├── LICENSE ├── README.md ├── euler_solver.pdf ├── results ├── case_1 │ ├── supersonic.png │ └── supersonic.txt ├── case_2 │ ├── transonic.png │ └── transonic.txt ├── case_3 │ ├── subsonic.png │ └── subsonic.txt ├── disturb_sub │ └── dist_sub.txt ├── disturb_sup │ └── dist_sup.txt ├── gridgen_bump │ └── bump.txt └── videos │ ├── disturb_sub │ └── sub1.avi │ ├── disturb_sup │ └── sup1.avi │ └── gridgen_bump │ └── bump.avi └── source ├── BUMP ├── INSTRUCTIONS ├── bump04perc.grd └── bump10perc.grd ├── calcResid.m ├── convU_V.m ├── convV_U.m ├── e_0.m ├── euler.m ├── fixTime.m ├── flux.m ├── fneg.m ├── fpos.m ├── h_0.m ├── speedsound.m ├── subsonic.mat ├── supersonic.mat └── transonic.mat /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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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 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Finite Volume Euler Solver 2 | Read the [technical brief](https://github.com/robojafar/euler_solver/blob/master/euler_solver.pdf) for a full explantion of the mechanics behind this code. 3 | 4 | ## Overview 5 | - Cell centered 6 | - Van Leer flux splitting method 7 | - m-stage time stepping 8 | - Written in Matlab 9 | 10 | 11 | 12 | ## Euler Code 13 | The code was divided into five major sections: 14 | - Loading/Creating a grid 15 | - Calculating grid metrics 16 | - Setting freestream condition and loop variables 17 | - Initializing the solution to freestream conditions 18 | - Executing the main loop in time 19 | - Calculating the residual 20 | 21 | ### Loading the Grid 22 | The code provides the option to create a Cartesian grid or load a grid in Plot3D format. When a grid is loaded, the number of zones is checked. If the number of zones is greater than one, then the grid will not be loaded because the code cannot handle multiple zones. If the grid passes this check, then the file is read and the x, y and z coordinates are stored in arrays. The code which completes this task is shown below: 23 | ```Matlab 24 | if (zones == 1) 25 | % Read in number of i,j,k points 26 | npi = fscanf(fid, '%d', 1); 27 | npj = fscanf(fid, '%d', 1); 28 | npk = fscanf(fid, '%d', 1); 29 | 30 | % Retrieve i,j,k coordinates 31 | x = fscanf(fid, '%f', [npi,npj]); 32 | y = fscanf(fid, '%f', [npi,npj]); 33 | z = fscanf(fid, '%f', [npi,npj]); 34 | 35 | disp('Grid read successfully'); 36 | end 37 | ``` 38 | 39 | ### Calculating Grid Metrics 40 | Once the grid is loaded, then the grid metrics can be calculated. Although it is feasible to calculate quantities during the iteration, it may be inefficient. Therefore, all necessary quantities will be calculated and stored in arrays before the iterations begin. Since this code is a cell-centered, finite volume solver, certain cell quantities will be needed such as the areas of each face (north, south, east, west), the outward normal vector of each face, and the volume of each cell. 41 | 42 | The area of each face is calculated by taking the square root of the square of the x and y lengths of the face. 43 | 44 | The volume of each cell is calculated using the formula for the volume of a parallelepiped (or the absolute value of the scalar triple product), which can be found in any calculus book. 45 | 46 | The normal vector for each face was found by crossing the unit normal vector of the face by the unit vector in the z-direction. The result is an outward normal of each face. 47 | 48 | The code which accomplishes these three tasks is shown below: 49 | 50 | ```Matlab 51 | % Compute volume of cell using A.BxC (volume of parallelepiped) 52 | volume(i,j) = abs(dot(z_width,cross(-1*[s_xlen,s_ylen,0],[e_xlen,e_ylen,0]))); 53 | 54 | % Compute area of cell 55 | sE(i,j) = sqrt((e_xlen)^2 + (e_ylen)^2); 56 | sN(i,j) = sqrt((n_xlen)^2 + (n_ylen)^2); 57 | sW(i,j) = sqrt((w_xlen)^2 + (w_ylen)^2); 58 | sS(i,j) = sqrt((s_xlen)^2 + (s_ylen)^2); 59 | 60 | % Compute outward normal of faces (return 3 component vector) 61 | temp_nE = cross([e_xlen,e_ylen, 0]/sE(i,j), z_width); 62 | temp_nN = cross([n_xlen,n_ylen, 0]/sN(i,j), z_width); 63 | temp_nW = cross([w_xlen,w_ylen, 0]/sW(i,j), z_width); 64 | temp_nS = cross([s_xlen,s_ylen, 0]/sS(i,j), z_width); 65 | ``` 66 | 67 | ### Setting Freestream Conditions and Loop Variables 68 | Before the solution can be initialized, the freestream conditions need to be specified. The following freestream quantities are given: 69 | - Density: 1.2 kg/m2 70 | - Temperature: 300 K 71 | - Pressure: 100,000 Pa 72 | - Mach: 0.3, 0.7, 1.5 (depending on test case) 73 | 74 | After the freestream conditions are defined, the speed of sound is calculated and used to find the u and v velocities. The primitive state vector, V, contains the primitive variables of the solution: 75 | - ρ is the density 76 | - u is the velocity in the x-dir. 77 | - v is the velocity in the y-dir. 78 | - P is the pressure 79 | 80 | Also, several looping variable are set. The number of iterations and the frequency of text output can are defined. The user can choose between local and global timestepping. If global timestepping is chosen, then a global timestep must be set. If local timestepping is chosen, then a CFL number must be set. The user also has the ability to plot contours of the primitive variables, which are updated during each iteration (or at a specified frequency). 81 | 82 | This code employs the m-stage timestepping scheme, as outlined by Jameson. This allows the user to choose the order of the timestepping scheme. For example, if the order of the scheme is 1, then the forward Euler step is used. If the order of the scheme is 4, then a modified fourth-order Runge Kutta timestepping scheme is used. However, for non-linear equations, the modified fourth-order Runge Kutta scheme is only second-order accurate. The fourth-order scheme enables the user to use a higher CFL number and less iterations to achieve an accurate result. 83 | 84 | ### Initializing the Solution 85 | Each cell in the grid is assigned the freestream primitive state vector, which is then converted to the conservative state vector via a function. Also, the residual of the cell is initialized to 0. The V, U, and resid variables are cell arrays. This is accomplished using the following code: 86 | 87 | ```Matlab 88 | % Loop through all cells and init PSV to freestream conditions 89 | % Convert PSV to conservative state vector 90 | % Init residual to 0 91 | for i = 1:nci 92 | for j = 1:ncj 93 | V{i,j} = V_free; 94 | U{i,j} = convV_U(V{i,j}); 95 | resid{i,j} = [0 0 0 0]; 96 | end 97 | end 98 | ``` 99 | 100 | Please read the [technical brief](https://github.com/robojafar/euler_solver/blob/master/euler_solver.pdf) for further explanation of the code. GitHub markdown can only do so much. 101 | -------------------------------------------------------------------------------- /euler_solver.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/robojafar/euler_solver/e9b7f4874ad2303e8c4fb03a17b5d83d281ab349/euler_solver.pdf -------------------------------------------------------------------------------- /results/case_1/supersonic.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/robojafar/euler_solver/e9b7f4874ad2303e8c4fb03a17b5d83d281ab349/results/case_1/supersonic.png -------------------------------------------------------------------------------- /results/case_1/supersonic.txt: -------------------------------------------------------------------------------- 1 | Freestream Conditions: 2 | Mach: 1.50 3 | Flow AOA: 0.00 deg 4 | u Velocity: 512.35 m/s 5 | v Velocity: 0.00 m/s 6 | Pressure: 1.00e+005 Pa 7 | Temperature: 300.00 K 8 | Density: 1.20 kg/m^3 9 | 10 | Iteration Variables: 11 | Iterations: 1000 12 | CFL: 0.50 13 | M-Stage: 4 14 | Timestepping local 15 | 16 | 17 | Iter cont. resid x-mom resid y-mom resid energy resid Time left 18 | 10 4.52e-001 4.46e-001 1.20e+001 4.48e-001 68:28 19 | 20 3.95e-001 3.98e-001 9.08e+000 3.96e-001 67:00 20 | 30 3.25e-001 3.32e-001 7.15e+000 3.26e-001 65:49 21 | 40 2.74e-001 2.85e-001 6.14e+000 2.77e-001 66:23 22 | 50 2.44e-001 2.57e-001 5.35e+000 2.47e-001 64:42 23 | 60 2.22e-001 2.36e-001 4.74e+000 2.24e-001 63:47 24 | 70 2.06e-001 2.17e-001 4.22e+000 2.06e-001 64:19 25 | 80 1.94e-001 1.96e-001 3.70e+000 1.88e-001 62:25 26 | 90 1.85e-001 1.74e-001 3.06e+000 1.71e-001 61:30 27 | 100 1.82e-001 1.67e-001 2.36e+000 1.66e-001 61:46 28 | 110 1.75e-001 1.64e-001 2.04e+000 1.62e-001 60:23 29 | 120 1.57e-001 1.41e-001 2.24e+000 1.42e-001 59:43 30 | 130 1.34e-001 1.08e-001 2.49e+000 1.13e-001 59:15 31 | 140 1.16e-001 8.70e-002 2.51e+000 9.32e-002 58:21 32 | 150 1.06e-001 8.06e-002 2.34e+000 8.46e-002 59:00 33 | 160 9.98e-002 7.93e-002 2.08e+000 8.10e-002 57:00 34 | 170 9.38e-002 7.51e-002 1.87e+000 7.61e-002 56:06 35 | 180 8.54e-002 6.51e-002 1.80e+000 6.73e-002 55:38 36 | 190 7.70e-002 5.39e-002 1.80e+000 5.87e-002 55:10 37 | 200 7.30e-002 4.99e-002 1.73e+000 5.69e-002 54:17 38 | 210 7.38e-002 5.38e-002 1.57e+000 6.13e-002 53:36 39 | 220 7.57e-002 5.83e-002 1.36e+000 6.60e-002 52:55 40 | 230 7.58e-002 5.94e-002 1.15e+000 6.73e-002 52:27 41 | 240 7.35e-002 5.66e-002 9.94e-001 6.51e-002 51:34 42 | 250 6.95e-002 5.14e-002 8.87e-001 6.07e-002 50:53 43 | 260 6.46e-002 4.55e-002 8.14e-001 5.53e-002 50:01 44 | 270 5.99e-002 3.98e-002 7.57e-001 5.01e-002 49:43 45 | 280 5.56e-002 3.49e-002 7.04e-001 4.55e-002 48:51 46 | 290 