├── .gitignore
├── LICENSE
├── README.md
├── assets
├── pylint.svg
├── realtime.gif
└── standingWave.gif
├── requirements-dev.txt
├── requirements.txt
├── setup.py
└── src
└── pythonsph
├── __init__.py
├── __main__.py
├── config.py
├── particle.py
└── physics.py
/.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 | pip-wheel-metadata/
24 | share/python-wheels/
25 | *.egg-info/
26 | .installed.cfg
27 | *.egg
28 | MANIFEST
29 |
30 | # PyInstaller
31 | # Usually these files are written by a python script from a template
32 | # before PyInstaller builds the exe, so as to inject date/other infos into it.
33 | *.manifest
34 | *.spec
35 |
36 | # Installer logs
37 | pip-log.txt
38 | pip-delete-this-directory.txt
39 |
40 | # Unit test / coverage reports
41 | htmlcov/
42 | .tox/
43 | .nox/
44 | .coverage
45 | .coverage.*
46 | .cache
47 | nosetests.xml
48 | coverage.xml
49 | *.cover
50 | *.py,cover
51 | .hypothesis/
52 | .pytest_cache/
53 |
54 | # Translations
55 | *.mo
56 | *.pot
57 |
58 | # Django stuff:
59 | *.log
60 | local_settings.py
61 | db.sqlite3
62 | db.sqlite3-journal
63 |
64 | # Flask stuff:
65 | instance/
66 | .webassets-cache
67 |
68 | # Scrapy stuff:
69 | .scrapy
70 |
71 | # Sphinx documentation
72 | docs/_build/
73 |
74 | # PyBuilder
75 | target/
76 |
77 | # Jupyter Notebook
78 | .ipynb_checkpoints
79 |
80 | # IPython
81 | profile_default/
82 | ipython_config.py
83 |
84 | # pyenv
85 | .python-version
86 |
87 | # pipenv
88 | # According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
89 | # However, in case of collaboration, if having platform-specific dependencies or dependencies
90 | # having no cross-platform support, pipenv may install dependencies that don't work, or not
91 | # install all needed dependencies.
92 | #Pipfile.lock
93 |
94 | # PEP 582; used by e.g. github.com/David-OConnor/pyflow
95 | __pypackages__/
96 |
97 | # Celery stuff
98 | celerybeat-schedule
99 | celerybeat.pid
100 |
101 | # SageMath parsed files
102 | *.sage.py
103 |
104 | # Environments
105 | .env
106 | .venv
107 | env/
108 | venv/
109 | ENV/
110 | env.bak/
111 | venv.bak/
112 |
113 | # Spyder project settings
114 | .spyderproject
115 | .spyproject
116 |
117 | # Rope project settings
118 | .ropeproject
119 |
120 | # mkdocs documentation
121 | /site
122 |
123 | # mypy
124 | .mypy_cache/
125 | .dmypy.json
126 | dmypy.json
127 |
128 | # Pyre type checker
129 | .pyre/
130 |
131 | # ML
132 | models
133 | logs
134 | wandb
135 | videos
136 | runs
137 |
138 | # Common
139 | temp.py
140 |
141 | # Photoshop
142 | *.psd
--------------------------------------------------------------------------------
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--------------------------------------------------------------------------------
/README.md:
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1 | # **Python Fluid Simulation**
2 |
3 | 
4 |
5 | A Python 2D fluid simulation using SPH
6 |
7 |
8 |
9 |
10 |
11 | Implementing smoothed particle hydrodynamics (SPH) in Python using this tutorial.
12 |
13 | See also the C# implementation in Unity here.
14 |
15 | ## **Installation**
16 |
17 | Make sure you have Python installed on your computer. Then, in a terminal, run the following commands:
18 |
19 | **1. Install the package with pip in your terminal:**
20 |
21 | ```bash
22 | pip install git+https://github.com/AlexandreSajus/Python-Fluid-Simulation.git
23 | ```
24 |
25 | **2. Run the simulation:**
26 |
27 | ```bash
28 | python -m pythonsph
29 | ```
30 |
31 | This will prompt a matplotlib animation window with a real-time simulation:
32 |
33 |
34 |
35 |
36 |
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/assets/pylint.svg:
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1 |
2 |
24 |
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/assets/realtime.gif:
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https://raw.githubusercontent.com/AlexandreSajus/Python-Fluid-Simulation/d3749d7fc159b00735ff8e9d84e01b6416da4808/assets/realtime.gif
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/assets/standingWave.gif:
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https://raw.githubusercontent.com/AlexandreSajus/Python-Fluid-Simulation/d3749d7fc159b00735ff8e9d84e01b6416da4808/assets/standingWave.gif
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/requirements-dev.txt:
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1 | black
2 | pytest
3 | pytest-cov
4 | pytest-check
5 | pylint
6 | pydocstyle
7 | mypy
8 | isort
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/requirements.txt:
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1 | numpy
2 | matplotlib
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/setup.py:
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1 | """Setups the package for installation."""
