02 136 | 2.59123e-01 -5.74010e-02 137 | 2.73005e-01 -5.74460e-02 138 | 2.87110e-01 -5.74310e-02 139 | 3.01426e-01 -5.73450e-02 140 | 3.15938e-01 -5.71760e-02 141 | 3.30631e-01 -5.69120e-02 142 | 3.45492e-01 -5.65400e-02 143 | 3.60505e-01 -5.60490e-02 144 | 3.75655e-01 -5.54310e-02 145 | 3.90929e-01 -5.46820e-02 146 | 4.06309e-01 -5.37940e-02 147 | 4.21783e-01 -5.27630e-02 148 | 4.37333e-01 -5.15810e-02 149 | 4.52946e-01 -5.02370e-02 150 | 4.68605e-01 -4.87200e-02 151 | 4.84295e-01 -4.70170e-02 152 | 5.00000e-01 -4.51170e-02 153 | 5.15705e-01 -4.30110e-02 154 | 5.31395e-01 -4.07120e-02 155 | 5.47054e-01 -3.82360e-02 156 | 5.62667e-01 -3.55980e-02 157 | 5.78217e-01 -3.28140e-02 158 | 5.93691e-01 -2.99040e-02 159 | 6.09071e-01 -2.68970e-02 160 | 6.24345e-01 -2.38260e-02 161 | 6.39495e-01 -2.07240e-02 162 | 6.54508e-01 -1.76240e-02 163 | 6.69369e-01 -1.45560e-02 164 | 6.84062e-01 -1.15390e-02 165 | 6.98574e-01 -8.59100e-03 166 | 7.12890e-01 -5.72900e-03 167 | 7.26995e-01 -2.96900e-03 168 | 7.40877e-01 -3.27000e-04 169 | 7.54520e-01 2.19200e-03 170 | 7.67913e-01 4.58600e-03 171 | 7.81042e-01 6.85100e-03 172 | 7.93893e-01 8.98500e-03 173 | 8.06453e-01 1.09830e-02 174 | 8.18711e-01 1.28370e-02 175 | 8.30655e-01 1.45360e-02 176 | 8.42273e-01 1.60710e-02 177 | 8.53553e-01 1.74320e-02 178 | 8.64484e-01 1.86120e-02 179 | 8.75055e-01 1.96140e-02 180 | 8.85256e-01 2.04470e-02 181 | 8.95077e-01 2.11180e-02 182 | 9.04508e-01 2.16340e-02 183 | 9.13540e-01 2.20030e-02 184 | 9.22163e-01 2.22350e-02 185 | 9.30370e-01 2.23410e-02 186 | 9.38153e-01 2.23310e-02 187 | 9.45503e-01 2.22150e-02 188 | 9.52413e-01 2.20070e-02 189 | 9.58877e-01 2.17260e-02 190 | 9.64888e-01 2.13950e-02 191 | 9.70441e-01 2.10370e-02 192 | 9.75528e-01 2.06740e-02 193 | 9.80146e-01 2.03270e-02 194 | 9.84289e-01 2.00010e-02 195 | 9.87955e-01 1.97000e-02 196 | 9.91141e-01 1.94290e-02 197 | 9.93844e-01 1.91900e-02 198 | 9.96061e-01 1.89870e-02 199 | 9.97788e-01 1.88240e-02 200 | 9.99022e-01 1.87040e-02 201 | 9.99760e-01 1.86320e-02 202 | 1.00000e+00 1.86100e-02 203 | -------------------------------------------------------------------------------- /examples/airfoils/lann_4.dat: -------------------------------------------------------------------------------- 1 | # LANN Airfoil 5 2 | 1.00000e+00 -3.82000e-03 3 | 9.99760e-01 -3.75400e-03 4 | 9.99022e-01 -3.61600e-03 5 | 9.97788e-01 -3.40500e-03 6 | 9.96061e-01 -3.11900e-03 7 | 9.93844e-01 -2.75600e-03 8 | 9.91141e-01 -2.31500e-03 9 | 9.87955e-01 -1.79300e-03 10 | 9.84289e-01 -1.19000e-03 11 | 9.80146e-01 -5.03000e-04 12 | 9.75528e-01 2.70000e-04 13 | 9.70441e-01 1.12800e-03 14 | 9.64888e-01 2.06600e-03 15 | 9.58877e-01 3.07900e-03 16 | 9.52413e-01 4.16000e-03 17 | 9.45503e-01 5.30300e-03 18 | 9.38153e-01 6.50200e-03 19 | 9.30370e-01 7.76300e-03 20 | 9.22163e-01 9.09100e-03 21 | 9.13540e-01 1.04910e-02 22 | 9.04508e-01 1.19710e-02 23 | 8.95077e-01 1.35320e-02 24 | 8.85256e-01 1.51650e-02 25 | 8.75055e-01 1.68570e-02 26 | 8.64484e-01 1.85960e-02 27 | 8.53553e-01 2.03680e-02 28 | 8.42273e-01 2.21620e-02 29 | 8.30655e-01 2.39720e-02 30 | 8.18711e-01 2.57930e-02 31 | 8.06453e-01 2.76190e-02 32 | 7.93893e-01 2.94460e-02 33 | 7.81042e-01 3.12670e-02 34 | 7.67913e-01 3.30670e-02 35 | 7.54520e-01 3.48320e-02 36 | 7.40877e-01 3.65450e-02 37 | 7.26995e-01 3.81910e-02 38 | 7.12890e-01 3.97580e-02 39 | 6.98574e-01 4.12490e-02 40 | 6.84062e-01 4.26700e-02 41 | 6.69369e-01 4.40280e-02 42 | 6.54508e-01 4.53280e-02 43 | 6.39495e-01 4.65760e-02 44 | 6.24345e-01 4.77720e-02 45 | 6.09071e-01 4.89150e-02 46 | 5.93691e-01 5.00030e-02 47 | 5.78217e-01 5.10350e-02 48 | 5.62667e-01 5.20100e-02 49 | 5.47054e-01 5.29240e-02 50 | 5.31395e-01 5.37740e-02 51 | 5.15705e-01 5.45560e-02 52 | 5.00000e-01 5.52680e-02 53 | 4.84295e-01 5.59050e-02 54 | 4.68605e-01 5.64680e-02 55 | 4.52946e-01 5.69570e-02 56 | 4.37333e-01 5.73740e-02 57 | 4.21783e-01 5.77190e-02 58 | 4.06309e-01 5.79930e-02 59 | 3.90929e-01 5.82000e-02 60 | 3.75655e-01 5.83430e-02 61 | 3.60505e-01 5.84280e-02 62 | 3.45492e-01 5.84580e-02 63 | 3.30631e-01 5.84360e-02 64 | 3.15938e-01 5.83590e-02 65 | 3.01426e-01 5.82240e-02 66 | 2.87110e-01 5.80280e-02 67 | 2.73005e-01 5.77670e-02 68 | 2.59123e-01 5.74380e-02 69 | 2.45480e-01 5.70420e-02 70 | 2.32087e-01 5.65830e-02 71 | 2.18958e-01 5.60620e-02 72 | 2.06107e-01 5.54810e-02 73 | 1.93547e-01 5.48430e-02 74 | 1.81288e-01 5.41440e-02 75 | 1.69345e-01 5.33820e-02 76 | 1.57727e-01 5.25530e-02 77 | 1.46447e-01 5.16540e-02 78 | 1.35516e-01 5.06840e-02 79 | 1.24945e-01 4.96430e-02 80 | 1.14744e-01 4.85340e-02 81 | 1.04923e-01 4.73610e-02 82 | 9.54920e-02 4.61260e-02 83 | 8.64600e-02 4.48310e-02 84 | 7.78370e-02 4.34680e-02 85 | 6.96300e-02 4.20300e-02 86 | 6.18470e-02 4.05100e-02 87 | 5.44970e-02 3.88980e-02 88 | 4.75870e-02 3.71880e-02 89 | 4.11230e-02 3.53700e-02 90 | 3.51120e-02 3.34380e-02 91 | 2.95600e-02 3.13810e-02 92 | 2.44720e-02 2.91930e-02 93 | 1.98530e-02 2.68690e-02 94 | 1.57090e-02 2.44220e-02 95 | 1.20420e-02 2.18660e-02 96 | 8.85700e-03 1.92200e-02 97 | 6.15600e-03 1.64980e-02 98 | 3.94300e-03 1.37210e-02 99 | 2.22000e-03 1.09210e-02 100 | 9.87000e-04 8.13200e-03 101 | 2.47000e-04 5.39000e-03 102 | 0.00000e+00 2.73000e-03 103 | 2.47000e-04 1.79000e-04 104 | 9.87000e-04 -2.26300e-03 105 | 2.22000e-03 -4.60700e-03 106 | 3.94300e-03 -6.86200e-03 107 | 6.15600e-03 -9.03600e-03 108 | 8.85700e-03 -1.11390e-02 109 | 1.20420e-02 -1.31820e-02 110 | 1.57090e-02 -1.51750e-02 111 | 1.98530e-02 -1.71280e-02 112 | 2.44720e-02 -1.90530e-02 113 | 2.95600e-02 -2.09570e-02 114 | 3.51120e-02 -2.28370e-02 115 | 4.11230e-02 -2.46880e-02 116 | 4.75870e-02 -2.65020e-02 117 | 5.44970e-02 -2.82740e-02 118 | 6.18470e-02 -3.00010e-02 119 | 6.96300e-02 -3.16950e-02 120 | 7.78370e-02 -3.33720e-02 121 | 8.64600e-02 -3.50470e-02 122 | 9.54920e-02 -3.67340e-02 123 | 1.04923e-01 -3.84440e-02 124 | 1.14744e-01 -4.01710e-02 125 | 1.24945e-01 -4.19010e-02 126 | 1.35516e-01 -4.36230e-02 127 | 1.46447e-01 -4.53250e-02 128 | 1.57727e-01 -4.69950e-02 129 | 1.69345e-01 -4.86220e-02 130 | 1.81288e-01 -5.01950e-02 131 | 1.93547e-01 -5.17030e-02 132 | 2.06107e-01 -5.31350e-02 133 | 2.18958e-01 -5.44830e-02 134 | 2.32087e-01 -5.57380e-02 135 | 2.45480e-01 -5.68950e-02 136 | 2.59123e-01 -5.79470e-02 137 | 2.73005e-01 -5.88900e-02 138 | 2.87110e-01 -5.97180e-02 139 | 3.01426e-01 -6.04300e-02 140 | 3.15938e-01 -6.10250e-02 141 | 3.30631e-01 -6.15030e-02 142 | 3.45492e-01 -6.18640e-02 143 | 3.60505e-01 -6.21060e-02 144 | 3.75655e-01 -6.22230e-02 145 | 3.90929e-01 -6.22050e-02 146 | 4.06309e-01 -6.20440e-02 147 | 4.21783e-01 -6.17320e-02 148 | 4.37333e-01 -6.12620e-02 149 | 4.52946e-01 -6.06270e-02 150 | 4.68605e-01 -5.98230e-02 151 | 4.84295e-01 -5.88440e-02 152 | 5.00000e-01 -5.76860e-02 153 | 5.15705e-01 -5.63450e-02 154 | 5.31395e-01 -5.48240e-02 155 | 5.47054e-01 -5.31290e-02 156 | 5.62667e-01 -5.12640e-02 157 | 5.78217e-01 -4.92340e-02 158 | 5.93691e-01 -4.70500e-02 159 | 6.09071e-01 -4.47410e-02 160 | 6.24345e-01 -4.23440e-02 161 | 6.39495e-01 -3.98960e-02 162 | 6.54508e-01 -3.74310e-02 163 | 6.69369e-01 -3.49810e-02 164 | 6.84062e-01 -3.25490e-02 165 | 6.98574e-01 -3.01360e-02 166 | 7.12890e-01 -2.77410e-02 167 | 7.26995e-01 -2.53610e-02 168 | 7.40877e-01 -2.30030e-02 169 | 7.54520e-01 -2.06890e-02 170 | 7.67913e-01 -1.84470e-02 171 | 7.81042e-01 -1.63070e-02 172 | 7.93893e-01 -1.42960e-02 173 | 8.06453e-01 -1.24390e-02 174 | 8.18711e-01 -1.07350e-02 175 | 8.30655e-01 -9.18200e-03 176 | 8.42273e-01 -7.77400e-03 177 | 8.53553e-01 -6.50800e-03 178 | 8.64484e-01 -5.37900e-03 179 | 8.75055e-01 -4.39100e-03 180 | 8.85256e-01 -3.54500e-03 181 | 8.95077e-01 -2.84500e-03 182 | 9.04508e-01 -2.29200e-03 183 | 9.13540e-01 -1.88600e-03 184 | 9.22163e-01 -1.61700e-03 185 | 9.30370e-01 -1.47000e-03 186 | 9.38153e-01 -1.43000e-03 187 | 9.45503e-01 -1.48400e-03 188 | 9.52413e-01 -1.61800e-03 189 | 9.58877e-01 -1.82100e-03 190 | 9.64888e-01 -2.08200e-03 191 | 9.70441e-01 -2.39000e-03 192 | 9.75528e-01 -2.73500e-03 193 | 9.80146e-01 -3.10600e-03 194 | 9.84289e-01 -3.49000e-03 195 | 9.87955e-01 -3.87200e-03 196 | 9.91141e-01 -4.23800e-03 197 | 9.93844e-01 -4.57500e-03 198 | 9.96061e-01 -4.86800e-03 199 | 9.97788e-01 -5.10500e-03 200 | 9.99022e-01 -5.27000e-03 201 | 9.99760e-01 -5.34900e-03 202 | 1.00000e+00 -5.33000e-03 203 | -------------------------------------------------------------------------------- /examples/airfoils/lann_3.dat: -------------------------------------------------------------------------------- 1 | # LANN Airfoil 4 2 | 1.00000e+00 -1.16500e-02 3 | 9.99760e-01 -1.16150e-02 4 | 9.99022e-01 -1.14970e-02 5 | 9.97788e-01 -1.12970e-02 6 | 9.96061e-01 -1.10160e-02 7 | 9.93844e-01 -1.06550e-02 8 | 9.91141e-01 -1.02150e-02 9 | 9.87955e-01 -9.69700e-03 10 | 9.84289e-01 -9.10100e-03 11 | 9.80146e-01 -8.42800e-03 12 | 9.75528e-01 -7.68000e-03 13 | 9.70441e-01 -6.85500e-03 14 | 9.64888e-01 -5.95400e-03 15 | 9.58877e-01 -4.97200e-03 16 | 9.52413e-01 -3.90800e-03 17 | 9.45503e-01 -2.75900e-03 18 | 9.38153e-01 -1.52400e-03 19 | 9.30370e-01 -2.09000e-04 20 | 9.22163e-01 1.17600e-03 21 | 9.13540e-01 2.62500e-03 22 | 9.04508e-01 4.12800e-03 23 | 8.95077e-01 5.67900e-03 24 | 