5.19e-002 3.09e-002 6.53e-001 4.16e-002 48:10 47 | 300 4.87e-002 2.77e-002 6.02e-001 3.84e-002 47:30 48 | 310 4.61e-002 2.50e-002 5.52e-001 3.56e-002 46:49 49 | 320 4.37e-002 2.27e-002 5.03e-001 3.33e-002 46:08 50 | 330 4.17e-002 2.07e-002 4.57e-001 3.11e-002 45:17 51 | 340 4.00e-002 1.89e-002 4.12e-001 2.92e-002 44:36 52 | 350 3.84e-002 1.72e-002 3.69e-001 2.74e-002 43:56 53 | 360 3.70e-002 1.58e-002 3.28e-001 2.58e-002 43:25 54 | 370 3.58e-002 1.45e-002 2.89e-001 2.44e-002 42:45 55 | 380 3.47e-002 1.33e-002 2.53e-001 2.31e-002 42:14 56 | 390 3.37e-002 1.23e-002 2.19e-001 2.19e-002 41:23 57 | 400 3.28e-002 1.14e-002 1.87e-001 2.08e-002 40:14 58 | 410 3.20e-002 1.06e-002 1.59e-001 1.99e-002 39:53 59 | 420 3.13e-002 9.97e-003 1.33e-001 1.90e-002 39:21 60 | 430 3.06e-002 9.43e-003 1.11e-001 1.82e-002 38:49 61 | 440 2.99e-002 8.98e-003 9.26e-002 1.76e-002 38:08 62 | 450 2.93e-002 8.62e-003 7.92e-002 1.70e-002 37:19 63 | 460 2.87e-002 8.32e-003 7.13e-002 1.64e-002 36:38 64 | 470 2.81e-002 8.08e-003 6.88e-002 1.59e-002 35:57 65 | 480 2.74e-002 7.88e-003 7.09e-002 1.54e-002 35:25 66 | 490 2.68e-002 7.71e-003 7.59e-002 1.49e-002 34:28 67 | 500 2.62e-002 7.55e-003 8.23e-002 1.45e-002 33:55 68 | 510 2.55e-002 7.40e-003 8.91e-002 1.41e-002 33:22 69 | 520 2.49e-002 7.26e-003 9.56e-002 1.37e-002 32:34 70 | 530 2.42e-002 7.11e-003 1.02e-001 1.33e-002 31:46 71 | 540 2.35e-002 6.95e-003 1.07e-001 1.29e-002 31:05 72 | 550 2.28e-002 6.79e-003 1.11e-001 1.25e-002 30:32 73 | 560 2.21e-002 6.62e-003 1.15e-001 1.21e-002 29:37 74 | 570 2.14e-002 6.43e-003 1.17e-001 1.17e-002 29:04 75 | 580 2.07e-002 6.24e-003 1.19e-001 1.13e-002 28:23 76 | 590 2.00e-002 6.04e-003 1.20e-001 1.09e-002 27:49 77 | 600 1.92e-002 5.83e-003 1.20e-001 1.05e-002 27:14 78 | 610 1.85e-002 5.61e-003 1.20e-001 1.01e-002 26:21 79 | 620 1.78e-002 5.39e-003 1.19e-001 9.69e-003 25:59 80 | 630 1.71e-002 5.17e-003 1.17e-001 9.29e-003 25:12 81 | 640 1.64e-002 4.94e-003 1.15e-001 8.90e-003 24:20 82 | 650 1.57e-002 4.71e-003 1.13e-001 8.52e-003 23:45 83 | 660 1.50e-002 4.48e-003 1.10e-001 8.15e-003 23:41 84 | 670 1.43e-002 4.26e-003 1.07e-001 7.78e-003 22:23 85 | 680 1.36e-002 4.04e-003 1.04e-001 7.41e-003 21:47 86 | 690 1.30e-002 3.82e-003 1.00e-001 7.06e-003 20:57 87 | 700 1.24e-002 3.60e-003 9.68e-002 6.72e-003 20:26 88 | 710 1.18e-002 3.40e-003 9.31e-002 6.38e-003 19:40 89 | 720 1.12e-002 3.20e-003 8.93e-002 6.06e-003 18:55 90 | 730 1.06e-002 3.00e-003 8.54e-002 5.74e-003 18:15 91 | 740 1.00e-002 2.81e-003 8.15e-002 5.44e-003 17:38 92 | 750 9.48e-003 2.64e-003 7.77e-002 5.15e-003 16:54 93 | 760 8.96e-003 2.46e-003 7.39e-002 4.87e-003 16:17 94 | 770 8.46e-003 2.30e-003 7.01e-002 4.59e-003 15:40 95 | 780 7.98e-003 2.14e-003 6.64e-002 4.33e-003 14:55 96 | 790 7.52e-003 2.00e-003 6.28e-002 4.08e-003 14:21 97 | 800 7.07e-003 1.86e-003 5.92e-002 3.84e-003 13:37 98 | 810 6.65e-003 1.73e-003 5.58e-002 3.62e-003 12:53 99 | 820 6.25e-003 1.60e-003 5.25e-002 3.40e-003 12:12 100 | 830 5.86e-003 1.48e-003 4.93e-002 3.19e-003 11:29 101 | 840 5.49e-003 1.37e-003 4.62e-002 2.99e-003 10:51 102 | 850 5.14e-003 1.27e-003 4.33e-002 2.80e-003 10:10 103 | 860 4.81e-003 1.18e-003 4.05e-002 2.62e-003 9:30 104 | 870 4.49e-003 1.09e-003 3.78e-002 2.45e-003 11:21 105 | 880 4.19e-003 1.00e-003 3.52e-002 2.29e-003 8:10 106 | 890 3.91e-003 9.23e-004 3.28e-002 2.14e-003 7:27 107 | 900 3.64e-003 8.50e-004 3.05e-002 1.99e-003 6:48 108 | 910 3.39e-003 7.83e-004 2.83e-002 1.85e-003 6:06 109 | 920 3.15e-003 7.20e-004 2.62e-002 1.72e-003 5:25 110 | 930 2.92e-003 6.62e-004 2.43e-002 1.60e-003 4:46 111 | 940 2.71e-003 6.08e-004 2.25e-002 1.49e-003 4:04 112 | 950 2.51e-003 5.58e-004 2.08e-002 1.38e-003 3:23 113 | 960 2.32e-003 5.11e-004 1.92e-002 1.28e-003 2:42 114 | 970 2.15e-003 4.69e-004 1.77e-002 1.18e-003 2:02 115 | 980 1.98e-003 4.29e-004 1.62e-002 1.09e-003 1:21 116 | 990 1.83e-003 3.93e-004 1.49e-002 1.01e-003 0:40 117 | 1000 1.68e-003 3.59e-004 1.37e-002 9.30e-004 0:00 118 | Elapsed time is 4096.290953 seconds. 119 | -------------------------------------------------------------------------------- /results/case_2/transonic.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/robojafar/euler_solver/e9b7f4874ad2303e8c4fb03a17b5d83d281ab349/results/case_2/transonic.png -------------------------------------------------------------------------------- /results/case_2/transonic.txt: -------------------------------------------------------------------------------- 1 | Freestream Conditions: 2 | Mach: 0.70 3 | Flow AOA: 0.00 deg 4 | u Velocity: 239.10 m/s 5 | v Velocity: 0.00 m/s 6 | Pressure: 1.00e+005 Pa 7 | Temperature: 300.00 K 8 | Density: 1.20 kg/m^3 9 | 10 | Iteration Variables: 11 | Iterations: 1000 12 | CFL: 0.50 13 | M-Stage: 4 14 | Timestepping local 15 | 16 | 17 | Iter cont. resid x-mom resid y-mom resid energy resid Time left 18 | 10 4.20e-001 4.82e-001 7.90e+000 4.22e-001 53:32 19 | 20 3.46e-001 4.09e-001 5.24e+000 3.47e-001 52:44 20 | 30 2.78e-001 3.64e-001 4.24e+000 2.80e-001 52:12 21 | 40 2.42e-001 3.44e-001 3.56e+000 2.44e-001 51:40 22 | 50 2.20e-001 3.31e-001 3.04e+000 2.21e-001 51:07 23 | 60 2.14e-001 3.23e-001 2.49e+000 2.13e-001 50:35 24 | 70 2.23e-001 3.11e-001 1.71e+000 2.18e-001 50:17 25 | 80 2.16e-001 2.77e-001 1.14e+000 2.05e-001 50:42 26 | 90 1.95e-001 2.52e-001 1.44e+000 1.83e-001 49:12 27 | 100 1.83e-001 2.36e-001 1.60e+000 1.71e-001 48:26 28 | 110 1.73e-001 1.97e-001 1.50e+000 1.56e-001 47:54 29 | 120 1.62e-001 1.59e-001 1.40e+000 1.41e-001 47:21 30 | 130 1.51e-001 1.35e-001 1.36e+000 1.28e-001 47:02 31 | 140 1.44e-001 1.22e-001 1.32e+000 1.19e-001 46:17 32 | 150 1.44e-001 1.26e-001 1.14e+000 1.19e-001 45:44 33 | 160 1.45e-001 1.38e-001 8.54e-001 1.22e-001 45:12 34 | 170 1.42e-001 1.47e-001 6.83e-001 1.20e-001 44:53 35 | 180 1.34e-001 1.50e-001 7.52e-001 1.11e-001 44:07 36 | 190 1.26e-001 1.54e-001 8.97e-001 1.03e-001 43:23 37 | 200 1.21e-001 1.63e-001 1.02e+000 9.93e-002 43:03 38 | 210 1.19e-001 1.75e-001 1.11e+000 1.00e-001 42:55 39 | 220 1.19e-001 1.85e-001 1.18e+000 1.02e-001 41:58 40 | 230 1.18e-001 1.93e-001 1.22e+000 1.03e-001 41:26 41 | 240 1.19e-001 1.98e-001 1.19e+000 1.06e-001 40:54 42 | 250 1.23e-001 2.04e-001 1.08e+000 1.11e-001 41:20 43 | 260 1.28e-001 2.12e-001 8.98e-001 1.18e-001 39:49 44 | 270 1.34e-001 2.22e-001 6.83e-001 1.26e-001 39:05 45 | 280 1.40e-001 2.32e-001 5.12e-001 1.33e-001 38:33 46 | 290 1.44e-001 2.42e-001 4.71e-001 1.40e-001 38:01 47 | 300 1.49e-001 2.50e-001 5.42e-001 1.46e-001 37:40 48 | 310 1.53e-001 2.55e-001 6.26e-001 1.53e-001 36:57 49 | 320 1.57e-001 2.56e-001 6.67e-001 1.59e-001 36:25 50 | 330 1.60e-001 2.54e-001 6.56e-001 1.63e-001 36:03 51 | 340 1.61e-001 2.49e-001 6.13e-001 1.64e-001 35:10 52 | 350 1.58e-001 2.42e-001 5.67e-001 1.62e-001 34:48 53 | 360 1.52e-001 2.35e-001 5.44e-001 1.55e-001 34:26 54 | 370 1.44e-001 2.26e-001 5.44e-001 1.47e-001 33:44 55 | 380 1.34e-001 2.17e-001 5.57e-001 1.36e-001 33:12 56 | 390 1.23e-001 2.07e-001 5.64e-001 1.24e-001 32:40 57 | 400 1.13e-001 1.97e-001 5.63e-001 1.12e-001 32:17 58 | 410 1.03e-001 1.88e-001 5.75e-001 1.01e-001 31:36 59 | 420 9.27e-002 1.79e-001 5.94e-001 8.91e-002 31:58 60 | 430 8.33e-002 1.72e-001 6.42e-001 7.83e-002 30:31 61 | 440 7.63e-002 1.66e-001 6.97e-001 6.91e-002 32:45 62 | 450 7.39e-002 1.63e-001 7.37e-001 6.30e-002 29:27 63 | 460 7.75e-002 1.63e-001 7.43e-001 6.16e-002 28:46 64 | 470 8.60e-002 1.63e-001 7.05e-001 6.52e-002 28:31 65 | 480 9.86e-002 1.59e-001 6.39e-001 7.38e-002 27:51 66 | 490 9.90e-002 1.58e-001 6.63e-001 7.56e-002 27:18 67 | 500 8.06e-002 1.60e-001 5.00e-001 6.63e-002 26:46 68 | 510 7.33e-002 1.63e-001 4.20e-001 6.39e-002 26:14 69 | 520 7.29e-002 1.67e-001 3.94e-001 6.55e-002 25:42 70 | 530 7.51e-002 1.74e-001 3.77e-001 6.87e-002 25:03 71 | 540 8.46e-002 1.81e-001 3.67e-001 7.55e-002 24:38 72 | 550 9.56e-002 1.79e-001 3.70e-001 8.41e-002 24:13 73 | 560 9.93e-002 1.78e-001 4.95e-001 8.84e-002 23:40 74 | 570 8.37e-002 1.77e-001 4.20e-001 8.19e-002 23:01 75 | 580 7.55e-002 1.73e-001 3.86e-001 7.83e-002 22:36 76 | 590 7.23e-002 1.69e-001 3.61e-001 7.63e-002 22:29 77 | 600 7.31e-002 1.63e-001 3.33e-001 7.55e-002 21:37 78 | 610 8.64e-002 1.60e-001 3.00e-001 8.00e-002 20:53 79 | 620 7.74e-002 1.48e-001 3.61e-001 7.52e-002 20:27 80 | 630 6.78e-002 1.41e-001 3.13e-001 6.93e-002 19:54 81 | 640 6.17e-002 1.35e-001 2.72e-001 6.52e-002 19:22 82 | 650 5.78e-002 1.28e-001 2.44e-001 6.19e-002 18:50 83 | 660 5.62e-002 1.22e-001 2.19e-001 5.98e-002 18:17 84 | 670 5.63e-002 1.17e-001 2.01e-001 5.85e-002 17:45 85 | 680 5.70e-002 1.11e-001 2.20e-001 5.78e-002 17:13 86 | 690 5.28e-002 1.06e-001 2.00e-001 5.49e-002 16:45 87 | 700 4.94e-002 1.01e-001 1.81e-001 5.22e-002 16:08 88 | 710 4.67e-002 9.58e-002 1.67e-001 4.98e-002 15:36 89 | 720 4.44e-002 9.06e-002 1.55e-001 4.75e-002 14:59 90 | 730 4.24e-002 8.53e-002 1.43e-001 4.53e-002 14:36 91 | 740 4.05e-002 8.01e-002 1.33e-001 4.30e-002 14:11 92 | 750 3.90e-002 7.50e-002 1.24e-001 4.09e-002 13:27 93 | 760 3.72e-002 6.99e-002 1.15e-001 3.86e-002 12:55 94 | 770 3.58e-002 6.50e-002 1.09e-001 3.65e-002 12:22 95 | 780 3.44e-002 6.03e-002 1.08e-001 3.44e-002 11:50 96 | 790 3.24e-002 5.59e-002 9.98e-002 3.21e-002 11:14 97 | 800 3.07e-002 5.19e-002 9.40e-002 2.99e-002 10:45 98 | 810 2.91e-002 4.83e-002 9.05e-002 2.78e-002 10:13 99 | 820 2.76e-002 4.50e-002 8.92e-002 2.58e-002 9:41 100 | 830 2.62e-002 4.21e-002 8.97e-002 2.39e-002 9:11 101 | 840 2.50e-002 3.96e-002 9.16e-002 2.21e-002 8:36 102 | 850 2.39e-002 3.76e-002 9.43e-002 2.05e-002 8:06 103 | 860 2.29e-002 3.60e-002 9.71e-002 1.90e-002 7:32 104 | 870 2.21e-002 3.49e-002 9.94e-002 1.77e-002 6:59 105 | 880 2.14e-002 3.43e-002 1.01e-001 1.65e-002 6:25 106 | 890 2.09e-002 3.42e-002 1.01e-001 1.57e-002 5:53 107 | 900 2.06e-002 3.45e-002 1.01e-001 1.51e-002 5:21 108 | 910 2.05e-002 3.52e-002 9.96e-002 1.49e-002 4:59 109 | 920 2.05e-002 3.62e-002 9.77e-002 1.49e-002 4:18 110 | 930 2.07e-002 3.74e-002 9.52e-002 1.53e-002 3:46 111 | 940 2.10e-002 3.87e-002 9.27e-002 1.59e-002 3:12 112 | 950 2.14e-002 4.02e-002 9.01e-002 1.66e-002 2:42 113 | 960 2.17e-002 4.16e-002 8.81e-002 1.74e-002 2:08 114 | 970 2.21e-002 4.30e-002 8.64e-002 1.83e-002 1:36 115 | 980 2.26e-002 4.42e-002 8.50e-002 1.92e-002 1:04 116 | 990 2.29e-002 4.53e-002 8.34e-002 2.00e-002 0:32 117 | 1000 2.33e-002 4.62e-002 8.24e-002 2.08e-002 0:00 118 | Elapsed time is 3236.847991 seconds. 