2 |
3 | from setuptools import setup
4 |
5 |
6 | def get_requirements():
7 | """Load requirements from file."""
8 | requirements_file = open("requirements.txt")
9 | return requirements_file.readlines()
10 |
11 |
12 | setup(install_requires=get_requirements())
13 |
--------------------------------------------------------------------------------
/src/pythonsph/__init__.py:
--------------------------------------------------------------------------------
1 | """A 2D Python Implementation of Smoothed Particle Hydrodynamics Fluid Simulation"""
2 |
--------------------------------------------------------------------------------
/src/pythonsph/__main__.py:
--------------------------------------------------------------------------------
1 | """
2 | Python 2D SPH by Alexandre Sajus
3 |
4 | This script generates a 2D animation of a dam break using Smoothed Particle Hydrodynamics
5 |
6 | More information at:
7 | https://github.com/AlexandreSajus
8 | https://web.archive.org/web/20090722233436/http://blog.brandonpelfrey.com/?p=303
9 | """
10 |
11 | import numpy as np
12 | from matplotlib import animation
13 | import matplotlib.pyplot as plt
14 |
15 | import pythonsph
16 | from pythonsph.config import Config
17 | from pythonsph.particle import Particle
18 | from pythonsph.physics import (
19 | start,
20 | calculate_density,
21 | create_pressure,
22 | calculate_viscosity,
23 | )
24 |
25 | print(f"Hello world from {pythonsph.__name__} ({pythonsph.__doc__})")
26 |
27 | (
28 | N,
29 | SIM_W,
30 | BOTTOM,
31 | DAM,
32 | DAM_BREAK,
33 | G,
34 | SPACING,
35 | K,
36 | K_NEAR,
37 | REST_DENSITY,
38 | R,
39 | SIGMA,
40 | MAX_VEL,
41 | WALL_DAMP,
42 | VEL_DAMP,
43 | ) = Config().return_config()
44 |
45 |
46 | def update(particles: list[Particle], dam: bool) -> list[Particle]:
47 | """
48 | Calculates a step of the simulation
49 | """
50 | # Update the state of the particles (apply forces, reset values, etc.)
51 | for particle in particles:
52 | particle.update_state(dam)
53 |
54 | # Calculate density
55 | calculate_density(particles)
56 |
57 | # Calculate pressure
58 | for particle in particles:
59 | particle.calculate_pressure()
60 |
61 | # Apply pressure force
62 | create_pressure(particles)
63 |
64 | # Apply viscosity force
65 | calculate_viscosity(particles)
66 |
67 | return particles
68 |
69 |
70 | # Setup matplotlib
71 | fig = plt.figure()
72 | axes = fig.add_subplot(xlim=(-SIM_W, SIM_W), ylim=(0, SIM_W))
73 | (POINTS,) = axes.plot([], [], "bo", ms=20)
74 |
75 | simulation_state = start(-SIM_W, DAM, BOTTOM, 0.03, N)
76 |
77 | frame = 0
78 |
79 | dam_built = True
80 |
81 | # Animation function
82 | def animate(i: int):
83 | """
84 | Animates the simulation in matplotlib
85 |
86 | Args:
87 | i: frame number
88 |
89 | Returns:
90 | points: the points to be plotted
91 | """
92 | global simulation_state, frame, dam_built
93 | if frame == 250: # Break the dam at frame 250
94 | print("Breaking the dam")
95 | dam_built = False
96 | simulation_state = update(simulation_state, dam_built)
97 | # Create an array with the x and y coordinates of the particles
98 | visual = np.array(
99 | [
100 | [particle.visual_x_pos, particle.visual_y_pos]
101 | for particle in simulation_state
102 | ]
103 | )
104 | POINTS.set_data(visual[:, 0], visual[:, 1]) # Updates the position of the particles
105 | frame += 1
106 | return (POINTS,)
107 |
108 |
109 | ani = animation.FuncAnimation(fig, animate, interval=10, blit=True)
110 | plt.show()
111 |
--------------------------------------------------------------------------------
/src/pythonsph/config.py:
--------------------------------------------------------------------------------
1 | """Configuration file defining the simulation parameters."""