8.85256e-01 7.27700e-03 25 | 8.75055e-01 8.92100e-03 26 | 8.64484e-01 1.06110e-02 27 | 8.53553e-01 1.23480e-02 28 | 8.42273e-01 1.41280e-02 29 | 8.30655e-01 1.59410e-02 30 | 8.18711e-01 1.77720e-02 31 | 8.06453e-01 1.96090e-02 32 | 7.93893e-01 2.14380e-02 33 | 7.81042e-01 2.32470e-02 34 | 7.67913e-01 2.50340e-02 35 | 7.54520e-01 2.68000e-02 36 | 7.40877e-01 2.85450e-02 37 | 7.26995e-01 3.02680e-02 38 | 7.12890e-01 3.19700e-02 39 | 6.98574e-01 3.36430e-02 40 | 6.84062e-01 3.52780e-02 41 | 6.69369e-01 3.68690e-02 42 | 6.54508e-01 3.84070e-02 43 | 6.39495e-01 3.98860e-02 44 | 6.24345e-01 4.13050e-02 45 | 6.09071e-01 4.26680e-02 46 | 5.93691e-01 4.39760e-02 47 | 5.78217e-01 4.52320e-02 48 | 5.62667e-01 4.64360e-02 49 | 5.47054e-01 4.75850e-02 50 | 5.31395e-01 4.86750e-02 51 | 5.15705e-01 4.97010e-02 52 | 5.00000e-01 5.06590e-02 53 | 4.84295e-01 5.15450e-02 54 | 4.68605e-01 5.23590e-02 55 | 4.52946e-01 5.31030e-02 56 | 4.37333e-01 5.37780e-02 57 | 4.21783e-01 5.43860e-02 58 | 4.06309e-01 5.49270e-02 59 | 3.90929e-01 5.54010e-02 60 | 3.75655e-01 5.58070e-02 61 | 3.60505e-01 5.61450e-02 62 | 3.45492e-01 5.64120e-02 63 | 3.30631e-01 5.66110e-02 64 | 3.15938e-01 5.67460e-02 65 | 3.01426e-01 5.68220e-02 66 | 2.87110e-01 5.68470e-02 67 | 2.73005e-01 5.68270e-02 68 | 2.59123e-01 5.67650e-02 69 | 2.45480e-01 5.66580e-02 70 | 2.32087e-01 5.64980e-02 71 | 2.18958e-01 5.62790e-02 72 | 2.06107e-01 5.59940e-02 73 | 1.93547e-01 5.56390e-02 74 | 1.81288e-01 5.52140e-02 75 | 1.69345e-01 5.47230e-02 76 | 1.57727e-01 5.41680e-02 77 | 1.46447e-01 5.35520e-02 78 | 1.35516e-01 5.28770e-02 79 | 1.24945e-01 5.21400e-02 80 | 1.14744e-01 5.13370e-02 81 | 1.04923e-01 5.04650e-02 82 | 9.54920e-02 4.95180e-02 83 | 8.64600e-02 4.84950e-02 84 | 7.78370e-02 4.73870e-02 85 | 6.96300e-02 4.61900e-02 86 | 6.18470e-02 4.48970e-02 87 | 5.44970e-02 4.35030e-02 88 | 4.75870e-02 4.20010e-02 89 | 4.11230e-02 4.03830e-02 90 | 3.51120e-02 3.86430e-02 91 | 2.95600e-02 3.67740e-02 92 | 2.44720e-02 3.47680e-02 93 | 1.98530e-02 3.26220e-02 94 | 1.57090e-02 3.03570e-02 95 | 1.20420e-02 2.79970e-02 96 | 8.85700e-03 2.55660e-02 97 | 6.15600e-03 2.30900e-02 98 | 3.94300e-03 2.05840e-02 99 | 2.22000e-03 1.80410e-02 100 | 9.87000e-04 1.54420e-02 101 | 2.47000e-04 1.27700e-02 102 | 0.00000e+00 1.00100e-02 103 | 2.47000e-04 7.15800e-03 104 | 9.87000e-04 4.27300e-03 105 | 2.22000e-03 1.42600e-03 106 | 3.94300e-03 -1.31100e-03 107 | 6.15600e-03 -3.86600e-03 108 | 8.85700e-03 -6.18800e-03 109 | 1.20420e-02 -8.31300e-03 110 | 1.57090e-02 -1.03020e-02 111 | 1.98530e-02 -1.22110e-02 112 | 2.44720e-02 -1.41000e-02 113 | 2.95600e-02 -1.60160e-02 114 | 3.51120e-02 -1.79600e-02 115 | 4.11230e-02 -1.99220e-02 116 | 4.75870e-02 -2.18920e-02 117 | 5.44970e-02 -2.38590e-02 118 | 6.18470e-02 -2.58170e-02 119 | 6.96300e-02 -2.77700e-02 120 | 7.78370e-02 -2.97240e-02 121 | 8.64600e-02 -3.16870e-02 122 | 9.54920e-02 -3.36650e-02 123 | 1.04923e-01 -3.56620e-02 124 | 1.14744e-01 -3.76720e-02 125 | 1.24945e-01 -3.96830e-02 126 | 1.35516e-01 -4.16860e-02 127 | 1.46447e-01 -4.36700e-02 128 | 1.57727e-01 -4.56260e-02 129 | 1.69345e-01 -4.75410e-02 130 | 1.81288e-01 -4.94040e-02 131 | 1.93547e-01 -5.12030e-02 132 | 2.06107e-01 -5.29250e-02 133 | 2.18958e-01 -5.45590e-02 134 | 2.32087e-01 -5.60980e-02 135 | 2.45480e-01 -5.75340e-02 136 | 2.59123e-01 -5.88590e-02 137 | 2.73005e-01 -6.00660e-02 138 | 2.87110e-01 -6.11490e-02 139 | 3.01426e-01 -6.21070e-02 140 | 3.15938e-01 -6.29380e-02 141 | 3.30631e-01 -6.36430e-02 142 | 3.45492e-01 -6.42200e-02 143 | 3.60505e-01 -6.46680e-02 144 | 3.75655e-01 -6.49830e-02 145 | 3.90929e-01 -6.51590e-02 146 | 4.06309e-01 -6.51920e-02 147 | 4.21783e-01 -6.50750e-02 148 | 4.37333e-01 -6.48040e-02 149 | 4.52946e-01 -6.43740e-02 150 | 4.68605e-01 -6.37800e-02 151 | 4.84295e-01 -6.30170e-02 152 | 5.00000e-01 -6.20810e-02 153 | 5.15705e-01 -6.09690e-02 154 | 5.31395e-01 -5.96830e-02 155 | 5.47054e-01 -5.82280e-02 156 | 5.62667e-01 -5.66080e-02 157 | 5.78217e-01 -5.48270e-02 158 | 5.93691e-01 -5.28940e-02 159 | 6.09071e-01 -5.08340e-02 160 | 6.24345e-01 -4.86760e-02 161 | 6.39495e-01 -4.64520e-02 162 | 6.54508e-01 -4.41900e-02 163 | 6.69369e-01 -4.19150e-02 164 | 6.84062e-01 -3.96370e-02 165 | 6.98574e-01 -3.73590e-02 166 | 7.12890e-01 -3.50850e-02 167 | 7.26995e-01 -3.28190e-02 168 | 7.40877e-01 -3.05680e-02 169 | 7.54520e-01 -2.83560e-02 170 | 7.67913e-01 -2.62060e-02 171 | 7.81042e-01 -2.41450e-02 172 | 7.93893e-01 -2.21980e-02 173 | 8.06453e-01 -2.03870e-02 174 | 8.18711e-01 -1.87160e-02 175 | 8.30655e-01 -1.71850e-02 176 | 8.42273e-01 -1.57950e-02 177 | 8.53553e-01 -1.45450e-02 178 | 8.64484e-01 -1.34380e-02 179 | 8.75055e-01 -1.24730e-02 180 | 8.85256e-01 -1.16520e-02 181 | 8.95077e-01 -1.09780e-02 182 | 9.04508e-01 -1.04510e-02 183 | 9.13540e-01 -1.00710e-02 184 | 9.22163e-01 -9.82300e-03 185 | 9.30370e-01 -9.69100e-03 186 | 9.38153e-01 -9.65700e-03 187 | 9.45503e-01 -9.70500e-03 188 | 9.52413e-01 -9.81900e-03 189 | 9.58877e-01 -9.98900e-03 190 | 9.64888e-01 -1.02080e-02 191 | 9.70441e-01 -1.04680e-02 192 | 9.75528e-01 -1.07600e-02 193 | 9.80146e-01 -1.10760e-02 194 | 9.84289e-01 -1.14040e-02 195 | 9.87955e-01 -1.17320e-02 196 | 9.91141e-01 -1.20470e-02 197 | 9.93844e-01 -1.23380e-02 198 | 9.96061e-01 -1.25910e-02 199 | 9.97788e-01 -1.27940e-02 200 | 9.99022e-01 -1.29350e-02 201 | 9.99760e-01 -1.30010e-02 202 | 1.00000e+00 -1.29800e-02 203 | -------------------------------------------------------------------------------- /examples/airfoils/lann_0.dat: -------------------------------------------------------------------------------- 1 | # LANN Airfoil 1 2 | 1.00000e+00 -2.20600e-02 3 | 9.99760e-01 -2.20230e-02 4 | 9.99022e-01 -2.19130e-02 5 | 9.97788e-01 -2.17300e-02 6 | 9.96061e-01 -2.14740e-02 7 | 9.93844e-01 -2.11440e-02 8 | 9.91141e-01 -2.07400e-02 9 | 9.87955e-01 -2.02620e-02 10 | 9.84289e-01 -1.97090e-02 11 | 9.80146e-01 -1.90820e-02 12 | 9.75528e-01 -1.83790e-02 13 | 9.70441e-01 -1.76010e-02 14 | 9.64888e-01 -1.67500e-02 15 | 9.58877e-01 -1.58250e-02 16 | 9.52413e-01 -1.48300e-02 17 | 9.45503e-01 -1.37640e-02 18 | 9.38153e-01 -1.26290e-02 19 | 9.30370e-01 -1.14270e-02 20 | 9.22163e-01 -1.01600e-02 21 | 9.13540e-01 -8.82900e-03 22 | 9.04508e-01 -7.43500e-03 23 | 8.95077e-01 -5.98000e-03 24 | 8.85256e-01 -4.46700e-03 25 | 8.75055e-01 -2.89800e-03 26 | 8.64484e-01 -1.27400e-03 27 | 8.53553e-01 4.01000e-04 28 | 8.42273e-01 2.12600e-03 29 | 8.30655e-01 3.89400e-03 30 | 8.18711e-01 5.69900e-03 31 | 8.06453e-01 7.53600e-03 32 | 7.93893e-01 9.39800e-03 33 | 7.81042e-01 1.12800e-02 34 | 7.67913e-01 1.31770e-02 35 | 7.54520e-01 1.50860e-02 36 | 7.40877e-01 1.70030e-02 37 | 7.26995e-01 1.89250e-02 38 | 7.12890e-01 2.08460e-02 39 | 6.98574e-01 2.27600e-02 40 | 6.84062e-01 2.46620e-02 41 | 6.69369e-01 2.65430e-02 42 | 6.54508e-01 2.83960e-02 43 | 6.39495e-01 3.02170e-02 44 | 6.24345e-01 3.20000e-02 45 | 6.09071e-01 3.37440e-02 46 | 5.93691e-01 3.54470e-02 47 | 5.78217e-01 3.71060e-02 48 | 5.62667e-01 3.87180e-02 49 | 5.47054e-01 4.02770e-02 50 | 5.31395e-01 4.17770e-02 51 | 5.15705e-01 4.32120e-02 52 | 5.00000e-01 4.45750e-02 53 | 4.84295e-01 4.58610e-02 54 | 4.68605e-01 4.70710e-02 55 | 4.52946e-01 4.82090e-02 56 | 4.37333e-01 4.92760e-02 57 | 4.21783e-01 5.02750e-02 58 | 4.06309e-01 5.12100e-02 59 | 3.90929e-01 5.20820e-02 60 | 3.75655e-01 5.28940e-02 61 | 3.60505e-01 5.36510e-02 62 | 3.45492e-01 5.43550e-02 63 | 3.30631e-01 5.50090e-02 64 | 3.15938e-01 5.56090e-02 65 | 3.01426e-01 5.61540e-02 66 | 2.87110e-01 5.66410e-02 67 | 2.73005e-01 5.70660e-02 68 | 2.59123e-01 5.74270e-02 69 | 2.45480e-01 5.77270e-02 70 | 2.32087e-01 5.79660e-02 71 | 2.18958e-01 5.81470e-02 72 | 2.06107e-01 5.82720e-02 73 | 1.93547e-01 5.83430e-02 74 | 1.81288e-01 5.83600e-02 75 | 1.69345e-01 5.83240e-02 76 | 1.57727e-01 5.82340e-02 77 | 1.46447e-01 5.80920e-02 78 | 1.35516e-01 5.78960e-02 79 | 1.24945e-01 5.76390e-02 80 | 1.14744e-01 5.73120e-02 81 | 1.04923e-01 5.69090e-02 82 | 9.54920e-02 5.64200e-02 83 | 8.64600e-02 5.58370e-02 84 | 7.78370e-02 5.51490e-02 85 | 6.96300e-02 5.43460e-02 86 | 6.18470e-02 5.34180e-02 87 | 5.44970e-02 5.23520e-02 88 | 4.75870e-02 5.11420e-02 89 | 4.11230e-02 4.97950e-02 90 | 3.51120e-02 4.83190e-02 91 | 2.95600e-02 4.67260e-02 92 | 2.44720e-02 4.50240e-02 93 | 1.98530e-02 4.32190e-02 94 | 1.57090e-02 4.12970e-02 95 | 1.20420e-02 3.92410e-02 96 | 8.85700e-03 3.70340e-02 97 | 6.15600e-03 3.46560e-02 98 | 3.94300e-03 3.21010e-02 99 | 2.22000e-03 2.93940e-02 100 | 9.87000e-04 2.65710e-02 101 | 2.47000e-04 2.36680e-02 102 | 0.00000e+00 2.07200e-02 103 | 2.47000e-04 1.77650e-02 104 | 9.87000e-04 1.48440e-02 105 | 2.22000e-03 1.19990e-02 106 | 3.94300e-03 9.27400e-03 107 | 6.15600e-03 6.71200e-03 108 | 8.85700e-03 4.33900e-03 109 | 1.20420e-02 2.11800e-03 110 | 1.57090e-02 -3.00000e-06 111 | 1.98530e-02 -2.07700e-03 112 | 2.44720e-02 -4.15500e-03 113 | 2.95600e-02 -6.28100e-03 114 | 3.51120e-02 -8.45800e-03 115 | 4.11230e-02 -1.06800e-02 116 | 4.75870e-02 -1.29380e-02 117 | 5.44970e-02 -1.52270e-02 118 | 6.18470e-02 -1.75410e-02 119 | 6.96300e-02 -1.98800e-02 120 | 7.78370e-02 -2.22450e-02 121 | 8.64600e-02 -2.46370e-02 122 | 9.54920e-02 -2.70580e-02 123 | 