119 | -------------------------------------------------------------------------------- /results/case_3/subsonic.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/robojafar/euler_solver/e9b7f4874ad2303e8c4fb03a17b5d83d281ab349/results/case_3/subsonic.png -------------------------------------------------------------------------------- /results/case_3/subsonic.txt: -------------------------------------------------------------------------------- 1 | Freestream Conditions: 2 | Mach: 0.30 3 | Flow AOA: 0.00 deg 4 | u Velocity: 102.47 m/s 5 | v Velocity: 0.00 m/s 6 | Pressure: 1.00e+005 Pa 7 | Temperature: 300.00 K 8 | Density: 1.20 kg/m^3 9 | 10 | Iteration Variables: 11 | Iterations: 1000 12 | CFL: 0.50 13 | M-Stage: 4 14 | Timestepping local 15 | 16 | 17 | Iter cont. resid x-mom resid y-mom resid energy resid Time left 18 | 10 4.16e-001 7.67e-001 5.37e+000 4.17e-001 75:40 19 | 20 2.97e-001 6.81e-001 3.59e+000 2.98e-001 74:54 20 | 30 2.42e-001 6.74e-001 2.80e+000 2.43e-001 74:08 21 | 40 2.13e-001 6.82e-001 2.27e+000 2.14e-001 73:22 22 | 50 2.20e-001 6.77e-001 1.73e+000 2.21e-001 72:37 23 | 60 2.37e-001 6.71e-001 7.73e-001 2.37e-001 71:51 24 | 70 2.02e-001 6.32e-001 8.85e-001 2.00e-001 71:05 25 | 80 1.80e-001 5.69e-001 1.03e+000 1.76e-001 70:33 26 | 90 1.72e-001 5.92e-001 8.56e-001 1.68e-001 68:51 27 | 100 1.58e-001 6.03e-001 8.44e-001 1.55e-001 69:01 28 | 110 1.57e-001 5.49e-001 8.35e-001 1.54e-001 68:29 29 | 120 1.56e-001 4.68e-001 8.78e-001 1.54e-001 67:29 30 | 130 1.44e-001 3.95e-001 1.01e+000 1.42e-001 66:57 31 | 140 1.34e-001 3.46e-001 1.04e+000 1.31e-001 65:44 32 | 150 1.35e-001 3.16e-001 8.60e-001 1.33e-001 65:11 33 | 160 1.43e-001 2.94e-001 5.14e-001 1.42e-001 63:59 34 | 170 1.41e-001 2.73e-001 4.80e-001 1.39e-001 63:13 35 | 180 1.22e-001 2.58e-001 8.29e-001 1.20e-001 62:40 36 | 190 9.24e-002 2.64e-001 1.08e+000 9.00e-002 61:55 37 | 200 6.48e-002 2.90e-001 1.16e+000 6.21e-002 61:09 38 | 210 5.64e-002 3.25e-001 1.06e+000 5.45e-002 60:35 39 | 220 7.04e-002 3.57e-001 8.10e-001 6.97e-002 59:37 40 | 230 8.52e-002 3.79e-001 4.63e-001 8.53e-002 58:39 41 | 240 9.12e-002 3.90e-001 1.60e-001 9.21e-002 59:04 42 | 250 9.08e-002 3.87e-001 2.45e-001 9.28e-002 57:19 43 | 260 8.91e-002 3.71e-001 4.00e-001 9.24e-002 56:45 44 | 270 8.93e-002 3.43e-001 4.50e-001 9.35e-002 55:59 45 | 280 9.08e-002 3.13e-001 3.96e-001 9.56e-002 59:09 46 | 290 9.03e-002 2.90e-001 3.02e-001 9.55e-002 54:27 47 | 300 8.46e-002 2.80e-001 3.22e-001 9.02e-002 54:57 48 | 310 7.34e-002 2.79e-001 4.46e-001 7.96e-002 52:44 49 | 320 6.09e-002 2.81e-001 5.36e-001 6.76e-002 52:51 50 | 330 5.42e-002 2.81e-001 5.33e-001 6.07e-002 51:12 51 | 340 5.62e-002 2.76e-001 4.38e-001 6.17e-002 50:16 52 | 350 6.12e-002 2.66e-001 3.06e-001 6.60e-002 49:51 53 | 360 6.31e-002 2.53e-001 2.66e-001 6.77e-002 49:35 54 | 370 6.00e-002 2.36e-001 3.64e-001 6.48e-002 48:09 55 | 380 5.39e-002 2.15e-001 4.61e-001 5.90e-002 47:23 56 | 390 4.88e-002 1.91e-001 4.86e-001 5.37e-002 46:37 57 | 400 4.65e-002 1.65e-001 4.27e-001 5.05e-002 45:51 58 | 410 4.55e-002 1.39e-001 3.01e-001 4.82e-002 47:24 59 | 420 4.27e-002 1.16e-001 1.50e-001 4.43e-002 44:29 60 | 430 3.70e-002 1.00e-001 8.83e-002 3.78e-002 43:43 61 | 440 2.97e-002 9.33e-002 1.77e-001 3.03e-002 42:48 62 | 450 2.42e-002 9.47e-002 2.38e-001 2.54e-002 42:02 63 | 460 2.36e-002 9.93e-002 2.44e-001 2.56e-002 41:16 64 | 470 2.59e-002 1.02e-001 2.05e-001 2.82e-002 43:40 65 | 480 2.72e-002 1.01e-001 1.46e-001 2.94e-002 39:44 66 | 490 2.59e-002 9.56e-002 1.08e-001 2.77e-002 38:51 67 | 500 2.23e-002 8.60e-002 1.15e-001 2.36e-002 38:13 68 | 510 1.82e-002 7.46e-002 1.32e-001 1.88e-002 37:27 69 | 520 1.56e-002 6.40e-002 1.29e-001 1.54e-002 36:41 70 | 530 1.50e-002 5.62e-002 1.06e-001 1.44e-002 35:55 71 | 540 1.53e-002 5.18e-002 7.62e-002 1.47e-002 35:02 72 | 550 1.54e-002 4.93e-002 6.71e-002 1.48e-002 34:30 73 | 560 1.48e-002 4.67e-002 8.47e-002 1.45e-002 33:38 74 | 570 1.40e-002 4.30e-002 1.04e-001 1.39e-002 32:58 75 | 580 1.33e-002 3.88e-002 1.12e-001 1.33e-002 32:06 76 | 590 1.28e-002 3.54e-002 1.07e-001 1.29e-002 31:26 77 | 600 1.23e-002 3.41e-002 9.00e-002 1.24e-002 30:47 78 | 610 1.19e-002 3.50e-002 6.38e-002 1.20e-002 29:36 79 | 620 1.16e-002 3.67e-002 3.43e-002 1.17e-002 29:08 80 | 630 1.11e-002 3.78e-002 2.89e-002 1.13e-002 28:16 81 | 640 1.02e-002 3.77e-002 5.77e-002 1.05e-002 27:31 82 | 650 8.93e-003 3.64e-002 8.59e-002 9.39e-003 26:50 83 | 660 7.57e-003 3.44e-002 1.03e-001 8.21e-003 26:04 84 | 670 6.97e-003 3.24e-002 1.05e-001 7.71e-003 25:13 85 | 680 7.49e-003 3.06e-002 9.14e-002 8.14e-003 24:27 86 | 690 8.37e-003 2.88e-002 6.57e-002 8.86e-003 23:41 87 | 700 8.71e-003 2.70e-002 3.69e-002 9.06e-003 22:55 88 | 710 8.16e-003 2.49e-002 2.86e-002 8.42e-003 22:05 89 | 720 6.99e-003 2.26e-002 4.59e-002 7.21e-003 21:32 90 | 730 6.04e-003 2.04e-002 5.91e-002 6.27e-003 20:42 91 | 740 6.13e-003 1.83e-002 6.02e-002 6.39e-003 19:52 92 | 750 6.95e-003 1.69e-002 5.06e-002 7.21e-003 19:10 93 | 760 7.50e-003 1.66e-002 3.73e-002 7.74e-003 18:20 94 | 770 7.24e-003 1.72e-002 3.31e-002 7.44e-003 17:38 95 | 780 6.20e-003 1.85e-002 4.05e-002 6.33e-003 16:49 96 | 790 4.93e-003 1.97e-002 4.65e-002 4.98e-003 16:03 97 | 800 4.41e-003 2.04e-002 4.35e-002 4.37e-003 15:17 98 | 810 4.95e-003 2.01e-002 3.07e-002 4.89e-003 14:43 99 | 820 5.66e-003 1.91e-002 1.23e-002 5.61e-003 13:45 100 | 830 5.77e-003 1.74e-002 1.72e-002 5.75e-003 13:12 101 | 840 5.12e-003 1.55e-002 3.68e-002 5.12e-003 12:16 102 | 850 4.01e-003 1.36e-002 5.02e-002 4.03e-003 11:46 103 | 860 3.19e-003 1.20e-002 5.36e-002 3.21e-003 10:44 104 | 870 3.39e-003 1.10e-002 4.65e-002 3.40e-003 9:58 105 | 880 4.08e-003 1.05e-002 3.10e-002 4.08e-003 9:14 106 | 890 4.43e-003 1.03e-002 1.19e-002 4.43e-003 8:27 107 | 900 4.14e-003 1.02e-002 1.30e-002 4.14e-003 7:41 108 | 910 3.30e-003 1.03e-002 2.85e-002 3.34e-003 6:52 109 | 920 2.42e-003 1.04e-002 3.76e-002 2.56e-003 6:08 110 | 930 2.30e-003 1.07e-002 3.84e-002 2.54e-003 5:23 111 | 940 2.92e-003 1.10e-002 3.18e-002 3.18e-003 4:37 112 | 950 3.45e-003 1.12e-002 2.08e-002 3.68e-003 3:50 113 | 960 3.48e-003 1.10e-002 1.27e-002 3.69e-003 3:04 114 | 970 2.98e-003 1.05e-002 1.66e-002 3.16e-003 2:17 115 | 980 2.18e-003 9.71e-003 2.30e-002 2.34e-003 1:32 116 | 990 1.61e-003 8.70e-003 2.49e-002 1.74e-003 0:46 117 | 1000 1.81e-003 7.62e-003 2.11e-002 1.88e-003 0:00 118 | Elapsed time is 4609.065844 seconds. 119 | -------------------------------------------------------------------------------- /results/disturb_sub/dist_sub.txt: -------------------------------------------------------------------------------- 1 | Freestream Conditions: 2 | Mach: 0.30 3 | Flow AOA: 0.00 deg 4 | u Velocity: 102.47 m/s 5 | v Velocity: 0.00 m/s 6 | Pressure: 1.00e+005 Pa 7 | Temperature: 300.00 K 8 | Density: 1.20 kg/m^3 9 | 10 | Iteration Variables: 11 | Iterations: 1000 12 | CFL: 0.50 13 | M-Stage: 4 14 | Timestepping local 15 | 16 | 17 | Iter cont. resid x-mom resid y-mom resid energy resid Time left 18 | 10 1.56e-001 9.77e-002 1.02e-001 3.57e-002 8:45 19 | 20 7.63e-002 4.01e-002 2.94e-002 1.94e-002 8:24 20 | 30 3.47e-002 1.96e-002 2.25e-002 1.08e-002 8:04 21 | 40 2.45e-002 1.22e-002 1.47e-002 6.54e-003 7:44 22 | 50 2.11e-002 1.29e-002 7.13e-003 5.72e-003 7:39 23 | 60 1.95e-002 1.11e-002 2.82e-003 6.37e-003 7:34 24 | 70 1.22e-002 1.56e-002 3.53e-003 4.20e-003 7:44 25 | 80 3.83e-003 1.85e-002 2.87e-003 1.41e-003 7:53 26 | 90 8.87e-003 1.63e-002 9.54e-004 2.34e-003 7:34 27 | 100 1.19e-002 1.30e-002 2.33e-003 2.99e-003 7:15 28 | 110 1.21e-002 1.30e-002 1.07e-003 2.78e-003 7:24 29 | 120 1.18e-002 1.50e-002 8.57e-004 2.72e-003 7:19 30 | 130 1.39e-002 1.58e-002 7.33e-004 4.00e-003 7:14 31 | 140 1.72e-002 1.45e-002 5.28e-004 5.58e-003 6:55 32 | 150 1.92e-002 1.19e-002 8.65e-004 6.49e-003 7:04 33 | 160 1.87e-002 9.06e-003 3.59e-004 6.40e-003 6:46 34 | 170 1.60e-002 7.44e-003 2.68e-004 5.42e-003 6:54 35 | 180 1.17e-002 7.69e-003 2.84e-004 3.88e-003 7:02 36 | 190 7.23e-003 9.17e-003 1.20e-004 2.22e-003 6:31 37 | 200 3.71e-003 1.08e-002 2.66e-004 9.89e-004 6:39 38 | 210 3.06e-003 1.20e-002 1.26e-004 1.17e-003 6:22 39 | 220 4.27e-003 1.23e-002 9.40e-005 1.78e-003 6:29 40 | 230 5.11e-003 1.19e-002 1.19e-004 2.11e-003 6:12 41 | 240 5.33e-003 1.09e-002 2.67e-005 2.17e-003 6:19 42 | 250 5.08e-003 9.56e-003 8.75e-005 2.05e-003 6:14 43 | 260 4.60e-003 8.12e-003 5.00e-005 1.83e-003 6:09 44 | 270 4.02e-003 6.73e-003 