2 |
3 | # Simulation parameters
4 | N = 250 # Number of particles
5 | SIM_W = 0.5 # Simulation space width
6 | BOTTOM = 0 # Simulation space ground
7 | DAM = -0.3 # Position of the dam, simulation space is between -0.5 and 0.5
8 | DAM_BREAK = 200 # Number of frames before the dam breaks
9 |
10 | # Physics parameters
11 | G = 0.02 * 0.25 # Acceleration of gravity
12 | SPACING = 0.08 # Spacing between particles, used to calculate pressure
13 | K = SPACING / 1000.0 # Pressure factor
14 | K_NEAR = K * 10 # Near pressure factor, pressure when particles are close to each other
15 | # Default density, will be compared to local density to calculate pressure
16 | REST_DENSITY = 3.0
17 | # Neighbour radius, if the distance between two particles is less than R, they are neighbours
18 | R = SPACING * 1.25
19 | SIGMA = 0.2 # Viscosity factor
20 | MAX_VEL = 2.0 # Maximum velocity of particles, used to avoid instability
21 | # Wall constraints factor, how much the particle is pushed away from the simulation walls
22 | WALL_DAMP = 0.05
23 | VEL_DAMP = 0.5 # Velocity reduction factor when particles are going above MAX_VEL
24 |
25 |
26 | class Config:
27 | """Contains the simulation parameters and the physics parameters."""
28 |
29 | def __init__(self):
30 | return None
31 |
32 | def return_config(self):
33 | """Returns the simulation parameters and the physics parameters."""
34 | return (
35 | N,
36 | SIM_W,
37 | BOTTOM,
38 | DAM,
39 | DAM_BREAK,
40 | G,
41 | SPACING,
42 | K,
43 | K_NEAR,
44 | REST_DENSITY,
45 | R,
46 | SIGMA,
47 | MAX_VEL,
48 | WALL_DAMP,
49 | VEL_DAMP,
50 | )
51 |
--------------------------------------------------------------------------------
/src/pythonsph/particle.py:
--------------------------------------------------------------------------------
1 | """Defines the Particle class."""
2 |
3 | from math import sqrt
4 | from pythonsph.config import Config
5 |
6 |
7 | (
8 | N,
9 | SIM_W,
10 | BOTTOM,
11 | DAM,
12 | DAM_BREAK,
13 | G,
14 | SPACING,
15 | K,
16 | K_NEAR,
17 | REST_DENSITY,
18 | R,
19 | SIGMA,
20 | MAX_VEL,
21 | WALL_DAMP,
22 | VEL_DAMP,
23 | ) = Config().return_config()
24 |
25 |
26 | class Particle:
27 | """
28 | A single particle of the simulated fluid
29 |
30 | Attributes:
31 | x_pos: x position of the particle
32 | y_pos: y position of the particle
33 | previous_x_pos: x position of the particle in the previous frame
34 | previous_y_pos: y position of the particle in the previous frame
35 | visual_x_pos: x position of the particle that is shown on the screen
36 | visual_y_pos: y position of the particle that is shown on the screen
37 | rho: density of the particle
38 | rho_near: near density of the particle, used to avoid collisions between particles
39 | press: pressure of the particle
40 | press_near: near pressure of the particle, used to avoid collisions between particles
41 | neighbors: list of the particle's neighbors
42 | x_vel: x velocity of the particle
43 | y_vel: y velocity of the particle
44 | x_force: x force applied to the particle
45 | y_force: y force applied to the particle
46 | """
47 |
48 | def __init__(self, x_pos: float, y_pos: float):
49 | self.x_pos = x_pos
50 | self.y_pos = y_pos
51 | self.previous_x_pos = x_pos
52 | self.previous_y_pos = y_pos
53 | self.visual_x_pos = x_pos
54 | self.visual_y_pos = y_pos
55 | self.rho = 0.0
56 | self.rho_near = 0.0
57 | self.press = 0.0
58 | self.press_near = 0.0
59 | self.neighbors = []
60 | self.x_vel = 0.0
61 | self.y_vel = 0.0
62 | self.x_force = 0.0
63 | self.y_force = -G
64 |
65 | def update_state(self, dam: bool):
66 | """
67 | Updates the state of the particle
68 | """
69 | # Reset previous position
70 | (self.previous_x_pos, self.previous_y_pos) = (self.x_pos, self.y_pos)
71 |
72 | # Apply force using Newton's second law and Euler integration with mass = 1 and dt = 1
73 | (self.x_vel, self.y_vel) = (
74 | self.x_vel + self.x_force,
75 | self.y_vel + self.y_force,
76 | )
77 |
78 | # Move particle according to its velocity using Euler integration with dt = 1