1.04923e-01 -2.95070e-02 124 | 1.14744e-01 -3.19740e-02 125 | 1.24945e-01 -3.44500e-02 126 | 1.35516e-01 -3.69230e-02 127 | 1.46447e-01 -3.93830e-02 128 | 1.57727e-01 -4.18180e-02 129 | 1.69345e-01 -4.42130e-02 130 | 1.81288e-01 -4.65540e-02 131 | 1.93547e-01 -4.88250e-02 132 | 2.06107e-01 -5.10100e-02 133 | 2.18958e-01 -5.30960e-02 134 | 2.32087e-01 -5.50740e-02 135 | 2.45480e-01 -5.69350e-02 136 | 2.59123e-01 -5.86710e-02 137 | 2.73005e-01 -6.02760e-02 138 | 2.87110e-01 -6.17410e-02 139 | 3.01426e-01 -6.30650e-02 140 | 3.15938e-01 -6.42450e-02 141 | 3.30631e-01 -6.52800e-02 142 | 3.45492e-01 -6.61690e-02 143 | 3.60505e-01 -6.69100e-02 144 | 3.75655e-01 -6.75040e-02 145 | 3.90929e-01 -6.79540e-02 146 | 4.06309e-01 -6.82620e-02 147 | 4.21783e-01 -6.84280e-02 148 | 4.37333e-01 -6.84540e-02 149 | 4.52946e-01 -6.83320e-02 150 | 4.68605e-01 -6.80540e-02 151 | 4.84295e-01 -6.76130e-02 152 | 5.00000e-01 -6.69990e-02 153 | 5.15705e-01 -6.62070e-02 154 | 5.31395e-01 -6.52400e-02 155 | 5.47054e-01 -6.41050e-02 156 | 5.62667e-01 -6.28090e-02 157 | 5.78217e-01 -6.13560e-02 158 | 5.93691e-01 -5.97560e-02 159 | 6.09071e-01 -5.80260e-02 160 | 6.24345e-01 -5.61880e-02 161 | 6.39495e-01 -5.42620e-02 162 | 6.54508e-01 -5.22680e-02 163 | 6.69369e-01 -5.02270e-02 164 | 6.84062e-01 -4.81540e-02 165 | 6.98574e-01 -4.60680e-02 166 | 7.12890e-01 -4.39860e-02 167 | 7.26995e-01 -4.19230e-02 168 | 7.40877e-01 -3.98950e-02 169 | 7.54520e-01 -3.79150e-02 170 | 7.67913e-01 -3.59920e-02 171 | 7.81042e-01 -3.41380e-02 172 | 7.93893e-01 -3.23620e-02 173 | 8.06453e-01 -3.06760e-02 174 | 8.18711e-01 -2.90880e-02 175 | 8.30655e-01 -2.76050e-02 176 | 8.42273e-01 -2.62360e-02 177 | 8.53553e-01 -2.49890e-02 178 | 8.64484e-01 -2.38710e-02 179 | 8.75055e-01 -2.28860e-02 180 | 8.85256e-01 -2.20360e-02 181 | 8.95077e-01 -2.13250e-02 182 | 9.04508e-01 -2.07550e-02 183 | 9.13540e-01 -2.03270e-02 184 | 9.22163e-01 -2.00330e-02 185 | 9.30370e-01 -1.98610e-02 186 | 9.38153e-01 -1.98000e-02 187 | 9.45503e-01 -1.98400e-02 188 | 9.52413e-01 -1.99690e-02 189 | 9.58877e-01 -2.01720e-02 190 | 9.64888e-01 -2.04340e-02 191 | 9.70441e-01 -2.07380e-02 192 | 9.75528e-01 -2.10690e-02 193 | 9.80146e-01 -2.14120e-02 194 | 9.84289e-01 -2.17570e-02 195 | 9.87955e-01 -2.20940e-02 196 | 9.91141e-01 -2.24130e-02 197 | 9.93844e-01 -2.27050e-02 198 | 9.96061e-01 -2.29600e-02 199 | 9.97788e-01 -2.31690e-02 200 | 9.99022e-01 -2.33210e-02 201 | 9.99760e-01 -2.34080e-02 202 | 1.00000e+00 -2.34200e-02 203 | -------------------------------------------------------------------------------- /examples/airfoils/lann_1.dat: -------------------------------------------------------------------------------- 1 | # LANN Airfoil 2 2 | 1.00000e+00 -1.78700e-02 3 | 9.99760e-01 -1.78300e-02 4 | 9.99022e-01 -1.77190e-02 5 | 9.97788e-01 -1.75380e-02 6 | 9.96061e-01 -1.72870e-02 7 | 9.93844e-01 -1.69640e-02 8 | 9.91141e-01 -1.65710e-02 9 | 9.87955e-01 -1.61070e-02 10 | 9.84289e-01 -1.55710e-02 11 | 9.80146e-01 -1.49640e-02 12 | 9.75528e-01 -1.42850e-02 13 | 9.70441e-01 -1.35350e-02 14 | 9.64888e-01 -1.27090e-02 15 | 9.58877e-01 -1.18060e-02 16 | 9.52413e-01 -1.08200e-02 17 | 9.45503e-01 -9.75100e-03 18 | 9.38153e-01 -8.59500e-03 19 | 9.30370e-01 -7.35800e-03 20 | 9.22163e-01 -6.04600e-03 21 | 9.13540e-01 -4.66600e-03 22 | 9.04508e-01 -3.22500e-03 23 | 8.95077e-01 -1.72800e-03 24 | 8.85256e-01 -1.79000e-04 25 | 8.75055e-01 1.41900e-03 26 | 8.64484e-01 3.06500e-03 27 | 8.53553e-01 4.75400e-03 28 | 8.42273e-01 6.48500e-03 29 | 8.30655e-01 8.25000e-03 30 | 8.18711e-01 1.00440e-02 31 | 8.06453e-01 1.18600e-02 32 | 7.93893e-01 1.36920e-02 33 | 7.81042e-01 1.55320e-02 34 | 7.67913e-01 1.73790e-02 35 | 7.54520e-01 1.92310e-02 36 | 7.40877e-01 2.10850e-02 37 | 7.26995e-01 2.29390e-02 38 | 7.12890e-01 2.47900e-02 39 | 6.98574e-01 2.66310e-02 40 | 6.84062e-01 2.84540e-02 41 | 6.69369e-01 3.02490e-02 42 | 6.54508e-01 3.20100e-02 43 | 6.39495e-01 3.37270e-02 44 | 6.24345e-01 3.53990e-02 45 | 6.09071e-01 3.70210e-02 46 | 5.93691e-01 3.85910e-02 47 | 5.78217e-01 4.01070e-02 48 | 5.62667e-01 4.15650e-02 49 | 5.47054e-01 4.29630e-02 50 | 5.31395e-01 4.42990e-02 51 | 5.15705e-01 4.55700e-02 52 | 5.00000e-01 4.67740e-02 53 | 4.84295e-01 4.79100e-02 54 | 4.68605e-01 4.89770e-02 55 | 4.52946e-01 4.99770e-02 56 | 4.37333e-01 5.09110e-02 57 | 4.21783e-01 5.17800e-02 58 | 4.06309e-01 5.25860e-02 59 | 3.90929e-01 5.33300e-02 60 | 3.75655e-01 5.40140e-02 61 | 3.60505e-01 5.46420e-02 62 | 3.45492e-01 5.52140e-02 63 | 3.30631e-01 5.57320e-02 64 | 3.15938e-01 5.61940e-02 65 | 3.01426e-01 5.65960e-02 66 | 2.87110e-01 5.69360e-02 67 | 2.73005e-01 5.72100e-02 68 | 2.59123e-01 5.74160e-02 69 | 2.45480e-01 5.75570e-02 70 | 2.32087e-01 5.76390e-02 71 | 2.18958e-01 5.76650e-02 72 | 2.06107e-01 5.76400e-02 73 | 1.93547e-01 5.75670e-02 74 | 1.81288e-01 5.74430e-02 75 | 1.69345e-01 5.72660e-02 76 | 1.57727e-01 5.70320e-02 77 | 1.46447e-01 5.67370e-02 78 | 1.35516e-01 5.63780e-02 79 | 1.24945e-01 5.59510e-02 80 | 1.14744e-01 5.54510e-02 81 | 1.04923e-01 5.48750e-02 82 | 9.54920e-02 5.42180e-02 83 | 8.64600e-02 5.34760e-02 84 | 7.78370e-02 5.26420e-02 85 | 6.96300e-02 5.17090e-02 86 | 6.18470e-02 5.06680e-02 87 | 5.44970e-02 4.95140e-02 88 | 4.75870e-02 4.82370e-02 89 | 4.11230e-02 4.68270e-02 90 | 3.51120e-02 4.52700e-02 91 | 2.95600e-02 4.35550e-02 92 | 2.44720e-02 4.16690e-02 93 | 1.98530e-02 3.96070e-02 94 | 1.57090e-02 3.73910e-02 95 | 1.20420e-02 3.50490e-02 96 | 8.85700e-03 3.26120e-02 97 | 6.15600e-03 3.01070e-02 98 | 3.94300e-03 2.75600e-02 99 | 2.22000e-03 2.49740e-02 100 | 9.87000e-04 2.23500e-02 101 | 2.47000e-04 1.96890e-02 102 | 0.00000e+00 1.69900e-02 103 | 2.47000e-04 1.42610e-02 104 | 9.87000e-04 1.15340e-02 105 | 2.22000e-03 8.85100e-03 106 | 3.94300e-03 6.25300e-03 107 | 6.15600e-03 3.77800e-03 108 | 8.85700e-03 1.45500e-03 109 | 1.20420e-02 -7.44000e-04 110 | 1.57090e-02 -2.85700e-03 111 | 1.98530e-02 -4.92500e-03 112 | 2.44720e-02 -6.98700e-03 113 | 2.95600e-02 -9.07700e-03 114 | 3.51120e-02 -1.11980e-02 115 | 4.11230e-02 -1.33470e-02 116 | 4.75870e-02 -1.55220e-02 117 | 5.44970e-02 -1.77210e-02 118 | 6.18470e-02 -1.99390e-02 119 | 6.96300e-02 -2.21770e-02 120 | 7.78370e-02 -2.44320e-02 121 | 8.64600e-02 -2.67030e-02 122 | 9.54920e-02 -2.89890e-02 123 | 1.04923e-01 -3.12870e-02 124 | 1.14744e-01 -3.35920e-02 125 | 1.24945e-01 -3.58960e-02 126 | 1.35516e-01 -3.81950e-02 127 | 1.46447e-01 -4.04810e-02 128 | 1.57727e-01 -4.27470e-02 129 | 1.69345e-01 -4.49780e-02 130 | 1.81288e-01 -4.71570e-02 131 | 1.93547e-01 -4.92710e-02 132 | 2.06107e-01 -5.13010e-02 133 | 2.18958e-01 -5.32350e-02 134 | 2.32087e-01 -5.50630e-02 135 | 2.45480e-01 -5.67760e-02 136 | 2.59123e-01 -5.83670e-02 137 | 2.73005e-01 -5.98280e-02 138 | 2.87110e-01 -6.11530e-02 139 | 3.01426e-01 -6.23400e-02 140 | 3.15938e-01 -6.33900e-02 141 | 3.30631e-01 -6.43040e-02 142 | 3.45492e-01 -6.50820e-02 143 | 3.60505e-01 -6.57250e-02 144 | 3.75655e-01 -6.62300e-02 145 | 3.90929e-01 -6.65950e-02 146 | 4.06309e-01 -6.68160e-02 147 | 4.21783e-01 -6.68900e-02 148 | 4.37333e-01 -6.68150e-02 149 | 4.52946e-01 -6.65870e-02 150 | 4.68605e-01 -6.61980e-02 151 | 4.84295e-01 -6.56460e-02 152 | 5.00000e-01 -6.49240e-02 153 | 5.15705e-01 -6.40290e-02 154 | 5.31395e-01 -6.29630e-02 155 | 5.47054e-01 -6.17300e-02 156 | 5.62667e-01 -6.03350e-02 157 | 5.78217e-01 -5.87800e-02 158 | 5.93691e-01 -5.70740e-02 159 | 6.09071e-01 -5.52350e-02 160 | 6.24345e-01 -5.32870e-02 161 | 6.39495e-01 -5.12530e-02 162 | 6.54508e-01 -4.91560e-02 163 | 6.69369e-01 -4.70190e-02 164 | 6.84062e-01 -4.48560e-02 165 | 6.98574e-01 -4.26810e-02 166 | 7.12890e-01 -4.05090e-02 167 | 7.26995e-01 -3.83530e-02 168 | 7.40877e-01 -3.62280e-02 169 | 7.54520e-01 -3.41500e-02 170 | 7.67913e-01 -3.21370e-02 171 | 7.81042e-01 -3.02050e-02 172 | 7.93893e-01 -2.83710e-02 173 | 8.06453e-01 -2.66510e-02 174 | 8.18711e-01 -2.50470e-02 175 | 8.30655e-01 -2.35610e-02 176 | 8.42273e-01 -2.21940e-02 177 | 8.53553e-01 -2.09470e-02 178 | 8.64484e-01 -1.98220e-02 179 | 8.75055e-01 -1.88260e-02 180 | 8.85256e-01 -1.79650e-02 181 | 8.95077e-01 -1.72480e-02 182 | 9.04508e-01 -1.66820e-02 183 | 9.13540e-01 -1.62700e-02 184 | 9.22163e-01 -1.59950e-02 185 | 9.30370e-01 -1.58380e-02 186 | 9.38153e-01 -1.57760e-02 187 | 9.45503e-01 -1.57900e-02 188 | 9.52413e-01 -1.58620e-02 189 | 9.58877e-01 -1.59830e-02 190 | 9.64888e-01 -1.61500e-02 191 | 9.70441e-01 -1.63590e-02 192 | 9.75528e-01 -1.66040e-02 193 | 9.80146e-01 -1.68810e-02 194 | 9.84289e-01 -1.71760e-02 195 | 9.87955e-01 -1.74760e-02 196 | 9.91141e-01 -1.77670e-02 197 | 9.93844e-01 -1.80370e-02 198 | 9.96061e-01 -1.82710e-02 199 | 9.97788e-01 -1.84560e-02 200 | 9.99022e-01 -1.85780e-02 201 | 9.99760e-01 -1.86240e-02 202 | 1.00000e+00 -1.85800e-02 203 | -------------------------------------------------------------------------------- /examples/airfoils/lann_2.dat: -------------------------------------------------------------------------------- 1 | # LANN Airfoil 3 2 | 1.00000e+00 -1.52500e-02 3 | 9.99760e-01 -1.52110e-02 4 | 9.99022e-01 -1.50970e-02 5 | 9.97788e-01 -1.49100e-02 6 | 9.96061e-01 -1.46480e-02 7 | 9.93844e-01 -1.43150e-02 8 | 9.91141e-01 -1.39090e-02 9 | 9.87955e-01 -1.34330e-02 10 | 9.84289e-01 -1.28860e-02 11 | 9.80146e-01 -1.22700e-02 12 | 9.75528e-01 -1.15850e-02 13 | 9.70441e-01 -1.08310e-02 14 | 9.64888e-01 -1.00030e-02 15 | 9.58877e-01 -9.09500e-03 16 | 9.52413e-01 -8.09900e-03 17 | 9.45503e-01 -7.00900e-03 18 | 9.38153e-01 -5.82200e-03 19 | 9.30370e-01 -4.54600e-03 20 | 9.22163e-01 -3.19100e-03 21 | 9.13540e-01 -1.76900e-03 22 | 9.04508e-01 -2.90000e-04 23 | 8.95077e-01 1.23700e-03 24 | 8.85256e-01 2.80900e-03 25 | 8.75055e-01 4.42500e-03 26 | 8.64484e-01 6.08500e-03 27 | 8.53553e-01 7.78800e-03 28 | 8.42273e-01 9.53100e-03 29 | 8.30655e-01 1.13090e-02 30 | 8.18711e-01 1.31120e-02 31 | 8.06453e-01 1.49320e-02 32 | 7.93893e-01 1.67610e-02 33 | 7.81042e-01 1.85910e-02 34 | 7.67913e-01 2.04180e-02 35 | 7.54520e-01 2.22400e-02 36 | 7.40877e-01 2.40550e-02 37 | 7.26995e-01 2.58600e-02 38 | 7.12890e-01 2.76510e-02 39 | 6.98574e-01 2.94240e-02 40 | 6.84062e-01 3.11700e-02 41 | 6.69369e-01 3.28840e-02 42 | 6.54508e-01 3.45600e-02 43 | 6.39495e-01 3.61900e-02 44 | 6.24345e-01 3.77720e-02 45 | 6.09071e-01 3.93030e-02 46 | 5.93691e-01 4.07820e-02 47 | 5.78217e-01 4.22040e-02 48 | 5.62667e-01 4.35680e-02 49 | 5.47054e-01 4.48710e-02 50 | 5.31395e-01 4.61100e-02 51 | 5.15705e-01 4.72830e-02 52 | 5.00000e-01 4.83860e-02 53 | 4.84295e-01 4.94180e-02 54 | 4.68605e-01 5.03780e-02 55 | 4.52946e-01 5.12700e-02 56 | 4.37333e-01 5.20940e-02 57 | 4.21783e-01 5.28530e-02 58 | 4.06309e-01 5.35470e-02 59 | 3.90929e-01 5.41800e-02 60 | 3.75655e-01 5.47560e-02 61 | 3.60505e-01 5.52770e-02 62 | 3.45492e-01 5.57480e-02 63 | 3.30631e-01 5.61710e-02 64 | 3.15938e-01 5.65410e-02 65 | 3.01426e-01 5.68540e-02 66 | 2.87110e-01 5.71060e-02 67 | 2.73005e-01 5.72910e-02 68 | 2.59123e-01 5.74050e-02 69 | 2.45480e-01 5.74500e-02 70 | 2.32087e-01 5.74290e-02 71 | 2.18958e-01 5.73420e-02 72 | 2.06107e-01 5.71930e-02 73 | 1.93547e-01 5.69830e-02 74 | 1.81288e-01 5.67130e-02 75 | 1.69345e-01 5.63840e-02 76 | 1.57727e-01 5.59970e-02 77 | 1.46447e-01 5.55520e-02 78 | 1.35516e-01 5.50490e-02 79 | 1.24945e-01 5.44860e-02 80 | 1.14744e-01 5.38620e-02 81 | 1.04923e-01 5.31740e-02 82 | 9.54920e-02 5.24210e-02 83 | 8.64600e-02 5.15970e-02 84 | 7.78370e-02 5.06870e-02 85 | 6.96300e-02 4.96730e-02 86 | 6.18470e-02 4.85360e-02 87 | 5.44970e-02 4.72580e-02 88 | 4.75870e-02 4.58280e-02 89 | 4.11230e-02 4.42570e-02 90 | 3.51120e-02 4.25650e-02 91 | 2.95600e-02 4.07710e-02 92 | 2.44720e-02 3.88920e-02 93 | 1.98530e-02 3.69370e-02 94 | 1.57090e-02 3.48620e-02 95 | 1.20420e-02 3.26130e-02 96 | 8.85700e-03 3.01360e-02 97 | 6.15600e-03 2.73770e-02 98 | 3.94300e-03 2.43160e-02 99 | 2.22000e-03 2.10660e-02 100 | 9.87000e-04 1.77770e-02 101 | 2.47000e-04 1.45990e-02 102 | 0.00000e+00 1.16800e-02 103 | 2.47000e-04 9.12700e-03 104 | 9.87000e-04 6.87800e-03 105 | 2.22000e-03 4.82900e-03 106 | 3.94300e-03 2.87600e-03 107 | 6.15600e-03 9.15000e-04 108 | 8.85700e-03 -1.13400e-03 109 | 1.20420e-02 -3.26200e-03 110 | 1.57090e-02 -5.43200e-03 111 | 1.98530e-02 -7.61000e-03 112 | 2.44720e-02 -9.76300e-03 113 | 2.95600e-02 -1.18640e-02 114 | 3.51120e-02 -1.39240e-02 115 | 4.11230e-02 -1.59610e-02 116 | 4.75870e-02 -1.79960e-02 117 | 5.44970e-02 -2.00480e-02 118 | 6.18470e-02 -2.21310e-02 119 | 6.96300e-02 -2.42450e-02 120 | 7.78370e-02 -2.63860e-02 121 | 8.64600e-02 -2.85500e-02 122 | 9.54920e-02 -3.07310e-02 123 | 1.04923e-01 -3.29250e-02 124 | 1.14744e-01 -3.51250e-02 125 | 1.24945e-01 -3.73230e-02 126 | 1.35516e-01 -3.95110e-02 127 | 1.46447e-01 -4.16820e-02 128 | 1.57727e-01 -4.38250e-02 129 | 1.69345e-01 -4.59300e-02 130 | 1.81288e-01 -4.79820e-02 131 | 1.93547e-01 -4.99690e-02 132 | 2.06107e-01 -5.18760e-02 133 | 2.18958e-01 -5.36920e-02 134 | 2.32087e-01 -5.54080e-02 135 | 2.45480e-01 -5.70150e-02 136 | 2.59123e-01 -5.85060e-02 137 | 2.73005e-01 -5.98740e-02 138 | 2.87110e-01 -6.11100e-02 139 | 3.01426e-01 -6.22140e-02 140 | 3.15938e-01 -6.31850e-02 141 | 3.30631e-01 -6.40240e-02 142 | 3.45492e-01 -6.47300e-02 143 | 3.60505e-01 -6.53010e-02 144 | 3.75655e-01 -6.57360e-02 145 | 3.90929e-01 -6.60300e-02 146 | 4.06309e-01 -6.61790e-02 147 | 4.21783e-01 -6.61790e-02 148 | 4.37333e-01 -6.60280e-02 149 | 4.52946e-01 -6.57200e-02 150 | 4.68605e-01 -6.52500e-02 151 | 4.84295e-01 -6.46140e-02 152 | 5.00000e-01 -6.38080e-02 153 | 5.15705e-01 -6.28280e-02 154 | 5.31395e-01 -6.16770e-02 155 | 5.47054e-01 -6.03600e-02 156 | 5.62667e-01 -5.88800e-02 157 | 5.78217e-01 -5.72430e-02 158 | 5.93691e-01 -5.54560e-02 159 | 6.09071e-01 -5.35400e-02 160 | 6.24345e-01 -5.15170e-02 161 | 6.39495e-01 -4.94100e-02 162 | 6.54508e-01 -4.72450e-02 163 | 6.69369e-01 -4.50420e-02 164 | 6.84062e-01 -4.28170e-02 165 | 6.98574e-01 -4.05850e-02 166 | 7.12890e-01 -3.83600e-02 167 | 7.26995e-01 -3.61580e-02 168 | 7.40877e-01 -3.39920e-02 169 | 7.54520e-01 -3.18780e-02 170 | 7.67913e-01 -2.98320e-02 171 | 7.81042e-01 -2.78700e-02 172 | 7.93893e-01 -2.60070e-02 173 | 8.06453e-01 -2.42570e-02 174 | 8.18711e-01 -2.26280e-02 175 | 8.30655e-01 -2.11230e-02 176 | 8.42273e-01 -1.97490e-02 177 | 8.53553e-01 -1.85100e-02 178 | 8.64484e-01 -1.74100e-02 179 | 8.75055e-01 -1.64500e-02 180 | 8.85256e-01 -1.56290e-02 181 | 8.95077e-01 -1.49480e-02 182 | 9.04508e-01 -1.44060e-02 183 | 9.13540e-01 -1.40000e-02 184 | 9.22163e-01 -1.37190e-02 185 | 9.30370e-01 -1.35450e-02 186 | 9.38153e-01 -1.34660e-02 187 | 9.45503e-01 -1.34650e-02 188 | 9.52413e-01 -1.35280e-02 189 | 9.58877e-01 -1.36480e-02 190 | 9.64888e-01 -1.38190e-02 191 | 9.70441e-01 -1.40350e-02 192 | 9.75528e-01 -1.42890e-02 193 | 9.80146e-01 -1.45730e-02 194 | 9.84289e-01 -1.48770e-02 195 | 9.87955e-01 -1.51870e-02 196 | 9.91141e-01 -1.54890e-02 197 | 9.93844e-01 -1.57710e-02 198 | 9.96061e-01 -1.60200e-02 199 | 9.97788e-01 -1.62220e-02 200 | 9.99022e-01 -1.63650e-02 201 | 9.99760e-01 -1.64350e-02 202 | 1.00000e+00 -1.64200e-02 203 | -------------------------------------------------------------------------------- /examples/airfoils/onera_m6.dat: -------------------------------------------------------------------------------- 1 | ONERA M6 2 | 1.000000000000000 0.0 3 | 0.997803000000000 0.000287600000000 4 | 0.995208000000000 0.000627100000000 5 | 0.992143800000000 0.001028000000000 6 | 0.988525200000000 0.001501400000000 7 | 0.984250800000000 0.002060600000000 8 | 0.979202000000000 0.002721100000000 9 | 0.973236100000000 0.003501500000000 10 | 0.966186000000000 0.004424000000000 11 | 0.957851100000000 0.005514400000000 12 | 0.947994600000000 0.006803800000000 13 | 0.936334600000000 0.008326500000000 14 | 0.922533600000000 0.010113800000000 15 | 0.906190500000000 0.012195200000000 16 | 0.886823500000000 0.014505100000000 17 | 0.863856400000000 0.017091500000000 18 | 0.840732400000000 0.019583800000000 19 | 0.817482800000000 0.021984200000000 20 | 0.794105500000000 0.024302700000000 21 | 0.770599800000000 0.026550500000000 22 | 0.746965800000000 0.028736500000000 23 | 0.723199500000000 0.030866200000000 24 | 0.699302700000000 0.032940200000000 25 | 0.675272600000000 0.034954200000000 26 | 0.651109300000000 0.036899000000000 27 | 0.626810400000000 0.038761300000000 28 | 0.602375700000000 0.040524100000000 29 | 0.577804300000000 0.042168400000000 30 | 0.553093700000000 0.043674100000000 31 | 0.528242600000000 0.045020900000000 32 | 0.503251400000000 0.046190300000000 33 | 0.478119700000000 0.047166100000000 34 | 0.452844100000000 0.047935100000000 35 | 0.427422300000000 0.048483300000000 36 | 0.401856700000000 0.048820200000000 37 | 0.376144600000000 0.048929600000000 38 | 0.350283000000000 0.048818300000000 39 | 0.324272600000000 0.048490200000000 40 | 0.298111300000000 0.047949400000000 41 | 0.271797800000000 0.047198700000000 42 | 0.245331000000000 0.046235800000000 43 | 0.218709600000000 0.045050700000000 44 | 0.191932700000000 0.043621400000000 45 | 0.164997600000000 0.041908900000000 46 | 0.137896300000000 0.039852200000000 47 | 0.114979600000000 0.037792300000000 48 | 0.095635400000000 0.035774200000000 49 | 0.079336600000000 0.033837200000000 50 | 0.065630300000000 0.032013800000000 51 | 0.054124800000000 0.030327800000000 52 | 0.044485200000000 0.028791200000000 53 | 0.036426100000000 0.027331700000000 54 | 0.029700800000000 0.025824500000000 55 | 0.024106700000000 0.024200400000000 56 | 0.019460900000000 0.022454500000000 57 | 0.015617100000000 0.020622000000000 58 | 0.012447900000000 0.018753700000000 59 | 0.009841300000000 0.016898400000000 60 | 0.007711200000000 0.015095100000000 61 | 0.005975100000000 0.013370800000000 62 | 0.004570400000000 0.011741900000000 63 | 0.003442800000000 0.010216300000000 64 | 0.002544100000000 0.008795800000000 65 | 0.001836400000000 0.007478400000000 66 | 0.001286800000000 0.006259800000000 67 | 0.000865700000000 0.005134300000000 68 | 0.000550800000000 0.004095900000000 69 | 0.000323200000000 0.003138200000000 70 | 0.000167500000000 0.002255400000000 71 | 0.000069600000000 0.001441600000000 72 | 0.000016500000000 0.000691400000000 73 | 0.0 0.0 74 | 0.000016500000000 -0.000691400000000 75 | 0.000069600000000 -0.001441600000000 76 | 0.000167500000000 -0.002255400000000 77 | 0.000323200000000 -0.003138200000000 78 | 0.000550800000000 -0.004095900000000 79 | 0.000865700000000 -0.005134300000000 