3.17e-005 1.58e-003 6:38 45 | 280 3.45e-003 5.49e-003 4.71e-005 1.34e-003 5:48 46 | 290 2.94e-003 4.42e-003 9.51e-006 1.13e-003 5:43 47 | 300 2.48e-003 3.50e-003 3.00e-005 9.39e-004 5:38 48 | 310 2.08e-003 2.73e-003 2.00e-005 7.78e-004 5:33 49 | 320 1.72e-003 2.07e-003 1.02e-005 6.37e-004 5:39 50 | 330 1.40e-003 1.53e-003 1.78e-005 5.14e-004 5:34 51 | 340 1.12e-003 1.07e-003 4.40e-006 4.07e-004 5:19 52 | 350 8.68e-004 7.10e-004 1.03e-005 3.15e-004 5:14 53 | 360 6.51e-004 4.34e-004 7.89e-006 2.35e-004 5:09 54 | 370 4.63e-004 2.55e-004 3.13e-006 1.67e-004 5:04 55 | 380 3.03e-004 2.06e-004 6.57e-006 1.09e-004 4:59 56 | 390 1.70e-004 2.52e-004 2.04e-006 6.06e-005 5:04 57 | 400 7.91e-005 3.08e-004 3.48e-006 2.39e-005 4:50 58 | 410 8.66e-005 3.44e-004 3.09e-006 2.36e-005 4:54 59 | 420 1.43e-004 3.58e-004 9.28e-007 4.53e-005 4:49 60 | 430 1.88e-004 3.50e-004 2.38e-006 6.23e-005 4:44 61 | 440 2.17e-004 3.24e-004 9.15e-007 7.27e-005 4:30 62 | 450 2.28e-004 2.86e-004 1.16e-006 7.67e-005 4:25 63 | 460 2.24e-004 2.39e-004 1.19e-006 7.53e-005 4:21 64 | 470 2.09e-004 1.88e-004 2.78e-007 6.96e-005 4:24 65 | 480 1.86e-004 1.38e-004 8.56e-007 6.11e-005 4:19 66 | 490 1.58e-004 9.18e-005 3.96e-007 5.10e-005 4:06 67 | 500 1.28e-004 5.56e-005 3.78e-007 4.02e-005 4:09 68 | 510 9.90e-005 4.04e-005 4.55e-007 2.97e-005 4:04 69 | 520 7.20e-005 5.04e-005 9.40e-008 2.01e-005 3:59 70 | 530 4.86e-005 6.71e-005 3.04e-007 1.19e-005 3:54 71 | 540 3.02e-005 8.10e-005 1.66e-007 5.83e-006 3:42 72 | 550 1.93e-005 9.01e-005 1.20e-007 4.82e-006 3:44 73 | 560 1.91e-005 9.46e-005 1.71e-007 7.79e-006 3:32 74 | 570 2.44e-005 9.51e-005 3.82e-008 1.06e-005 3:27 75 | 580 2.96e-005 9.23e-005 1.06e-007 1.26e-005 3:29 76 | 590 3.31e-005 8.70e-005 6.79e-008 1.37e-005 3:24 77 | 600 3.48e-005 8.00e-005 3.71e-008 1.41e-005 3:19 78 | 610 3.50e-005 7.19e-005 6.38e-008 1.39e-005 3:08 79 | 620 3.40e-005 6.31e-005 1.72e-008 1.33e-005 3:09 80 | 630 3.19e-005 5.43e-005 3.68e-008 1.24e-005 3:04 81 | 640 2.92e-005 4.56e-005 2.72e-008 1.12e-005 2:54 82 | 650 2.61e-005 3.75e-005 1.10e-008 9.89e-006 2:54 83 | 660 2.27e-005 3.00e-005 2.35e-008 8.54e-006 2:49 84 | 670 1.92e-005 2.33e-005 7.80e-009 7.19e-006 2:39 85 | 680 1.59e-005 1.74e-005 1.26e-008 5.89e-006 2:39 86 | 690 1.27e-005 1.24e-005 1.07e-008 4.68e-006 2:34 87 | 700 9.73e-006 8.36e-006 3.12e-009 3.58e-006 2:29 88 | 710 7.12e-006 5.23e-006 8.55e-009 2.61e-006 2:20 89 | 720 4.87e-006 3.16e-006 3.45e-009 1.77e-006 2:19 90 | 730 3.00e-006 2.45e-006 4.24e-009 1.08e-006 2:10 91 | 740 1.54e-006 2.77e-006 4.16e-009 5.34e-007 2:09 92 | 750 7.46e-007 3.25e-006 8.55e-010 2.01e-007 2:04 93 | 760 1.06e-006 3.54e-006 3.08e-009 3.25e-007 1:59 94 | 770 1.57e-006 3.58e-006 1.48e-009 5.22e-007 1:51 95 | 780 1.93e-006 3.42e-006 1.41e-009 6.51e-007 1:49 96 | 790 2.11e-006 3.11e-006 1.59e-009 7.14e-007 1:44 97 | 800 2.15e-006 2.69e-006 2.55e-010 7.24e-007 1:36 98 | 810 2.07e-006 2.22e-006 1.09e-009 6.93e-007 1:34 99 | 820 1.91e-006 1.73e-006 6.21e-010 6.32e-007 1:27 100 | 830 1.70e-006 1.26e-006 4.61e-010 5.52e-007 1:22 101 | 840 1.45e-006 8.39e-007 6.02e-010 4.63e-007 1:19 102 | 850 1.19e-006 5.01e-007 1.02e-010 3.70e-007 1:14 103 | 860 9.38e-007 3.47e-007 3.85e-010 2.79e-007 1:07 104 | 870 7.00e-007 4.36e-007 2.54e-010 1.96e-007 1:02 105 | 880 4.89e-007 5.95e-007 1.50e-010 1.22e-007 0:59 106 | 890 3.15e-007 7.32e-007 2.25e-010 6.35e-008 0:53 107 | 900 1.97e-007 8.26e-007 4.95e-011 4.07e-008 0:49 108 | 910 1.69e-007 8.78e-007 1.34e-010 6.36e-008 0:43 109 | 920 2.11e-007 8.92e-007 1.02e-010 9.14e-008 0:39 110 | 930 2.63e-007 8.75e-007 4.91e-011 1.12e-007 0:34 111 | 940 3.02e-007 8.32e-007 8.35e-011 1.26e-007 0:29 112 | 950 3.25e-007 7.72e-007 2.40e-011 1.32e-007 0:24 113 | 960 3.32e-007 6.98e-007 4.60e-011 1.32e-007 0:19 114 | 970 3.26e-007 6.18e-007 4.05e-011 1.28e-007 0:14 115 | 980 3.09e-007 5.34e-007 1.66e-011 1.20e-007 0:09 116 | 990 2.85e-007 4.52e-007 3.07e-011 1.09e-007 0:04 117 | 1000 2.56e-007 3.73e-007 1.11e-011 9.72e-008 0:00 118 | Elapsed time is 518.061816 seconds. 119 | -------------------------------------------------------------------------------- /results/disturb_sup/dist_sup.txt: -------------------------------------------------------------------------------- 1 | Freestream Conditions: 2 | Mach: 1.50 3 | Flow AOA: 0.00 deg 4 | u Velocity: 512.35 m/s 5 | v Velocity: 0.00 m/s 6 | Pressure: 1.00e+005 Pa 7 | Temperature: 300.00 K 8 | Density: 1.20 kg/m^3 9 | 10 | Iteration Variables: 11 | Iterations: 500 12 | CFL: 0.50 13 | M-Stage: 4 14 | Timestepping local 15 | 16 | 17 | Iter cont. resid x-mom resid y-mom resid energy resid Time left 18 | 10 5.15e-001 2.27e-001 1.33e-001 6.10e-002 3:41 19 | 20 3.13e-001 1.32e-001 7.40e-002 3.35e-002 3:29 20 | 30 2.07e-001 8.38e-002 4.81e-002 2.11e-002 3:25 21 | 40 1.37e-001 5.26e-002 2.08e-002 1.40e-002 3:20 22 | 50 7.50e-002 2.43e-002 2.30e-002 4.77e-003 3:16 23 | 60 5.55e-002 1.79e-002 4.78e-003 3.85e-003 3:05 24 | 70 3.80e-002 1.14e-002 3.25e-003 2.67e-003 3:14 25 | 80 2.48e-002 5.78e-003 2.19e-003 2.02e-003 3:03 26 | 90 1.85e-002 3.05e-003 1.06e-003 1.66e-003 3:05 27 | 100 1.55e-002 2.12e-003 6.17e-004 1.44e-003 3:00 28 | 110 1.34e-002 1.74e-003 4.17e-004 1.26e-003 2:50 29 | 120 1.16e-002 1.49e-003 2.84e-004 1.09e-003 2:51 30 | 130 1.01e-002 1.29e-003 1.90e-004 9.53e-004 2:41 31 | 140 9.03e-003 1.15e-003 1.24e-004 8.51e-004 2:37 32 | 150 8.39e-003 1.07e-003 7.83e-005 7.90e-004 2:38 33 | 160 7.98e-003 1.02e-003 4.81e-005 7.51e-004 2:28 34 | 170 7.52e-003 9.59e-004 2.86e-005 7.08e-004 2:29 35 | 180 6.87e-003 8.76e-004 1.64e-005 6.46e-004 2:19 36 | 190 6.02e-003 7.68e-004 9.12e-006 5.67e-004 2:15 37 | 200 5.05e-003 6.45e-004 4.88e-006 4.76e-004 2:11 38 | 210 4.07e-003 5.20e-004 2.52e-006 3.83e-004 2:02 39 | 220 3.16e-003 4.03e-004 1.25e-006 2.97e-004 2:02 40 | 230 2.36e-003 3.01e-004 5.96e-007 2.22e-004 2:02 41 | 240 1.71e-003 2.18e-004 2.74e-007 1.61e-004 1:57 42 | 250 1.20e-003 1.53e-004 1.23e-007 1.13e-004 1:53 43 | 260 8.22e-004 1.05e-004 5.59e-008 7.74e-005 1:48 44 | 270 5.49e-004 7.00e-005 2.75e-008 5.17e-005 1:40 45 | 280 3.58e-004 4.57e-005 1.53e-008 3.37e-005 1:39 46 | 290 2.28e-004 2.91e-005 9.09e-009 2.15e-005 1:31 47 | 300 1.43e-004 1.82e-005 5.47e-009 1.35e-005 1:24 48 | 310 8.78e-005 1.12e-005 3.22e-009 8.26e-006 1:22 49 | 320 5.30e-005 6.77e-006 1.84e-009 4.99e-006 1:18 50 | 330 3.15e-005 4.02e-006 1.02e-009 2.97e-006 1:14 51 | 340 1.84e-005 2.36e-006 5.53e-010 1.74e-006 1:12 52 | 350 1.06e-005 1.36e-006 2.92e-010 1.00e-006 1:05 53 | 360 6.07e-006 7.75e-007 1.51e-010 5.71e-007 1:03 54 | 370 3.41e-006 4.36e-007 7.62e-011 3.21e-007 0:58 55 | 380 1.90e-006 2.42e-007 3.79e-011 1.79e-007 0:52 56 | 390 1.04e-006 1.33e-007 1.85e-011 9.83e-008 0:49 57 | 400 5.68e-007 7.25e-008 8.94e-012 5.35e-008 0:42 58 | 410 3.06e-007 3.91e-008 4.25e-012 2.88e-008 0:46 59 | 420 1.63e-007 2.08e-008 2.00e-012 1.54e-008 0:36 60 | 430 8.63e-008 1.10e-008 9.31e-013 8.13e-009 0:30 61 | 440 4.53e-008 5.78e-009 4.31e-013 4.26e-009 0:26 62 | 450 2.35e-008 3.01e-009 2.06e-013 2.22e-009 0:21 63 | 460 1.21e-008 1.55e-009 1.01e-013 1.14e-009 0:17 64 | 470 6.22e-009 7.94e-010 6.70e-014 5.86e-010 0:13 65 | 480 3.16e-009 4.04e-010 5.82e-014 2.98e-010 0:09 66 | 490 1.60e-009 2.04e-010 5.37e-014 1.50e-010 0:04 67 | 500 8.01e-010 1.02e-010 5.89e-014 7.54e-011 0:00 68 | Elapsed time is 221.957171 seconds. 69 | -------------------------------------------------------------------------------- /results/gridgen_bump/bump.txt: -------------------------------------------------------------------------------- 1 | Freestream Conditions: 2 | Mach: 1.50 3 | Flow AOA: 0.00 deg 4 | u Velocity: 512.35 m/s 5 | v Velocity: 0.00 m/s 6 | Pressure: 1.00e+005 Pa 7 | Temperature: 300.00 K 8 | Density: 1.20 kg/m^3 9 | 10 | Iteration Variables: 11 | Iterations: 300 12 | CFL: 0.70 13 | M-Stage: 4 14 | Timestepping local 15 | 16 | 17 | Iter cont. resid x-mom resid y-mom resid energy resid Time left 18 | 10 4.05e-001 3.73e-001 6.10e+000 4.19e-001 5:39 19 | 20 2.78e-001 2.38e-001 3.89e+000 2.76e-001 5:23 20 | 30 2.18e-001 1.81e-001 2.81e+000 2.10e-001 5:24 21 | 40 1.89e-001 1.58e-001 2.27e+000 1.77e-001 5:04 22 | 50 1.80e-001 1.50e-001 1.90e+000 1.65e-001 4:56 23 | 60 1.83e-001 1.52e-001 1.39e+000 1.70e-001 4:40 24 | 70 1.57e-001 1.07e-001 1.42e+000 1.37e-001 4:32 25 | 80 1.36e-001 6.99e-002 1.41e+000 1.12e-001 4:24 26 | 90 1.26e-001 5.76e-002 1.26e+000 1.02e-001 4:08 27 | 100 1.19e-001 5.31e-002 1.13e+000 9.67e-002 3:57 28 | 110 1.15e-001 5.38e-002 1.03e+000 9.37e-002 3:42 29 | 120 1.14e-001 5.68e-002 9.58e-001 9.30e-002 3:33 30 | 130 1.17e-001 5.89e-002 8.88e-001 9.51e-002 3:24 31 | 140 1.26e-001 5.99e-002 7.89e-001 1.03e-001 3:12 32 | 150 1.28e-001 6.13e-002 7.44e-001 1.09e-001 3:00 33 | 160 1.25e-001 6.21e-002 7.14e-001 1.12e-001 2:48 34 | 170 1.22e-001 6.28e-002 6.92e-001 1.12e-001 2:34 35 | 180 1.18e-001 6.25e-002 6.59e-001 1.12e-001 2:24 36 | 190 1.14e-001 6.11e-002 6.44e-001 1.10e-001 2:12 37 | 200 1.12e-001 6.02e-002 6.36e-001 1.10e-001 2:00 38 | 210 1.11e-001 6.08e-002 6.20e-001 1.12e-001 1:49 39 | 220 1.11e-001 6.27e-002 6.10e-001 1.15e-001 1:36 40 | 230 1.11e-001 6.49e-002 6.10e-001 1.17e-001 1:26 41 | 240 1.12e-001 6.70e-002 6.22e-001 1.19e-001 1:13 42 | 250 1.12e-001 6.86e-002 6.40e-001 1.21e-001 1:00 43 | 260 1.11e-001 6.98e-002 6.60e-001 1.21e-001 0:48 44 | 270 1.10e-001 7.07e-002 6.76e-001 1.22e-001 0:36 45 | 280 1.09e-001 7.13e-002 6.88e-001 1.21e-001 0:24 46 | 290 1.08e-001 7.17e-002 6.96e-001 1.21e-001 0:12 47 | 300 1.07e-001 7.19e-002 7.01e-001 1.20e-001 0:00 48 | Elapsed time is 366.816779 seconds. 49 | -------------------------------------------------------------------------------- /results/videos/disturb_sub/sub1.avi: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/robojafar/euler_solver/e9b7f4874ad2303e8c4fb03a17b5d83d281ab349/results/videos/disturb_sub/sub1.avi -------------------------------------------------------------------------------- /results/videos/disturb_sup/sup1.avi: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/robojafar/euler_solver/e9b7f4874ad2303e8c4fb03a17b5d83d281ab349/results/videos/disturb_sup/sup1.avi -------------------------------------------------------------------------------- /results/videos/gridgen_bump/bump.avi: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/robojafar/euler_solver/e9b7f4874ad2303e8c4fb03a17b5d83d281ab349/results/videos/gridgen_bump/bump.avi -------------------------------------------------------------------------------- /source/BUMP/INSTRUCTIONS: -------------------------------------------------------------------------------- 1 | All three runs use p=1 bar (10^5 Pa) and T=300K 2 | 3 | Case 1. Supersonic (M=1.5), use 4% bump grid (bump04perc.grd) 4 | Case 2. Transonic (M=0.7), use 10% bump grid (bump10perc.grd) 5 | Case 3. Subsonic (M=0.3), use 10% bump grid ( "" ) 6 | 7 | ***RECOMMENDATION: Use global time step of 1.0E-5 seconds and run for few 1000 cycles 8 | 9 | 10 | -------------------------------------------------------------------------------- /source/BUMP/bump04perc.grd: -------------------------------------------------------------------------------- 1 | 1 2 | 57 25 1 3 | -1.00000000000e+00 -9.00000000000e-01 -8.08146102843e-01 -7.23393216340e-01 4 | -6.44866227081e-01 -5.71826709527e-01 -5.03647160979e-01 -4.39790849372e-01 5 | -3.79795897113e-01 -3.23262597069e-01 -2.69843219774e-01 -2.19233758879e-01 6 | -1.71167197821e-01 -1.25407980143e-01 -8.17474394609e-02 -4.00000000000e-02 7 | 0.00000000000e+00 3.95309484413e-02 7.95991317402e-02 1.20164477423e-01 8 | 1.61184567345e-01 2.02614791383e-01 2.44408573485e-01 2.86517715694e-01 9 | 3.28892190366e-01 3.71480575906e-01 4.14230345627e-01 4.57088131893e-01 10 | 5.00000000000e-01 5.42911868107e-01 5.85769654373e-01 6.28519424094e-01 11 | 6.71107809634e-01 7.13482284306e-01 7.55591426515e-01 7.97385208617e-01 12 | 8.38815432655e-01 8.79835522577e-01 9.20400868260e-01 9.60469051559e-01 13 | 1.00000000000e+00 1.04000000000e+00 1.08174743946e+00 1.12540798014e+00 14 | 1.17116719782e+00 1.21923375888e+00 1.26984321977e+00 1.32326259707e+00 15 | 1.37979589711e+00 1.43979084937e+00 1.50364716098e+00 1.57182670953e+00 16 | 1.64486622708e+00 1.72339321634e+00 1.80814610284e+00 1.90000000000e+00 17 | 2.00000000000e+00 -1.00000000000e+00 -8.99999999841e-01 -8.08146102564e-01 18 | -7.23393215864e-01 -6.44866226359e-01 -5.71826708307e-01 -5.03647159242e-01 19 | -4.39790847102e-01 -3.79795894323e-01 -3.23262593951e-01 -2.69843216366e-01 20 | -2.19233755424e-01 -1.71167194417e-01 -1.25407976955e-01 -8.17474368300e-02 21 | -3.99999962924e-02 -1.53149622465e-03 3.66034355964e-02 7.69263699756e-02 22 | 1.17749624264e-01 1.59030511978e-01 2.00724138555e-01 2.42783633099e-01 23 | 2.85160490556e-01 3.27804365935e-01 3.70663510246e-01 4.13685063820e-01 24 | 4.56815319168e-01 4.99999999442e-01 5.43184680309e-01 5.86314935986e-01 25 | 6.29336489665e-01 6.72195634070e-01 7.14839509450e-01 7.57216366906e-01 26 | 7.99275861447e-01 8.40969488021e-01 8.82250375736e-01 9.23073630024e-01 27 | 9.63396564404e-01 1.00153149622e+00 1.03999999629e+00 1.08174743683e+00 28 | 1.12540797696e+00 1.17116719442e+00 1.21923375542e+00 1.26984321637e+00 29 | 1.32326259395e+00 1.37979589432e+00 1.43979084710e+00 1.50364715924e+00 30 | 1.57182670831e+00 1.64486622636e+00 1.72339321586e+00 1.80814610256e+00 31 | 1.89999999984e+00 2.00000000000e+00 -1.00000000000e+00 -8.99999999795e-01 32 | -8.08146302434e-01 -7.23392732893e-01 -6.44863765747e-01 -5.71820830259e-01 33 | -5.03636447943e-01 -4.39774056697e-01 -3.79772117609e-01 -3.23231510692e-01 34 | -2.69805529533e-01 -2.19192072327e-01 -1.71128070164e-01 -1.25387555397e-01 35 | -8.17911545797e-02 -4.02743255834e-02 -2.36245297444e-03 3.54096935569e-02 36 | 7.56981632756e-02 1.16630605357e-01 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0.00000000000e+00 977 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 978 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 979 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 980 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 981 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 982 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 983 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 984 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 985 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 986 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 987 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 988 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 989 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 990 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 991 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 992 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 993 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 994 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 995 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 996 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 997 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 998 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 999 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1000 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1001 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1002 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1003 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1004 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1005 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1006 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1007 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1008 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1009 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1010 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1011 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1012 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1013 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1014 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1015 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1016 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1017 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1018 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1019 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1020 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1021 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1022 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1023 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1024 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1025 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1026 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1027 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1028 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1029 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1030 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1031 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1032 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1033 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1034 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1035 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1036 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1037 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1038 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1039 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1040 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1041 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1042 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1043 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1044 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1045 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1046 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1047 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1048 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1049 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1050 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1051 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1052 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1053 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1054 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1055 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1056 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1057 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1058 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1059 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1060 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1061 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1062 