80 | 0.001286800000000 -0.006259800000000 81 | 0.001836400000000 -0.007478400000000 82 | 0.002544100000000 -0.008795800000000 83 | 0.003442800000000 -0.010216300000000 84 | 0.004570400000000 -0.011741900000000 85 | 0.005975100000000 -0.013370800000000 86 | 0.007711200000000 -0.015095100000000 87 | 0.009841300000000 -0.016898400000000 88 | 0.012447900000000 -0.018753700000000 89 | 0.015617100000000 -0.020622000000000 90 | 0.019460900000000 -0.022454500000000 91 | 0.024106700000000 -0.024200400000000 92 | 0.029700800000000 -0.025824500000000 93 | 0.036426100000000 -0.027331700000000 94 | 0.044485200000000 -0.028791200000000 95 | 0.054124800000000 -0.030327800000000 96 | 0.065630300000000 -0.032013800000000 97 | 0.079336600000000 -0.033837200000000 98 | 0.095635400000000 -0.035774200000000 99 | 0.114979600000000 -0.037792300000000 100 | 0.137896300000000 -0.039852200000000 101 | 0.164997600000000 -0.041908900000000 102 | 0.191932700000000 -0.043621400000000 103 | 0.218709600000000 -0.045050700000000 104 | 0.245331000000000 -0.046235800000000 105 | 0.271797800000000 -0.047198700000000 106 | 0.298111300000000 -0.047949400000000 107 | 0.324272600000000 -0.048490200000000 108 | 0.350283000000000 -0.048818300000000 109 | 0.376144600000000 -0.048929600000000 110 | 0.401856700000000 -0.048820200000000 111 | 0.427422300000000 -0.048483300000000 112 | 0.452844100000000 -0.047935100000000 113 | 0.478119700000000 -0.047166100000000 114 | 0.503251400000000 -0.046190300000000 115 | 0.528242600000000 -0.045020900000000 116 | 0.553093700000000 -0.043674100000000 117 | 0.577804300000000 -0.042168400000000 118 | 0.602375700000000 -0.040524100000000 119 | 0.626810400000000 -0.038761300000000 120 | 0.651109300000000 -0.036899000000000 121 | 0.675272600000000 -0.034954200000000 122 | 0.699302700000000 -0.032940200000000 123 | 0.723199500000000 -0.030866200000000 124 | 0.746965800000000 -0.028736500000000 125 | 0.770599800000000 -0.026550500000000 126 | 0.794105500000000 -0.024302700000000 127 | 0.817482800000000 -0.021984200000000 128 | 0.840732400000000 -0.019583800000000 129 | 0.863856400000000 -0.017091500000000 130 | 0.886823500000000 -0.014505100000000 131 | 0.906190500000000 -0.012195200000000 132 | 0.922533600000000 -0.010113800000000 133 | 0.936334600000000 -0.008326500000000 134 | 0.947994600000000 -0.006803800000000 135 | 0.957851100000000 -0.005514400000000 136 | 0.966186000000000 -0.004424000000000 137 | 0.973236100000000 -0.003501500000000 138 | 0.979202000000000 -0.002721100000000 139 | 0.984250800000000 -0.002060600000000 140 | 0.988525200000000 -0.001501400000000 141 | 0.992143800000000 -0.001028000000000 142 | 0.995208000000000 -0.000627100000000 143 | 0.997803000000000 -0.000287600000000 144 | 1.000000000000000 0.0 -------------------------------------------------------------------------------- /gmshcfd/utils.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | 3 | # GmshCFD 4 | # Copyright (C) 2023 Adrien Crovato 5 | # 6 | # This program is free software: you can redistribute it and/or modify 7 | # it under the terms of the GNU General Public License as published by 8 | # the Free Software Foundation, either version 3 of the License, or 9 | # (at your option) any later version. 10 | # This program is distributed in the hope that it will be useful, 11 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | # GNU General Public License for more details. 14 | # You should have received a copy of the GNU General Public License 15 | # along with this program. If not, see . 16 | 17 | import numpy as np 18 | from scipy.interpolate import PchipInterpolator 19 | import os, os.path 20 | 21 | def compute_wing_cfg(spans, tapers, sweeps, dihedrals, root_chord): 22 | """Compute the leading edge coordinates and the chord length of the airfoil at the tip of each planform 23 | 24 | Parameters: 25 | spans: list of float 26 | lengths of each planform 27 | tapers: list of float 28 | taper ratios of each planform 29 | sweeps: list of float 30 | sweep angle of leading edge (in degrees) 31 | dihedrals: list of float 32 | dihedral angle of leading edge (in degrees) 33 | root_chord: float 34 | chord length of wing root 35 | 36 | Return: 37 | le_coords: list of list of float 38 | leading edge coordinates 39 | chords: list of float 40 | chord lengths 41 | """ 42 | le_coords = [[0., 0., 0.]] 43 | chords = [root_chord] 44 | for i in range(len(spans)): 45 | lec = [0., 0., 0.] 46 | lec[0] = le_coords[i][0] + np.tan(sweeps[i] * np.pi / 180) * spans[i] 47 | lec[1] = le_coords[i][1] + spans[i] 48 | lec[2] = le_coords[i][2] + np.tan(dihedrals[i] * np.pi / 180) * spans[i] 49 | le_coords.append(lec) 50 | chords.append(chords[i] * tapers[i]) 51 | return le_coords, chords 52 | 53 | def compute_ff_mesh_size(surface_size, domain_length, factor): 54 | """Compute the mesh size at the farfield boundary 55 | 56 | Parameters: 57 | surface_size: float 58 | mesh size at surface boundaries 59 | domain_length: float 60 | distance between surface boundaries and farfield boundary 61 | factor: float 62 | progression factor 63 | 64 | Return: 65 | _: float 66 | mesh size at farfield boundary 67 | """ 68 | n = np.log(1 - (1 - factor) * domain_length / surface_size) / np.log(factor) 69 | return surface_size * pow(factor, n - 1) 70 | 71 | def add_section(le_coords, chords, incidences, airf_path, y_sec=0.99): 72 | """Add a section to the wing planform 73 | 74 | Parameters: 75 | le_coords: list of list of float 76 | leading edge coordinates of each cross-section 77 | chords: list of float 78 | chord length of each cross-section 79 | incidences: list of float 80 | angles of incidence of each cross-section 81 | airf_path : list of string 82 | path to files containing airfoil coordinates of each cross-section 83 | y_sec: float 84 | normalized y-coordinate of cross-section to add (between 0 and 1) 85 | 86 | Return: 87 | le_coords: list of list of float 88 | leading edge coordinates with added cross-section 89 | chords: list of float 90 | chord lengths with added cross-section 91 | incidences: list of float 92 | angles of incidence with added cross-section 93 | airf_path : list of string 94 | path to files containing airfoil coordinates with added cross-section 95 | """ 96 | # Check if input is in range 97 | if y_sec <= 0. or y_sec >= 1.: 98 | raise RuntimeError('add_section: Parameter "y_sec" must be between 0 and 1!\n') 99 | 100 | # Compute y-coordinate of section and find sections between which to interpolate 101 | y = y_sec * le_coords[-1][1] 102 | for isec in range(len(le_coords)): 103 | if y == le_coords[isec][1]: 104 | print('Section to add corresponds to one of the input sections, nothing done.') 105 | return le_coords, chords, airf_path 106 | if y - le_coords[isec][1] < 0.: 107 | break 108 | 109 | # Read airfoil coordinates, header and file name 110 | fnames = [] 111 | header = [] 112 | airfoil_coords = [] 113 | for ipth in [isec - 1, isec]: 114 | fnames.append(os.path.basename(airf_path[ipth]).split('.')[0]) 115 | file = open(airf_path[ipth]) 116 | header.append(file.readline().strip()) 117 | file.close() 118 | airfoil_coords.append(np.loadtxt(airf_path[ipth], skiprows=1)) 119 | 120 | # Compute interpolation parameter 121 | a = (y - le_coords[isec - 1][1]) / (le_coords[isec][1] - le_coords[isec - 1][1]) 122 | # Interpolate leading edge coordinates 123 | if le_coords[isec - 1][0] == le_coords[isec][0] and le_coords[isec - 1][2] == le_coords[isec][2]: 124 | new_le_coords = [le_coords[isec - 1][0], y, le_coords[isec - 1][2]] 125 | else: 126 | new_le_coords = list((1 - a) * np.array(le_coords[isec - 1]) + a * np.array(le_coords[isec])) 127 | # Interpolate chord length 128 | if chords[isec - 1] == chords[isec]: 129 | new_chord = chords[isec - 1] 130 | else: 131 | new_chord = (1 - a) * chords[isec - 1] + a * chords[isec] 132 | # Interpolate incidence angle 133 | if incidences[isec - 1] == incidences[isec]: 134 | new_incidence = incidences[isec - 1] 135 | else: 136 | new_incidence = (1 - a) * incidences[isec - 1] + a * incidences[isec] 137 | # Interpolate airfoil coordinates 138 | if fnames[0] == fnames[1]: 139 | new_fpath = airf_path[0] 140 | else: 141 | new_airfoil_coords = (1 - a) * interpolate_coords(airfoil_coords[0]) + a * interpolate_coords(airfoil_coords[1]) 142 | new_fname = f'{fnames[0]}_{fnames[1]}.dat' 143 | np.savetxt(new_fname, new_airfoil_coords, fmt='%1.5e', header=f'{header[0]} - {header[1]}') 144 | new_fpath = os.path.join(os.getcwd(), new_fname) 145 | 146 | # Add new section to lists 147 | le_coords.insert(isec, new_le_coords) 148 | chords.insert(isec, new_chord) 149 | incidences.insert(isec, new_incidence) 150 | airf_path.insert(isec, new_fpath) 151 | return le_coords, chords, incidences, airf_path 152 | 153 | def interpolate_coords(coords, n_pts=80, flip=False): 154 | """Interpolate coordinates 155 | 156 | Parameters: 157 | coords: ndarray 158 | airfoil coordinates 159 | n_pts: int 160 | number of interpolation points along x-axis 161 | flip: bool 162 | whether to reverse order of coordinates along x-axis 163 | 164 | Return: 165 | new_coords: ndarray 166 | interpolated coordinates 167 | """ 168 | # Revert coordinates order if not Selig 169 | if flip: 170 | coords = np.flipud(coords) 171 | 172 | # Split suction and pressure sides 173 | le = np.argmin(coords[:, 0]) 174 | x_u = coords[:le+1, 0] 175 | y_u = coords[:le+1, 1] 176 | x_l = coords[le:, 0] 177 | y_l = coords[le:, 1] 178 | 179 | # Interpolate using half-cosine spacing 180 | x_new = 0.5 * (1 - np.cos(np.linspace(0., np.pi, n_pts))) 181 | y_u_new = PchipInterpolator(np.flipud(x_u), np.flipud(y_u))(x_new) 182 | y_l_new = PchipInterpolator(x_l, y_l)(x_new) 183 | 184 | # Concatenate and remove duplicated LE 185 | new_coords = np.vstack((np.hstack((np.flipud(x_new[1:]), x_new)), 186 | np.hstack((np.flipud(y_u_new[1:]), y_l_new)))) 187 | return new_coords.T 188 | 189 | def sharpen_te(fpath, n_change=10, gui=False): 190 | """Convert a blunt trailing edge to a sharp trailing edge and write coordinates 191 | 192 | Parameters: 193 | fpath: str 194 | path to file containing airfoil coordinates 195 | n_change: int 196 | number of points to be altered 197 | gui: bool 198 | whether to display the airfoil 199 | """ 200 | # Read header and coordinates 201 | file = open(fpath) 202 | header = file.readline().strip() 203 | file.close() 204 | coords = np.loadtxt(fpath, skiprows=1) 205 | new_coords = coords.copy() 206 | 207 | # Convert blunt TE to sharp TE 208 | z_mean = (coords[0:n_change, 1] + coords[-1:-n_change-1:-1, 1]) / 2 209 | tck = (coords[0:n_change, 1] - coords[-1:-n_change-1:-1, 1]) / 2 210 | new_tck = np.linspace(0, tck[-1], n_change) 211 | new_coords[0:n_change, 1] = z_mean + new_tck; 212 | new_coords[-1:-n_change-1:-1, 1] = z_mean - new_tck; 213 | 214 | # Write file 215 | fname = os.path.basename(fpath).split('.')[0] + '_ste.dat' 216 | np.savetxt(fname, new_coords, fmt='%1.5e', header=header + ' sharp TE') 217 | 218 | # Display 219 | if gui: 220 | import matplotlib.pyplot as plt 221 | plt.plot(coords[:, 0], coords[:, 1], marker='o') 222 | plt.plot(new_coords[:, 0], new_coords[:, 1], marker='o', mfc=None) 223 | plt.xlabel('x') 224 | plt.ylabel('y') 225 | plt.show() 226 | -------------------------------------------------------------------------------- /gmshcfd/domain.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | 3 | # GmshCFD 4 | # Copyright (C) 2023 Adrien Crovato 5 | # 6 | # This program is free software: you can redistribute it and/or modify 7 | # it under the terms of the GNU General Public License as published by 8 | # the Free Software Foundation, either version 3 of the License, or 9 | # (at your option) any later version. 10 | # This program is distributed in the hope that it will be useful, 11 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | # GNU General Public License for more details. 14 | # You should have received a copy of the GNU General Public License 15 | # along with this program. If not, see . 16 | 17 | import gmsh 18 | 19 | class Box: 20 | """Box-shaped domain 21 | 22 | Parameters: 23 | wings: list 24 | list of lifting surfaces 25 | cfg: dict 26 | parameters to configure domain 27 | mesh_cfg: dict 28 | parameters to configure mesh 29 | """ 30 | def __init__(self, wings, cfg, mesh_cfg): 31 | # Create Gmsh box domain model 32 | wing_order = self.__order_wakes(wings) 33 | self.__create_model(wings, wing_order, cfg, mesh_cfg) 34 | 35 | def __order_wakes(self, wings): 36 | """Order the lifting surfaces according to the z-coordinate of their trailing edge on the symmetry plane 37 | """ 38 | idx = [] 39 | zc = [] 40 | for i in range(len(wings)): 41 | idx.append(i) 42 | zc.append(wings[i].height) 43 | return [x for _, x in sorted(zip(zc, idx))] 44 | 45 | def __create_model(self, wings, wing_order, cfg, mesh_cfg): 46 | """Create domain points, curves, surfaces and volume in Gmsh model 47 | """ 48 | # Add points 49 | ptags = [] 50 | for i in range(2): 51 | ptag = [] 52 | ptag.append(gmsh.model.geo.add_point(cfg['length'], i*cfg['length'], cfg['length'])) 53 | ptag.append(gmsh.model.geo.add_point(-cfg['length'], i*cfg['length'], cfg['length'])) 54 | ptag.append(gmsh.model.geo.add_point(-cfg['length'], i*cfg['length'], -cfg['length'])) 55 | ptag.append(gmsh.model.geo.add_point(cfg['length'], i*cfg['length'], -cfg['length'])) 56 | ptags.append(ptag) 57 | 58 | # Add curves 59 | oxz_ctags = [] 60 | # oxz plane, symmetry side 61 | ctag = [] 62 | for i in range(3): 63 | ctag.append(gmsh.model.geo.add_line(ptags[0][i], ptags[0][i+1])) 64 | ctag.append(gmsh.model.geo.add_line(ptags[0][3], wings[wing_order[0]].wake.tags['symmetry_point'])) 65 | for i in range(len(wing_order) - 1): 66 | ctag.append(gmsh.model.geo.add_line(wings[wing_order[i]].wake.tags['symmetry_point'], wings[wing_order[i+1]].wake.tags['symmetry_point'])) 67 | ctag.append(gmsh.model.geo.add_line(wings[wing_order[-1]].wake.tags['symmetry_point'], ptags[0][0])) 68 | oxz_ctags.append(ctag) 69 | # oxz plane, back side 70 | ctag = [] 71 | for i in range(4): 72 | ctag.append(gmsh.model.geo.add_line(ptags[1][i], ptags[1][(i+1) % 4])) 73 | oxz_ctags.append(ctag) 74 | # oxy plane 75 | oyz_ctags = [] 76 | for i in range(4): 77 | oyz_ctags.append(gmsh.model.geo.add_line(ptags[0][i], ptags[1][i])) 78 | 79 | # Add surfaces 80 | stags = [] 81 | # symmetry 82 | cltag_wings = [] 83 | for i in range(len(wings)): 84 | cltag_wings.append(gmsh.model.geo.add_curve_loop(wings[i].tags['symmetry_curves'])) 85 | cltag = gmsh.model.geo.add_curve_loop(list(reversed(oxz_ctags[0]))) 86 | stags.append(gmsh.model.geo.add_plane_surface([-cltag] + cltag_wings)) 87 | # upstream 88 | cltag = gmsh.model.geo.add_curve_loop([oxz_ctags[0][1], oyz_ctags[2], -oxz_ctags[1][1], -oyz_ctags[1]]) 89 | stags.append(gmsh.model.geo.add_plane_surface([cltag])) 90 | # downstream 91 | cltag = gmsh.model.geo.add_curve_loop([oyz_ctags[0], -oxz_ctags[1][3], -oyz_ctags[3]] + oxz_ctags[0][3:]) 92 | stags.append(gmsh.model.geo.add_plane_surface([cltag])) 93 | # farfield 94 | cltag = gmsh.model.geo.add_curve_loop([oxz_ctags[0][0], oyz_ctags[1], -oxz_ctags[1][0], -oyz_ctags[0]]) 95 | stags.append(gmsh.model.geo.add_plane_surface([cltag])) 96 | cltag = gmsh.model.geo.add_curve_loop([oyz_ctags[3], -oxz_ctags[1][2], -oyz_ctags[2], oxz_ctags[0][2]]) 97 | stags.append(gmsh.model.geo.add_plane_surface([cltag])) 98 | cltag = gmsh.model.geo.add_curve_loop(oxz_ctags[1]) 99 | stags.append(gmsh.model.geo.add_plane_surface([cltag])) 100 | 101 | # Add volume 102 | wing_tags = [] 103 | for w in wings: 104 | wing_tags.extend(w.tags['wing_surfaces']) 105 | sltag = gmsh.model.geo.add_surface_loop(stags + wing_tags) 106 | vtag = gmsh.model.geo.add_volume([sltag]) 107 | 108 | # Add embbeded entities 109 | symmetry_tags = [] 110 | trailing_tags = [] 111 | wake_tags = [] 112 | for w in wings: 113 | symmetry_tags.append(w.wake.tags['symmetry_curve']) 114 | trailing_tags.extend(w.wake.tags['trailing_curves']) 115 | wake_tags.extend(w.wake.tags['wake_surfaces']) 116 | gmsh.model.geo.synchronize() 117 | gmsh.model.mesh.embed(1, symmetry_tags, 2, stags[0]) 118 | gmsh.model.mesh.embed(1, trailing_tags, 2, stags[2]) 119 | gmsh.model.mesh.embed(2, wake_tags, 3, vtag) 120 | 121 | # Add physical groups 122 | gmsh.model.geo.synchronize() 123 | gmsh.model.add_physical_group(2, [stags[0]], name='symmetry') 124 | gmsh.model.add_physical_group(2, [stags[1]], name='upstream') 125 | gmsh.model.add_physical_group(2, [stags[2]], name='downstream') 126 | gmsh.model.add_physical_group(2, stags[3:], name='farfield') 127 | gmsh.model.add_physical_group(3, [vtag], name='field') 128 | 129 | # Add meshing constraints 130 | for i in range(2): 131 | for j in range(len(ptags[i])): 132 | gmsh.model.mesh.set_size([(0, ptags[i][j])], mesh_cfg['domain_size']) 133 | 134 | class Sphere: 135 | """Sphere-shaped domain 136 | 137 | Parameters: 138 | wings: list 139 | list of lifting surfaces 140 | cfg: dict 141 | parameters to configure domain 142 | mesh_cfg: dict 143 | parameters to configure mesh 144 | """ 145 | def __init__(self, wings, cfg, mesh_cfg): 146 | # Create Gmsh sphere domain model 147 | self.__create_model(wings, cfg, mesh_cfg) 148 | 149 | def __create_model(self, wings, cfg, mesh_cfg): 150 | """Create domain points, curves, surfaces and volume in Gmsh model 151 | """ 152 | # Add points 153 | c_ptag = gmsh.model.geo.add_point(0., 0., 0.) # center of the sphere 154 | ptags = [] 155 | ptags.append(gmsh.model.geo.add_point(cfg['length'], 0., 0.)) 156 | ptags.append(gmsh.model.geo.add_point(0., 0., cfg['length'])) 157 | ptags.append(gmsh.model.geo.add_point(-cfg['length'], 0., 0.)) 158 | ptags.append(gmsh.model.geo.add_point(0., 0., -cfg['length'])) 159 | ptags.append(gmsh.model.geo.add_point(0., cfg['length'], 0.)) 