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1063 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1064 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1065 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1066 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1067 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1068 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1069 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1070 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1071 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1072 | 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 0.00000000000e+00 1073 | 0.00000000000e+00 1074 | -------------------------------------------------------------------------------- /source/calcResid.m: -------------------------------------------------------------------------------- 1 | %% CALCULATE RESIDUAL OF GRID %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | function resid = calcResid(V, V_free, normals, areas, nci, ncj) 3 | % Inputs: V - Cell array containing the primitive state vector for 4 | % each cell in the grid 5 | % V_free - Primitive state vector containing freestream conditions 6 | % normals - Cell array containing all of the face normals for each 7 | % cell 8 | % areas - Cell array containing all of the face areas for each 9 | % cell 10 | % nci,ncj - Number of cell in i and j 11 | 12 | % Parse out normal vectors in smaller, specialized cell arrays 13 | nE = normals{1}; 14 | nN = normals{2}; 15 | nW = normals{3}; 16 | nS = normals{4}; 17 | 18 | % Parse out areas vectors in smaller, specialized cell arrays 19 | sE = areas{1}; 20 | sN = areas{2}; 21 | sW = areas{3}; 22 | sS = areas{4}; 23 | 24 | % Initialize cell array containing the flux for each face 25 | e_flux = cell(nci,ncj); 26 | w_flux = cell(nci,ncj); 27 | n_flux = cell(nci,ncj); 28 | s_flux = cell(nci,ncj); 29 | 30 | % Initialize residual cell array 31 | resid = cell(nci,ncj); 32 | 33 | % Assemble freestream velocity vector 34 | free_vel = [V_free(2) V_free(3)]; 35 | 36 | % Calculate freestream Mach number 37 | free_a = speedsound(V_free(4), V_free(1)); 38 | 39 | % Loop through all cells 40 | for i = 1:nci 41 | for j = 1:ncj 42 | % Calculate speed of sound for cell 43 | cell_a = speedsound(V{i,j}(4),V{i,j}(1)); 44 | 45 | % Assemble velocity vector of cell 46 | vel = [V{i,j}(2) V{i,j}(3)]; 47 | 48 | % Contravariant Mach for face 49 | %conM = dot(vel,nE{i,j})/cell_a; 50 | conM = (vel(1)*nE{i,j}(1) + vel(2)*nE{i,j}(2))/cell_a; 51 | 52 | % If east face is at the outflow boundary 53 | if i == nci 54 | % Boundary normal equal to face normal 55 | nB = nE{i,j}; 56 | 57 | % Check to see is contravariant M >= 1 58 | if conM >= 1 59 | % Assign boundary flux to nci cell flux 60 | Vb = V{i,j}; 61 | 62 | % Calculate east face flux 63 | e_flux{i,j} = flux(Vb,nB); 64 | else 65 | % Calculate positive & negative Riemann invariants 66 | rpos = (vel.*nB) + 2/(1.4-1)*cell_a; 67 | rneg = (free_vel.*nB) - 2/(1.4-1)*free_a; 68 | 69 | % Average invariants to get normal velocities 70 | un = (rpos+rneg)/2; 71 | 72 | % Obtain velocities at boundaries 73 | ub = vel + (un - vel).*nB; 74 | 75 | % Vb is primitive state vector at outflow boundary 76 | % Density is extrapolated 77 | % u,v are calculated 78 | % Pressure is extrapolated 79 | Vb = [V{i,j}(1) ub(1) ub(2) V{i,j}(4)]; 80 | 81 | % Calculate East face flux 82 | e_flux{i,j} = flux(Vb,nB); 83 | end 84 | % If east face is internal 85 | else 86 | % Check to see is contravariant M >= 1 87 | if conM >= 1 88 | % Calculate east face flux using full flux 89 | e_flux{i,j} = flux(V{i,j},nE{i,j}); 90 | else 91 | % Calculate east face flux using f+ and f- 92 | e_flux{i,j} = fpos(V{i,j},nE{i,j}) + fneg(V{i+1,j},nE{i,j}); 93 | end 94 | end 95 | 96 | 97 | % Contravariant Mach for face 98 | %conM = dot(vel,nN{i,j})/cell_a; 99 | conM = (vel(1)*nN{i,j}(1) + vel(2)*nN{i,j}(2))/cell_a; 100 | 101 | % If north face is invicid wall 102 | if j == ncj 103 | % Boundary normal equal to face normal 104 | nB = nN{i,j}; 105 | 106 | % Contravariant velocity: 107 | % Dot product of the u,v velocity of cell(i,ncj) 108 | % and the wall normal vector 109 | conV = dot(vel, nB); 110 | 111 | % Wall velocity: 112 | % Velocity of cell(i,ncj) - contravariant vel. * wall normal 113 | % vector 114 | velB = vel - conV*nB; 115 | 116 | % Vb is primitive state vector at the wall 117 | % Density is extrapolated 118 | % u,v are calculated 119 | % Pressure is extrapolated 120 | Vb = [V{i,j}(1) velB(1) velB(2) V{i,j}(4)]; 121 | 122 | % Calculate north face flux 123 | n_flux{i,j} = flux(Vb,nB); 124 | else 125 | % Check to see is contravariant M >= 1 126 | if conM >=1 127 | % Calculate north face flux using full flux 128 | n_flux{i,j} = flux(V{i,j},nN{i,j}); 129 | else 130 | % Calculate north face flux using f+ and f- 131 | n_flux{i,j} = fpos(V{i,j},nN{i,j}) + fneg(V{i,j+1},nN{i,j}); 132 | end 133 | end 134 | 135 | 136 | % Contravariant Mach for face 137 | %conM = dot(vel,nW{i,j})/cell_a; 138 | conM = (vel(1)*nW{i,j}(1) + vel(2)*nW{i,j}(2))/cell_a; 139 | 140 | % If west face is inflow boundary 141 | if i == 1 142 | % Boundary normal equal to face normal 143 | nB = nW{i,j}; 144 | 145 | if conM >= 1 146 | % Assign boundary state vec to freestream vals 147 | Vb = V_free; 148 | 149 | % Calc flux for west face 150 | w_flux{i,j} = flux(Vb,nB); 151 | else 152 | % Calculate positive & negative Riemann invariant 153 | rpos = (vel.*nB) + 2/(1.4-1)*cell_a; 154 | rneg = (free_vel.*nB) - 2/(1.4-1)*free_a; 155 | 156 | % Average invariants to get normal velocities 157 | un = (rpos+rneg)/2; 158 | 159 | % Obtain velocities at boundaries 160 | ub = free_vel + (un + free_vel).*nB; 161 | 162 | % Vb is primitive state vector at inflow boundary 163 | % Density is freestream 164 | % u,v are calculated 165 | % Pressure is freesteam 166 | Vb = [V_free(1) ub(1) ub(2) V_free(4)]; 167 | 168 | % Calculate west face flux 169 | w_flux{i,j} = flux(Vb,nB); 170 | end 171 | else 172 | % Check to see is contravariant M >= 1 173 | if conM >=1 174 | % Calculate west face flux using full flux 175 | w_flux{i,j} = flux(V{i,j},nW{i,j}); 176 | else 177 | % Calculate west face flux using the negative 178 | % of the adjacent cell east face flux 179 | w_flux{i,j} = -1*e_flux{i-1,j}; 180 | end 181 | end 182 | 183 | 184 | % Contravariant Mach for face 185 | %conM = dot(vel,nS{i,j})/cell_a; 186 | conM = (vel(1)*nS{i,j}(1) + vel(2)*nS{i,j}(2))/cell_a; 187 | 188 | % If south face is invicid wall 189 | if j == 1 190 | % Boundary normal equal to face normal 191 | nB = nS{i,j}; 192 | 193 | % Contravariant velocity: 194 | % Dot product of the u,v velocity of cell(i,1) 195 | % and the wall normal vector 196 | conV = dot(vel, nB); 197 | 198 | % Wall velocity: 199 | % Velocity of cell(i,1) - contravariant vel. * wall normal 200 | % vector 201 | velB = vel - conV*nB; 202 | 203 | % Vb is primitive state vector at the wall 204 | % Density is extrapolated 205 | % u,v are calculated 206 | % Pressure is extrapolated 207 | Vb = [V{i,j}(1) velB(1) velB(2) V{i,j}(4)]; 208 | 209 | % Calculate south face flux 210 | s_flux{i,j} = flux(Vb,nB); 211 | else 212 | % Check to see is contravariant M >= 1 213 | if conM >= 1 214 | % Calculate south face flux using full flux 215 | s_flux{i,j} = flux(V{i,j},nS{i,j}); 216 | else 217 | % Calculate south face flux using the negative 218 | % of the adjacent cell north face flux 219 | s_flux{i,j} = -1*n_flux{i,j-1}; 220 | end 221 | end 222 | 223 | % Assemble residual: 224 | % SUM(face flux * face area) 225 | resid{i,j} = e_flux{i,j}*sE(i,j) + ... 226 | n_flux{i,j}*sN(i,j) + ... 227 | w_flux{i,j}*sW(i,j) + ... 228 | s_flux{i,j}*sS(i,j); 229 | end 230 | end -------------------------------------------------------------------------------- /source/convU_V.m: -------------------------------------------------------------------------------- 1 | %% CALCULATE PRIMITIVE STATE VECTOR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | function V = convU_V(U) 3 | % Inputs: Conservative state vector from a cell 4 | 5 | % Parse out variables and apply more names 6 | rho = U(1); % Density 7 | rho_u = U(2); % Density * u vel. 8 | rho_v = U(3); % Density * v vel. 9 | rho_e = U(4); % Density * total energy 10 | 11 | % V = [rho u_vel v_vel pressure] 12 | V(1) = rho; 13 | V(2) = rho_u/rho; 14 | V(3) = rho_v/rho; 15 | V(4) = (rho_e - rho/2*(V(2)^2+V(3)^2))*(1.4-1); -------------------------------------------------------------------------------- /source/convV_U.m: -------------------------------------------------------------------------------- 1 | %% CALCULATE CONSERVATIVE STATE VECTOR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | function U = convV_U(V) 3 | % Inputs: Primitive state vector from a cell 4 | 5 | % Parse out variables and apply more names 6 | rho = V(1); % Density 7 | u = V(2); % u velocity 8 | v = V(3); % v velocity 9 | P = V(4); % Pressure 10 | 11 | % U = [rho rho*u_vel rho*v_vel rho*energy] 12 | U(1) = rho; 13 | U(2) = rho*u; 14 | U(3) = rho*v; 15 | U(4) = rho*e_0(V); -------------------------------------------------------------------------------- /source/e_0.m: -------------------------------------------------------------------------------- 1 | %% CALCULATE TOTAL ENERGY %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | function e = e_0(V) 3 | % Inputs: Primitive state