160 | 161 | # Add curves 162 | ctags = [] 163 | # symmetry plane 164 | ctag = [] 165 | for i in range(4): 166 | ctag.append(gmsh.model.geo.add_circle_arc(ptags[i], c_ptag, ptags[(i+1) % 4])) 167 | ctags.append(ctag) 168 | # outside symmetry plane 169 | ctag = [] 170 | for i in range(4): 171 | ctag.append(gmsh.model.geo.add_circle_arc(ptags[i], c_ptag, ptags[-1])) 172 | ctags.append(ctag) 173 | 174 | # Add surfaces 175 | stags = [] 176 | # symmetry 177 | cltag_wings = [] 178 | for i in range(len(wings)): 179 | cltag_wings.append(gmsh.model.geo.add_curve_loop(wings[i].tags['symmetry_curves'])) 180 | cltag = gmsh.model.geo.add_curve_loop(list(reversed(ctags[0]))) 181 | stags.append(gmsh.model.geo.add_plane_surface([-cltag] + cltag_wings)) 182 | # farfield 183 | for i in range(4): 184 | cltag = gmsh.model.geo.add_curve_loop([ctags[0][i], ctags[1][(i+1) % 4], -ctags[1][i]]) 185 | stags.append(gmsh.model.geo.add_surface_filling([cltag])) 186 | 187 | # Add volume 188 | wing_tags = [] 189 | tag_name = 'boundary_layer_top' if cfg['type'] == 'rans' else 'wing' 190 | for w in wings: 191 | wing_tags.extend(w.tags[tag_name + '_surfaces']) 192 | sltag = gmsh.model.geo.add_surface_loop(stags + wing_tags) 193 | vtag = gmsh.model.geo.add_volume([sltag]) 194 | 195 | # Add physical groups 196 | gmsh.model.geo.synchronize() 197 | sym_stags = [stags[0]] 198 | if cfg['type'] == 'rans': 199 | for w in wings: 200 | sym_stags.extend(w.tags['boundary_layer_symmetry_surfaces']) 201 | vtags = [vtag] 202 | if cfg['type'] == 'rans': 203 | for w in wings: 204 | vtags.extend(w.tags['boundary_layer_volume']) 205 | gmsh.model.add_physical_group(2, sym_stags, name='symmetry') 206 | gmsh.model.add_physical_group(2, stags[1:], name='farfield') 207 | gmsh.model.add_physical_group(3, vtags, name='field') 208 | 209 | # Add meshing constraints 210 | for i in range(len(ptags)): 211 | gmsh.model.mesh.set_size([(0, ptags[i])], mesh_cfg['domain_size']) 212 | -------------------------------------------------------------------------------- /gmshcfd/wing.py: -------------------------------------------------------------------------------- 1 | # -*- coding: utf-8 -*- 2 | 3 | # GmshCFD 4 | # Copyright (C) 2023 Adrien Crovato 5 | # 6 | # This program is free software: you can redistribute it and/or modify 7 | # it under the terms of the GNU General Public License as published by 8 | # the Free Software Foundation, either version 3 of the License, or 9 | # (at your option) any later version. 10 | # This program is distributed in the hope that it will be useful, 11 | # but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | # GNU General Public License for more details. 14 | # You should have received a copy of the GNU General Public License 15 | # along with this program. If not, see . 16 | 17 | from .wake import Wake 18 | from .errors import GmshCFDError 19 | import gmsh 20 | import numpy as np 21 | 22 | class Wing: 23 | """Lifting surface 24 | 25 | Parameters: 26 | name: string 27 | name of the lifting surface 28 | cfg: dict 29 | parameters to configure lifting surface 30 | domain_cfg: dict 31 | parameters to configure domain 32 | mesh_cfg: dict 33 | parameters to configure mesh 34 | 35 | Attributes: 36 | height: float 37 | z_coordinate of the airfoil trailing edge on the symmetry plane 38 | wake: gmshcfd.Wake object 39 | wake attached to the lifting surface 40 | tags: dict 41 | gmsh tags of remarkable curves/surfaces of the lifting surface 42 | """ 43 | def __init__(self, name, cfg, domain_cfg, mesh_cfg): 44 | # Compute airfoil coordinates 45 | is_closed, n_airf, coords, le_idx, tp_idx = self.__compute_coordinates(cfg, domain_cfg) 46 | # Create Gmsh wing and wake models 47 | if is_closed: 48 | self.__create_model_closed(n_airf, coords, le_idx, name, domain_cfg, mesh_cfg) 49 | else: 50 | self.__create_model_open(n_airf, coords, le_idx, tp_idx, name, domain_cfg, mesh_cfg) 51 | 52 | def __compute_coordinates(self, cfg, domain_cfg): 53 | """Read airfoil coordinates from files and transform them using wing planform configuration 54 | """ 55 | # Get number of airfoils 56 | n_airf = len(cfg['airfoils']) 57 | 58 | # Read coordinates 59 | coords = [] 60 | for fname in cfg['airfoils']: 61 | coords.append(np.loadtxt(fname, skiprows=1)) 62 | # Find local index of leading edge point 63 | le_idx = [] 64 | for c in coords: 65 | le_idx.append(np.argmin(c[:, 0])) 66 | # Find local index of c/20 point at tip 67 | tp_idx = np.argmin(abs(coords[-1][:, 0] - 0.05)) 68 | 69 | # Transform airfoil coordinates using chord length, incidence and offset 70 | for i in range(n_airf): 71 | # Check if TE is duplicated and if x-coordinate is 1 72 | if coords[i][0][0] != 1.0 or coords[i][-1][0] != 1.0: 73 | raise GmshCFDError('airfoil coordinates must be ordered using Selig format: TE point must be first and last, duplicated, and its x-coordinate must be equal to 1.0!\n', self) 74 | # Reverse order of coordinates if not in standard Selig format 75 | if coords[i][1, 1] < coords[i][-2, 1]: 76 | coords[i] = np.flipud(coords[i]) 77 | # Check if airfoil is closed or open 78 | if coords[i][0][1] == coords[i][-1][1]: 79 | is_closed = True 80 | if domain_cfg['type'] == 'rans': 81 | raise GmshCFDError('sharp trailing edge airfoils cannot be used with extruded boundary layers (rans domain type)!\n', self) 82 | coords[i] = np.delete(coords[i], (-1), axis=0) # delete duplicated last point 83 | else: 84 | is_closed = False 85 | if domain_cfg['type'] == 'potential': 86 | raise GmshCFDError('blunt trailing edge airfoils cannot be used with wakes (potential domain type)!\n', self) 87 | # Scale according to chord length 88 | coords[i] *= cfg['chords'][i] 89 | # Rotate around quarter-chord according to incidence angle 90 | cos = np.cos(cfg['incidences'][i] * np.pi / 180) 91 | sin = np.sin(cfg['incidences'][i] * np.pi / 180) 92 | coords[i] = np.dot(coords[i], np.array([[cos, -sin],[sin, cos]])) 93 | # Add x and z offset 94 | coords[i][:, 0] += cfg['le_offsets'][i][0] + cfg['offset'][0] 95 | coords[i][:, 1] += cfg['le_offsets'][i][2] + cfg['offset'][1] 96 | # Insert y-coordinates 97 | coords[i] = np.hstack((coords[i], cfg['le_offsets'][i][1] * np.ones([coords[i].shape[0], 1]))) 98 | coords[i][:, [1, 2]] = np.fliplr(coords[i][:, [1, 2]]) 99 | 100 | # Get the trailing edge z_coordinate of the airfoil on the symmetry plane 101 | self.height = coords[0][0, 0] 102 | 103 | return is_closed, n_airf, coords, le_idx, tp_idx 104 | 105 | def __create_model_closed(self, n_airf, coords, le_idx, name, domain_cfg, mesh_cfg): 106 | """Create points, curves and surfaces for wing with sharp trailing edge in Gmsh model 107 | """ 108 | # Add airfoil points 109 | ptags = [] 110 | for c in coords: 111 | ptag = [] 112 | for row in c: 113 | ptag.append(gmsh.model.geo.add_point(row[0], row[1], row[2])) 114 | ptags.append(ptag) 115 | 116 | # Add airfoils splines 117 | airf_ctags = [] 118 | for i in range(n_airf): 119 | ctag_up = gmsh.model.geo.add_spline(ptags[i][0:le_idx[i]+1]) 120 | ctag_lw = gmsh.model.geo.add_spline(np.append(ptags[i][le_idx[i]:], ptags[i][0])) 121 | airf_ctags.append([ctag_up, ctag_lw]) 122 | # Add TE and LE lines 123 | plan_ctags = [] 124 | for i in range(n_airf - 1): 125 | ctag_te = gmsh.model.geo.add_line(ptags[i][0], ptags[i+1][0]) 126 | ctag_le = gmsh.model.geo.add_line(ptags[i][le_idx[i]], ptags[i+1][le_idx[i+1]]) 127 | plan_ctags.append([ctag_te, ctag_le]) 128 | 129 | # Add planforms 130 | stags = [] 131 | for i in range(n_airf - 1): 132 | cltag = gmsh.model.geo.add_curve_loop([airf_ctags[i][0], plan_ctags[i][1], -airf_ctags[i+1][0], -plan_ctags[i][0]]) 133 | stags.append(gmsh.model.geo.add_surface_filling([-cltag])) 134 | cltag = gmsh.model.geo.add_curve_loop([airf_ctags[i][1], plan_ctags[i][0], -airf_ctags[i+1][1], -plan_ctags[i][1]]) 135 | stags.append(gmsh.model.geo.add_surface_filling([-cltag])) 136 | # Add cutoff wingtip 137 | cltag = gmsh.model.geo.add_curve_loop([airf_ctags[-1][0], airf_ctags[-1][1]]) 138 | stags.append(gmsh.model.geo.add_plane_surface([-cltag])) 139 | 140 | # Add physical groups 141 | gmsh.model.geo.synchronize() 142 | if domain_cfg['type'] == 'potential': 143 | gmsh.model.add_physical_group(1, [tags[0] for tags in plan_ctags], name=name+'Te') 144 | gmsh.model.add_physical_group(2, stags[0::2], name=name) 145 | gmsh.model.add_physical_group(2, stags[1:-1:2], name=name+'_') 146 | else: 147 | gmsh.model.add_physical_group(2, stags, name=name) 148 | 149 | # Add meshing constraint on TE and LE 150 | for i in range(n_airf): 151 | gmsh.model.mesh.set_size([(0, ptags[i][0])], mesh_cfg['wing_sizes'][name]['te'][i]) 152 | gmsh.model.mesh.set_size([(0, ptags[i][le_idx[i]])], mesh_cfg['wing_sizes'][name]['le'][i]) 153 | 154 | # Generate tag dictionary 155 | self.tags = {'symmetry_curves': airf_ctags[0], 'wing_surfaces': stags} 156 | 157 | # Create wake if requested 158 | if domain_cfg['type'] == 'potential': 159 | pte_ids = {} # TE point 160 | for i in range(n_airf): 161 | pte_ids[ptags[i][0]] = coords[i][0] 162 | cte_ids = [] # TE curves 163 | for i in range(n_airf - 1): 164 | cte_ids.append(plan_ctags[i][0]) 165 | self.wake = Wake(pte_ids, cte_ids, name+'Wake', domain_cfg, mesh_cfg['domain_size']) 166 | 167 | def __create_model_open(self, n_airf, coords, le_idx, tp_idx, name, domain_cfg, mesh_cfg): 168 | """Create points, curves and surfaces for wing with blunt trailing edge in Gmsh model 169 | """ 170 | # Add airfoil points 171 | ptags = [] 172 | for c in coords: 173 | ptag = [] 174 | for row in c: 175 | ptag.append(gmsh.model.geo.add_point(row[0], row[1], row[2])) 176 | ptags.append(ptag) 177 | # Add trailing edge and tip points and centers for blunt TE 178 | if domain_cfg['type'] == 'rans': 179 | # TE and TE center 180 | tec_ptags = [] 181 | te_ptags = [] 182 | for i in