vector from a cell 4 | 5 | % Parse out variables and apply more names 6 | rho = V(1); % Density 7 | u = V(2); % u velocity 8 | v = V(3); % v velocity 9 | P = V(4); % Pressure 10 | 11 | % Total energy = pressure/[(gamma-1)*rho] + 1/2(u^2+v^2) 12 | e = P/((1.4-1)*rho)+.5*(u^2+v^2); -------------------------------------------------------------------------------- /source/euler.m: -------------------------------------------------------------------------------- 1 | % Jafar Mohammed 2 | % AE516 Final Project 3 | 4 | % Euler Solver 5 | % First Order Van Leer Scheme 6 | % M-stage timestepping 7 | 8 | clear % Clear variables from memory 9 | clc % Clear the command window 10 | 11 | %% LOAD/GENERATE GRID %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 12 | loadGrid = 1; %0 - create cartesian grid 13 | %1 - load grid from file 14 | tic 15 | if loadGrid == 1 16 | % Open the file and assign it an ID 17 | %fid = fopen('BUMP/bump10perc.grd', 'r'); 18 | fid = fopen('BUMP/bump04perc.grd', 'r'); 19 | %fid = fopen('bump.grd', 'r'); 20 | 21 | if fid >= 1 22 | % Read in file headers 23 | zones = fscanf(fid, '%d', 1); 24 | 25 | % Code only handles 1 zone 26 | % Therefore, check for number of zones 27 | if (zones == 1) 28 | % Read in number of i,j,k points 29 | npi = fscanf(fid, '%d', 1); 30 | npj = fscanf(fid, '%d', 1); 31 | npk = fscanf(fid, '%d', 1); 32 | 33 | % Retrieve i,j,k coordinates 34 | x = fscanf(fid, '%f', [npi,npj]); 35 | y = fscanf(fid, '%f', [npi,npj]); 36 | z = fscanf(fid, '%f', [npi,npj]); 37 | disp('Grid read successfully'); 38 | end 39 | fclose(fid); 40 | end 41 | else 42 | % Generate cartesian grid using the meshgrid function 43 | npi = 21; % Num. of pts. in i-dir 44 | npj = 11; % Num. of pts. in j-dir 45 | xc = linspace(0,20,npi); % Distribution in i-dir 46 | yc = linspace(0,10,npj); % Distribution in j-dir 47 | [y,x] = meshgrid(yc,xc); % Creates 2D grid 48 | end 49 | 50 | % Visualizes the mesh in a plot window 51 | %mesh(x,y,zeros(npi,npj)) 52 | %axis image;view(2);drawnow; 53 | 54 | disp('Grid generated'); 55 | toc;disp(' '); 56 | 57 | %% GRID METRICS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 58 | tic 59 | z_width = [0,0,1]; % Unit vector in z-dir 60 | nci = npi-1; % Number of cells (pts-1) in i dir 61 | ncj = npj-1; % Number of cells (pts-1) in j dir 62 | 63 | for i = 1:nci 64 | for j = 1:ncj 65 | % Assemble the face lengths 66 | e_xlen = x(i+1,j+1)-x(i+1,j); 67 | e_ylen = y(i+1,j+1)-y(i+1,j); 68 | 69 | n_xlen = x(i,j+1)-x(i+1,j+1); 70 | n_ylen = y(i,j+1)-y(i+1,j+1); 71 | 72 | w_xlen = x(i,j)-x(i,j+1); 73 | w_ylen = y(i,j)-y(i,j+1); 74 | 75 | s_xlen = x(i+1,j)-x(i,j); 76 | s_ylen = y(i+1,j)-y(i,j); 77 | 78 | % Compute midpoint of cell (for plotting) 79 | xmid(i,j) = (x(i,j) + x(i+1,j))/2; 80 | ymid(i,j) = (y(i,j) + y(i,j+1))/2; 81 | 82 | % Compute volume of cell using A.BxC (volume of parallelepiped) 83 | volume(i,j) = abs(dot(z_width,cross(-1*[s_xlen,s_ylen,0],... 84 | [e_xlen,e_ylen,0]))); 85 | 86 | % Compute area of cell 87 | sE(i,j) = sqrt((e_xlen)^2 + (e_ylen)^2); 88 | sN(i,j) = sqrt((n_xlen)^2 + (n_ylen)^2); 89 | sW(i,j) = sqrt((w_xlen)^2 + (w_ylen)^2); 90 | sS(i,j) = sqrt((s_xlen)^2 + (s_ylen)^2); 91 | 92 | % Compute outward normal of faces (return 3 component vector) 93 | temp_nE = cross([e_xlen,e_ylen, 0]/sE(i,j), z_width); 94 | temp_nN = cross([n_xlen,n_ylen, 0]/sN(i,j), z_width); 95 | temp_nW = cross([w_xlen,w_ylen, 0]/sW(i,j), z_width); 96 | temp_nS = cross([s_xlen,s_ylen, 0]/sS(i,j), z_width); 97 | 98 | % Truncate normal vector to 2 components 99 | nE{i,j} = [temp_nE(1) temp_nE(2)]; 100 | nN{i,j} = [temp_nN(1) temp_nN(2)]; 101 | nW{i,j} = [temp_nW(1) temp_nW(2)]; 102 | nS{i,j} = [temp_nS(1) temp_nS(2)]; 103 | 104 | % Clear unecessary variables 105 | clear temp_nE temp_nN temp_nW temp_nS 106 | clear e_xlen n_xlen w_xlen s_xlen 107 | clear e_ylen n_ylen w_ylen s_ylen 108 | end 109 | end 110 | disp('Grid Metrics calculated'); 111 | toc;disp(' '); 112 | 113 | %% SET FREESTREAM CONDITIONS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 114 | free_rho = 1.2; % kg/m^3 115 | free_T = 300.00; % Kelvin 116 | free_P = 100000; % Pa 117 | free_M = 1.5; % Mach 118 | free_aoa = 0; % deg 119 | 120 | free_a = speedsound(free_P,free_rho); % m/s 121 | free_u = free_M*free_a*cosd(free_aoa); % m/s 122 | free_v = free_M*free_a*sind(free_aoa); % m/s 123 | free_vel = [free_u free_v]; 124 | 125 | % Freestream Primitive State Vector (PSV) 126 | V_free = [free_rho free_u free_v free_P]; 127 | 128 | diary('output.txt') 129 | fprintf('Freestream Conditions:\n'); 130 | fprintf('Mach: %10.2f\n',free_M); 131 | fprintf('Flow AOA: %10.2f deg\n',free_aoa); 132 | fprintf('u Velocity: %10.2f m/s\n',free_u); 133 | fprintf('v Velocity: %10.2f m/s\n',free_v); 134 | fprintf('Pressure: %10.2e Pa\n',free_P); 135 | fprintf('Temperature: %10.2f K\n',free_T); 136 | fprintf('Density: %10.2f kg/m^3\n\n',free_rho); 137 | 138 | %% SET ITERATION VARIABLES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 139 | % Iteration variables 140 | iterations = 100; % Number of iterations to run 141 | 142 | gbl_timestep = 0; % 0 = local timestepping 143 | % 1 = global timestepping 144 | 145 | timestep = 1e-5; % Timestep for global timestepping 146 | CFL = 0.5; % Courant number 147 | 148 | m_stage = 4; % m-stage time stepping 149 | % e.g. 1 for Euler step 150 | % 4 for 4th-order RK 151 | 152 | % Output variables 153 | freq = 10; % Reporting frequency for output 154 | 155 | plotcontours = 0; % Plot contours during iterations 156 | % 0 - off 157 | % 1 - Density 158 | % 2 - U Velocity 159 | % 3 - V Velocity 160 | % 4 - Pressure 161 | 162 | plots_on = 1 ; % Plot PSV contour plots after 163 | % completion 164 | 165 | fprintf('Iteration Variables:\n'); 166 | fprintf('Iterations: %5d\n',iterations); 167 | fprintf('CFL: %5.2f\n',CFL); 168 | fprintf('M-Stage: %5d\n',m_stage); 169 | if gbl_timestep == 0 170 | fprintf('Timestepping %5s\n\n','local'); 171 | else 172 | fprintf('Timestepping %5s\n\n','global'); 173 | end 174 | 175 | %% INITIALIZE SOLUTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 176 | tic 177 | resid_i = 0; % Iterative residual 178 | resid_0 = 0; % Step 0 residual 179 | start_iter = 0; % Used for multiple runs 180 | end_iter = 0; % Used for multiple runs 181 | residReduced = 0; % If divergence detected 182 | fm = 1; % Used for capturing movies 183 | 184 | % Combine normals and areas into big cell array which will be passed 185 | % to the function which computes the residual 186 | normals = {nE nN nW nS}; 187 | areas = {sE sN sW sS}; 188 | 189 | % Initalize variables which will allow for visualization 190 | % i.e. Plot Contours 191 | con_density = zeros([nci,ncj]); 192 | con_uvel = zeros([nci,ncj]); 193 | con_vvel = zeros([nci,ncj]); 194 | con_pres = zeros([nci,ncj]); 195 | 196 | % Loop through all cells and init PSV to freestream conditions 197 | % Convert PSV to conservative state vector 198 | % Init residual to 0 199 | for i = 1:nci 200 | for j = 1:ncj 201 | V{i,j} = V_free; 202 | U{i,j} = convV_U(V{i,j}); 203 | resid{i,j} = [0 0 0 0]; 204 | end 205 | end 206 | 207 | % Add a disturbance at cell (10,5) if cartesian grid created 208 | if loadGrid == 0 209 | V{10,5}(4) = 1.1*free_P; 210 | U{10,5} = convV_U(V{10,5}); 211 | end 212 | 213 | diary off 214 | disp('Solution initialized'); 215 | toc 216 | 217 | %% MAIN LOOP %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 218 | start_iter = start_iter + 1; % Start at iteration 1 219 | diary on 220 | 221 | % Create plot window 222 | if plotcontours == 1 223 | hc = figure('name','Density Contour'); 224 | elseif plotcontours == 2 225 | hc = figure('name','U Velocity Contour'); 226 | elseif plotcontours == 3 227 | hc = figure('name','V Velocity Contour'); 228 | elseif plotcontours == 4 229 | hc = figure('name','Pressure Contour'); 230 | end 231 | 232 | tic 233 | 234 | % Main loop in time 235 | for iter = start_iter:(end_iter + iterations) 236 | % Time variable used to measure time/iteration 237 | ti1 = cputime; 238 | 239 | % Initialize iteration residual to 0 240 | resid_i = 0; 241 | 242 | % Save CSV from this timestep (to be used in m-stage) 243 | U0 = U; 244 | 245 | % M-stage timestepping scheme 246 | for m = 1:m_stage 247 | % Calculate residual using function calcResid 248 | % Passes PSV, normals, areas cell array, 249 | % freestream PSV, and nci and ncj 250 | resid = calcResid(V, V_free, normals, areas, nci, ncj); 251 | 252 | % Loop through all cells to update solution 253 | for i = 1:nci 254 | for j = 1:ncj 255 | 256 | % If local timestepping, calculate timestep of the cell 257 | if gbl_timestep == 0 258 | vel = [V{i,j}(2) V{i,j}(3)]; 259 | cell_a = speedsound(V{i,j}(4),V{i,j}(1)); 260 | dt(1) = CFL * sE(i,j)/(abs(vel(1)*nE{i,j}(1) +... 261 | vel(2)*nE{i,j}(2))+cell_a); 262 | dt(2) = CFL * sN(i,j)/(abs(vel(1)*nN{i,j}(1) +... 263 | vel(2)*nN{i,j}(2))+cell_a); 264 | dt(3) = CFL * sW(i,j)/(abs(vel(1)*nW{i,j}(1) +... 265 | vel(2)*nW{i,j}(2))+cell_a); 266 | dt(4) = CFL * sS(i,j)/(abs(vel(1)*nS{i,j}(1) +... 267 | vel(2)*nS{i,j}(2))+cell_a); 268 | timestep = min(dt); 269 | end 270 | 271 | % Update solution using the saved CSV 272 | % Multiply by 'alpha' constant 273 | U{i,j} = U0{i,j} -... 