range(n_airf): 183 | c_coord = [0.5 * (coords[i][0, 0] + coords[i][-1, 0]), coords[i][0, 1], 0.5 * (coords[i][0, 2] + coords[i][-1, 2])] 184 | tec_ptags.append(gmsh.model.geo.add_point(c_coord[0], c_coord[1], c_coord[2])) 185 | te = gmsh.model.geo.copy([(0, ptags[i][0])]) 186 | gmsh.model.geo.rotate(te, c_coord[0], c_coord[1], c_coord[2], 0, 1, 0, np.pi / 2) 187 | te_ptags.append(te[0][1]) 188 | # Tip 189 | tip_ptags = [] 190 | for i in range(1, 10): 191 | idx = tp_idx * i // 9 192 | xc = 0.5 * (coords[-1][idx, 0] + coords[-1][-idx-1, 0]) 193 | zc = 0.5 * (coords[-1][idx, 2] + coords[-1][-idx-1, 2]) 194 | yc = coords[-1][idx, 1] + 0.5 * abs(coords[-1][idx, 2] - coords[-1][-idx-1, 2]) 195 | tip_ptags.append(gmsh.model.geo.add_point(xc, yc, zc)) 196 | 197 | # Add airfoils splines 198 | airf_ctags = [] 199 | for i in range(n_airf): 200 | ctag_up = gmsh.model.geo.add_spline(ptags[i][0:le_idx[i]+1]) 201 | ctag_lw = gmsh.model.geo.add_spline(ptags[i][le_idx[i]:]) 202 | airf_ctags.append([ctag_up, ctag_lw]) 203 | # Add TE and LE lines 204 | plan_ctags = [] 205 | for i in range(n_airf - 1): 206 | ctag_teu = gmsh.model.geo.add_line(ptags[i][0], ptags[i+1][0]) 207 | ctag_le = gmsh.model.geo.add_line(ptags[i][le_idx[i]], ptags[i+1][le_idx[i+1]]) 208 | ctag_tel = gmsh.model.geo.add_line(ptags[i][-1], ptags[i+1][-1]) 209 | plan_ctags.append([ctag_teu, ctag_le, ctag_tel]) 210 | # Add trailing edge curves and tip spline 211 | if domain_cfg['type'] == 'rans': 212 | # TE airfoil circles 213 | airf_te_ctags = [] 214 | for i in range(n_airf): 215 | ctag_teu = gmsh.model.geo.add_circle_arc(te_ptags[i], tec_ptags[i], ptags[i][0]) 216 | ctag_tel = gmsh.model.geo.add_circle_arc(ptags[i][-1], tec_ptags[i], te_ptags[i]) 217 | airf_te_ctags.append([ctag_teu, ctag_tel]) 218 | # TE planform line 219 | te_ctags = [] 220 | for i in range(n_airf-1): 221 | te_ctags.append(gmsh.model.geo.add_line(te_ptags[i], te_ptags[i+1])) 222 | # Tip 223 | tip_ctag = gmsh.model.geo.add_spline([te_ptags[-1]] + tip_ptags) 224 | tip_le_ctag = gmsh.model.geo.add_line(tip_ptags[-1], ptags[-1][le_idx[-1]]) 225 | else: 226 | # TE line 227 | airf_te_ctags = [] 228 | for i in range(n_airf): 229 | airf_te_ctags.append(gmsh.model.geo.add_line(ptags[i][-1], ptags[i][0])) 230 | 231 | # Add planforms 232 | stags = [] 233 | for i in range(n_airf - 1): 234 | cltag = gmsh.model.geo.add_curve_loop([airf_ctags[i][0], plan_ctags[i][1], -airf_ctags[i+1][0], -plan_ctags[i][0]]) 235 | stags.append(gmsh.model.geo.add_surface_filling([-cltag])) 236 | cltag = gmsh.model.geo.add_curve_loop([airf_ctags[i][1], plan_ctags[i][2], -airf_ctags[i+1][1], -plan_ctags[i][1]]) 237 | stags.append(gmsh.model.geo.add_surface_filling([-cltag])) 238 | # Add TE and wingtip 239 | if domain_cfg['type'] == 'rans': 240 | # Rounded TE 241 | for i in range(n_airf - 1): 242 | cltag = gmsh.model.geo.add_curve_loop([airf_te_ctags[i][0], plan_ctags[i][0], -airf_te_ctags[i+1][0], -te_ctags[i]]) 243 | stags.append(gmsh.model.geo.add_surface_filling([-cltag])) 244 | cltag = gmsh.model.geo.add_curve_loop([airf_te_ctags[i][1], te_ctags[i], -airf_te_ctags[i+1][1], -plan_ctags[i][2]]) 245 | stags.append(gmsh.model.geo.add_surface_filling([-cltag])) 246 | # Rounded wingtip 247 | cltag = gmsh.model.geo.add_curve_loop([airf_ctags[-1][0], -tip_le_ctag, -tip_ctag, airf_te_ctags[-1][0]]) 248 | stags.append(gmsh.model.geo.add_surface_filling([-cltag])) 249 | cltag = gmsh.model.geo.add_curve_loop([airf_te_ctags[-1][1], tip_ctag, tip_le_ctag, airf_ctags[-1][1]]) 250 | stags.append(gmsh.model.geo.add_surface_filling([-cltag])) 251 | else: 252 | # Cutoff TE 253 | for i in range(n_airf - 1): 254 | cltag = gmsh.model.geo.add_curve_loop([airf_te_ctags[i], plan_ctags[i][0], -airf_te_ctags[i+1], -plan_ctags[i][2]]) 255 | stags.append(gmsh.model.geo.add_plane_surface([-cltag])) 256 | # Cutoff wingtip 257 | cltag = gmsh.model.geo.add_curve_loop([airf_ctags[-1][0], airf_ctags[-1][1], airf_te_ctags[-1]]) 258 | stags.append(gmsh.model.geo.add_plane_surface([-cltag])) 259 | 260 | # Add boundary layer 261 | if domain_cfg['type'] == 'rans': 262 | # Extrude surfaces to create boundary layer 263 | N = mesh_cfg['boundary_layer']['wing']['num_layer'] # number of layers 264 | r = mesh_cfg['boundary_layer']['wing']['growth_ratio'] # ratio 265 | d = [mesh_cfg['boundary_layer']['wing']['hgt_first_layer']] # heigth of first layer 266 | for i in range(1, N): 267 | d.append(d[-1] + d[0] * r**i) 268 | bl = gmsh.model.geo.extrudeBoundaryLayer([(2, tag) for tag in stags], [1] * N, d, True) 269 | gmsh.model.geo.synchronize() 270 | # Get tags of top and symmetry surfaces, and volume 271 | bl_top_stags = [] 272 | bl_sym_stags = [] 273 | bl_vtags = [] 274 | for i in range(len(bl)): 275 | if bl[i][0] == 3: 276 | bl_top_stags.append(bl[i-1][1]) 277 | bl_vtags.append(bl[i][1]) 278 | # Get surfaces on symmetry plane (originate from 4 extruded surfaces, each giving 5 surfaces + 1 volume) 279 | if i < 12: 280 | bl_sym_stags.append(bl[i + 4]) 281 | bl_sym_stags.append(bl[2 * (n_airf - 1) * 6 + i + 4]) 282 | # Get the bounding curves on symmetry plane, gives 2 closed countours (inner and outer), so remove inner 283 | bl_sym_ctags = [c[1] for c in gmsh.model.getBoundary(bl_sym_stags)] 284 | for i in range(2): 285 | bl_sym_ctags.remove(-airf_ctags[0][i]) 286 | bl_sym_ctags.remove(-airf_te_ctags[0][i]) 287 | 288 | # Add physical groups 289 | gmsh.model.geo.synchronize() 290 | gmsh.model.add_physical_group(2, stags, name=name) 291 | if domain_cfg['type'] == 'rans' and mesh_cfg['boundary_layer']['write_tags']: 292 | gmsh.model.add_physical_group(2, bl_top_stags, tag=9998, name=name+'BoundaryLayerSurface') 293 | gmsh.model.add_physical_group(3, bl_vtags, tag=9999, name=name+'BoundaryLayerVolume') 294 | 295 | # Transfinite meshing constraints (RANS only) 296 | if 'num_cell_chord' in mesh_cfg['wing_sizes'][name]: 297 | if domain_cfg['type'] != 'rans': 298 | raise GmshCFDError('transfinite surface meshes are supported only for RANS (rans domain type)!\n', self) 299 | # Suction and pressure side curves 300 | for tags in airf_ctags: 301 | for j in range(2): 302 | gmsh.model.geo.mesh.set_transfinite_curve(tags[j], mesh_cfg['wing_sizes'][name]['num_cell_chord'] + 1, meshType='Bump', coef=mesh_cfg['wing_sizes'][name]['prog_chord']) 303 | for i in range(n_airf - 1): 304 | for j in range(3): 305 | gmsh.model.geo.mesh.set_transfinite_curve(plan_ctags[i][j], mesh_cfg['wing_sizes'][name]['num_cell_span'][i] + 1) 306 | # Trailing edge curves 307 | for i in range(n_airf - 1): 308 | gmsh.model.geo.mesh.set_transfinite_curve(te_ctags[i], mesh_cfg['wing_sizes'][name]['num_cell_span'][i] + 1) 309 | for i in range(n_airf): 310 | for j in range(2): 311 | gmsh.model.geo.mesh.set_transfinite_curve(airf_te_ctags[i][j], 2) 312 | # Tip curves 313 | gmsh.model.geo.mesh.set_transfinite_curve(tip_ctag, mesh_cfg['wing_sizes'][name]['num_cell_chord'] + 1, meshType='Bump', coef=mesh_cfg['wing_sizes'][name]['prog_chord']) 314 | gmsh.model.geo.mesh.set_transfinite_curve(tip_le_ctag, 2) 315 | # Surfaces 316 | for tag in stags: 317 | gmsh.model.geo.mesh.set_transfinite_surface(tag) 318 | gmsh.model.geo.mesh.set_recombine(2, tag) 319 | # Unstructured meshing constraints 320 | else: 321 | # Leading and trailing edges 322 | for i in range(n_airf): 323 | gmsh.model.mesh.set_size([(0, ptags[i][0]), (0, ptags[i][-1])], mesh_cfg['wing_sizes'][name]['te'][i]) 324 | gmsh.model.mesh.set_size([(0, ptags[i][le_idx[i]])], mesh_cfg['wing_sizes'][name]['le'][i]) 325 | # Tip and trailing edge 326 | if domain_cfg['type'] == 'rans': 327 | for i in range(n_airf): 328 | gmsh.model.mesh.set_size([(0, te_ptags[i])], mesh_cfg['wing_sizes'][name]['te'][i]) 329 | gmsh.model.mesh.set_size([(0, tip_ptags[-1])], mesh_cfg['wing_sizes'][name]['te'][i]) 330 | 331 | # Generate tag dictionary 332 | if domain_cfg['type'] == 'rans': 333 | self.tags = {'symmetry_curves': bl_sym_ctags, 334 | 'boundary_layer_top_surfaces': bl_top_stags, 335 | 'boundary_layer_symmetry_surfaces': [s[1] for s in bl_sym_stags], 336 | 'boundary_layer_volume': bl_vtags} 337 | else: 338 | self.tags = {'symmetry_curves': airf_ctags[0] + [airf_te_ctags[0]], 'wing_surfaces': stags} 339 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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No Surrender of Others' Freedom. 541 | 542 | If conditions are imposed on you (whether by court order, agreement or 543 | otherwise) that contradict the conditions of this License, they do not 544 | excuse you from the conditions of this License. If you cannot convey a 545 | covered work so as to satisfy simultaneously your obligations under this 546 | License and any other pertinent obligations, then as a consequence you may 547 | not convey it at all. For example, if you agree to terms that obligate you 548 | to collect a royalty for further conveying from those to whom you convey 549 | the Program, the only way you could satisfy both those terms and this 550 | License would be to refrain entirely from conveying the Program. 551 | 552 | 13. Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | --------------------------------------------------------------------------------