274 | 1/(m_stage-(m-1))*timestep/volume(i,j)*resid{i,j}; 275 | 276 | % Update cell PSV 277 | V{i,j} = convU_V(U{i,j}); 278 | 279 | % Update contour arrays used for plotting 280 | con_density(i,j) = V{i,j}(1); 281 | con_uvel(i,j) = V{i,j}(2); 282 | con_vvel(i,j) = V{i,j}(3); 283 | con_pres(i,j) = V{i,j}(4); 284 | 285 | % Assemble first part of L2 norm for residual 286 | resid_i = resid_i + resid{i,j}.^2; 287 | end 288 | end 289 | end 290 | 291 | % Assemble second part of L2 norm for residual 292 | resid_i = (resid_i).^.5/(nci*ncj); 293 | 294 | % Assign normalization value in first interation 295 | if iter == 1 296 | resid_0 = resid_i; 297 | 298 | % More detailed iurput 299 | fprintf('\nIter cont. resid x-mom resid y-mom resid energy resid Time left\n'); 300 | end 301 | 302 | % Detects extreme divergence (at the point of no return) 303 | % and shuts down simulation 304 | if isnan(resid_i/resid_0) 305 | break; 306 | disp('Solution corrupt.'); 307 | end 308 | 309 | % Detects divergence happening in x-mom resid and cuts CFL in half 310 | if ((resid_i(2)/resid_0(2)) >= (1e1)) 311 | if residReduced == 0 312 | CFL = CFL/2; 313 | notice = sprintf('Divergence detected. CFL reduced to %5.2f',CFL); 314 | disp(notice); 315 | residReduced = residReduced + 1; 316 | %elseif ((residReduced > 0) &&((resid_i(2)/resid_0(2)) >= (2e1))) 317 | % CFL = CFL/2; 318 | % notice = sprintf('Divergence detected. CFL reduced to %5.2f',CFL); 319 | % disp(notice); 320 | end 321 | end 322 | 323 | % Computes time/iteration 324 | ti2 = cputime-ti1; 325 | 326 | % Displays output and updates plots at user specified time 327 | % interval 328 | if mod(iter,freq) == 0 329 | % Plot contours if wanted 330 | if plotcontours == 1 331 | % Assembles contour plot 332 | [C,h] = contourf(xmid',ymid',con_density'); 333 | 334 | % Removes lines from contour plot 335 | set(h, 'LineStyle','none'); 336 | 337 | % Adds a title to the plot 338 | s = sprintf('Density Contour at %4d iterations',iter); 339 | title(s) 340 | 341 | % Adds gridlines, corrects aspect ratio 342 | grid on;axis image;drawnow; 343 | 344 | % Assembles array for movie viewing 345 | mov(fm) = getframe(gca); 346 | fm=fm+1; 347 | elseif plotcontours == 2 348 | [C,h] = contourf(xmid',ymid',con_uvel'); 349 | set(h, 'LineStyle','none'); 350 | s = sprintf('U-Vel. Contour at %4d iterations',iter); 351 | title(s) 352 | colorbar('peer',gca,'SouthOutside'); 353 | grid on;axis image;drawnow; 354 | mov(fm) = getframe(gca); 355 | fm=fm+1; 356 | elseif plotcontours == 3 357 | [C,h] = contourf(xmid',ymid',con_vvel'); 358 | set(h, 'LineStyle','none'); 359 | s = sprintf('V-Vel. Contour at %4d iterations',iter); 360 | title(s) 361 | colorbar('peer',gca,'SouthOutside'); 362 | grid on;axis image;drawnow; 363 | mov(fm) = getframe(gca); 364 | fm=fm+1; 365 | elseif plotcontours == 4 366 | [C,h] = contourf(xmid',ymid',con_pres'); 367 | set(h, 'LineStyle','none'); 368 | s = sprintf('Pressure Contour at %4d iterations',iter); 369 | title(s) 370 | colorbar('peer',gca,'SouthOutside'); 371 | grid on;axis image;drawnow; 372 | mov(fm) = getframe(gcf); 373 | fm=fm+1; 374 | end 375 | 376 | % More detailed output 377 | fprintf('%4d %11.2e %11.2e %11.2e %11.2e %7s\n',iter,... 378 | resid_i(1)/resid_0(1),... 379 | resid_i(2)/resid_0(2),... 380 | resid_i(3)/resid_0(3),... 381 | resid_i(4)/resid_0(4),... 382 | fixTime(ti2*(end_iter+iterations-iter))); 383 | end 384 | end 385 | 386 | start_iter = iter; 387 | end_iter = iter; 388 | toc 389 | diary off 390 | 391 | %% PLOT PRIMITIVE STATE VECTOR CONTOURS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 392 | % Creates a figure with 4 contour subplots 393 | % Plot 1: Density (kg/m^3) contour 394 | % Plot 2: U Velocity (m/s) contour 395 | % Plot 3: V Velocity (m/s) contour 396 | % Plot 4: Pressure (Pa) 397 | 398 | if plots_on == 1 399 | figure('name','Primitive State Variables'); 400 | 401 | subplot(221); 402 | contourf(xmid',ymid',con_density'); 403 | axis image; 404 | colorbar('peer',gca,'SouthOutside'); 405 | title('Density (kg/m^3)') 406 | 407 | subplot(222); 408 | contourf(xmid',ymid',con_uvel'); 409 | axis image; 410 | colorbar('peer',gca,'SouthOutside'); 411 | title('U Velocity (m/s)') 412 | 413 | subplot(223); 414 | contourf(xmid',ymid',con_vvel'); 415 | axis image; 416 | colorbar('peer',gca,'SouthOutside'); 417 | title('V Velocity (m/s)') 418 | 419 | subplot(224); 420 | contourf(xmid',ymid',con_pres'); 421 | axis image; 422 | colorbar('peer',gca,'SouthOutside'); 423 | title('Pressure (Pa)') 424 | end 425 | 426 | % Plots movie in new figure window 427 | %figure; 428 | %movie(mov); 429 | %movie2avi(mov,'movie.avi','fps',5) -------------------------------------------------------------------------------- /source/fixTime.m: -------------------------------------------------------------------------------- 1 | %% CALCULATE TIME REMAINING %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | function time = fixTime(s) 3 | % Input: time in seconds 4 | 5 | min = fix(s/60); 6 | sec = rem(s,60); 7 | sec = fix(sec); 8 | 9 | time = sprintf('%d:%02d',min,sec); -------------------------------------------------------------------------------- /source/flux.m: -------------------------------------------------------------------------------- 1 | %% CALCULATE FULL FLUX VECTOR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | function f = flux(V,n) 3 | % Inputs: Primitive state vector, V, from a cell 4 | % Normal vector, n, from a cell face 5 | 6 | % Parse out variables and apply more names 7 | rho = V(1); % Density 8 | u = V(2); % u velocity 9 | v = V(3); % v velocity 10 | P = V(4); % Pressure 11 | 12 | %conV = dot([u v],n); % Contravariant velocity 13 | conV = u*n(1) + v*n(2); 14 | 15 | % Assemble flux vector 16 | f(1) = rho*conV; 17 | f(2) = rho*u*conV + P*n(1); 18 | f(3) = rho*v*conV + P*n(2); 19 | f(4) = rho*h_0(V)*conV; -------------------------------------------------------------------------------- /source/fneg.m: -------------------------------------------------------------------------------- 1 | %% CALCULATE NEGATIVE FLUX VECTOR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | function f = fneg(V,n) 3 | % Inputs: Primitive state vector, V, from a cell 4 | % Normal vector, n, from a cell face 5 | 6 | % Parse out variables and apply more names 7 | rho = V(1); % Density 8 | u = V(2); % u velocity 9 | v = V(3); % v velocity 10 | P = V(4); % Pressure 11 | 12 | gamma = 1.4; % Gamma 13 | a = speedsound(P,rho); % Speed of sound 14 | %conV = dot([u v],n); % Contravariant velocity 15 | conV = u*n(1) + v*n(2); 16 | M = conV/a; % Contravarient Mach number 17 | 18 | % Assemble flux vector 19 | f(1) = -rho*a/4*(M-1)^2; 20 | f(2) = f(1) * (u + n(1)*(-conV-2*a)/gamma); 21 | f(3) = f(1) * (v + n(2)*(-conV-2*a)/gamma); 22 | f(4) = f(1) * (h_0(V) - a^2*(M+1)^2/(gamma + 1)); -------------------------------------------------------------------------------- /source/fpos.m: -------------------------------------------------------------------------------- 1 | %% CALCULATE POSITIVE FLUX VECTOR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | function f = fpos(V,n) 3 | % Inputs: Primitive state vector, V, from a cell 4 | % Normal vector, n, from a cell face 5 | 6 | % Parse out variables and apply more names 7 | rho = V(1); % Density 8 | u = V(2); % u velocity 9 | v = V(3); % v velocity 10 | P = V(4); % Pressure 11 | 12 | gamma = 1.4; % Gamma 13 | a = speedsound(P,rho); % Speed of sound 14 | %conV = dot([u v],n); % Contravariant velocity 15 | conV = u*n(1) + v*n(2); 16 | M = conV/a; % Contravarient Mach number 17 | 18 | % Assemble flux vector 19 | f(1) = rho*a/4*(M+1)^2; 20 | f(2) = f(1) * (u + n(1)*(-conV+2*a)/gamma); 21 | f(3) = f(1) * (v + n(2)*(-conV+2*a)/gamma); 22 | f(4) = f(1) * (h_0(V) - a^2*(M-1)^2/(gamma + 1)); -------------------------------------------------------------------------------- /source/h_0.m: -------------------------------------------------------------------------------- 1 | %% CALCULATE TOTAL ENTHALPY %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | function h = h_0(V) 3 | % Inputs: Primitive state vector from a cell 4 | 5 | % Parse out variables and apply more names 6 | rho = V(1); % Density 7 | u = V(2); % u velocity 8 | v = V(3); % v velocity 9 | P = V(4); % Pressure 10 | 11 | % Total enthalpy = total energy + pressure/rho 12 | h = e_0(V)+P/rho; -------------------------------------------------------------------------------- /source/speedsound.m: -------------------------------------------------------------------------------- 1 | %% CALCULATE SPEED OF SOUND %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2 | function c = speedsound(P,rho) 3 | % Inputs: Pressure and Density 4 | 5 | % speed of sound = sqrt(gamma*pressure/rho) 6 | c = sqrt(1.4*P/rho); -------------------------------------------------------------------------------- /source/subsonic.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/robojafar/euler_solver/e9b7f4874ad2303e8c4fb03a17b5d83d281ab349/source/subsonic.mat -------------------------------------------------------------------------------- /source/supersonic.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/robojafar/euler_solver/e9b7f4874ad2303e8c4fb03a17b5d83d281ab349/source/supersonic.mat -------------------------------------------------------------------------------- /source/transonic.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/robojafar/euler_solver/e9b7f4874ad2303e8c4fb03a17b5d83d281ab349/source/transonic.mat --------------------------------------------------------------------------------