79 | (self.x_pos, self.y_pos) = (self.x_pos + self.x_vel, self.y_pos + self.y_vel)
80 |
81 | # Set visual position. Visual position is the one shown on the screen
82 | # It is used to avoid unstable particles to be shown
83 | (self.visual_x_pos, self.visual_y_pos) = (self.x_pos, self.y_pos)
84 |
85 | # Reset force
86 | (self.x_force, self.y_force) = (0.0, -G)
87 |
88 | # Define velocity using Euler integration with dt = 1
89 | (self.x_vel, self.y_vel) = (
90 | self.x_pos - self.previous_x_pos,
91 | self.y_pos - self.previous_y_pos,
92 | )
93 |
94 | # Calculate velocity
95 | velocity = sqrt(self.x_vel**2 + self.y_vel**2)
96 |
97 | # Reduces the velocity if it is too high
98 | if velocity > MAX_VEL:
99 | self.x_vel *= VEL_DAMP
100 | self.y_vel *= VEL_DAMP
101 |
102 | # Wall constraints, if a particle is out of bounds, create a spring force to bring it back
103 | if self.x_pos < -SIM_W:
104 | self.x_force -= (self.x_pos - -SIM_W) * WALL_DAMP
105 | self.visual_x_pos = -SIM_W
106 |
107 | # Same thing as a wall constraint but for the dam that will move from dam to SIM_W
108 | if dam is True and self.x_pos > DAM:
109 | self.x_force -= (self.x_pos - DAM) * WALL_DAMP
110 |
111 | # Same thing for the right wall
112 | if self.x_pos > SIM_W:
113 | self.x_force -= (self.x_pos - SIM_W) * WALL_DAMP
114 | self.visual_x_pos = SIM_W
115 |
116 | # Same thing but for the floor
117 | if self.y_pos < BOTTOM:
118 | # We use SIM_W instead of BOTTOM here because otherwise particles are too low
119 | self.y_force -= (self.y_pos - SIM_W) * WALL_DAMP
120 | self.visual_y_pos = BOTTOM
121 |
122 | # Reset density
123 | self.rho = 0.0
124 | self.rho_near = 0.0
125 |
126 | # Reset neighbors
127 | self.neighbors = []
128 |
129 | def calculate_pressure(self):
130 | """
131 | Calculates the pressure of the particle
132 | """
133 | self.press = K * (self.rho - REST_DENSITY)
134 | self.press_near = K_NEAR * self.rho_near
135 |
--------------------------------------------------------------------------------
/src/pythonsph/physics.py:
--------------------------------------------------------------------------------
1 | """Utilities and physics calculations"""
2 |
3 | from math import sqrt
4 |
5 | from pythonsph.config import Config
6 | from pythonsph.particle import Particle
7 |
8 |
9 | (
10 | N,
11 | SIM_W,
12 | BOTTOM,
13 | DAM,
14 | DAM_BREAK,
15 | G,
16 | SPACING,
17 | K,
18 | K_NEAR,
19 | REST_DENSITY,
20 | R,
21 | SIGMA,
22 | MAX_VEL,
23 | WALL_DAMP,
24 | VEL_DAMP,
25 | ) = Config().return_config()
26 |
27 |
28 | def start(
29 | xmin: float, xmax: float, ymin: float, space: float, count: int
30 | ) -> list[Particle]:
31 | """
32 | Creates a rectangle of particles within xmin, xmax and ymin
33 | We start by creating a particle at (xmin, ymin)
34 | and then add particles until we reach count particles
35 | Particles are represented by their position [x, y]
36 |
37 | Args:
38 | xmin (float): x min bound of the rectangle
39 | xmax (float): x max bound of the rectangle
40 | ymin (float): y min bound of the rectangle
41 | space (float): space between particles
42 | count (int): number of particles
43 |
44 | Returns:
45 | list: list of Particle objects
46 | """
47 | result = []
48 | x_pos, y_pos = xmin, ymin
49 | for _ in range(count):
50 | result.append(Particle(x_pos, y_pos))
51 | x_pos += space
52 | if x_pos > xmax:
53 | x_pos = xmin
54 | y_pos += space
55 | return result
56 |
57 |
58 | def calculate_density(particles: list[Particle]) -> None:
59 | """
60 | Calculates density of particles
61 | Density is calculated by summing the relative distance of neighboring particles
62 | We distinguish density and near density to avoid particles to collide with each other
63 | which creates instability
64 |
65 | Args:
66 | particles (list[Particle]): list of particles
67 | """
68 | for i, particle_1 in enumerate(particles):
69 | density = 0.0
70 | density_near = 0.0
71 | # Density is calculated by summing the relative distance of neighboring particles
72 | for particle_2 in particles[i + 1 :]:
73 | distance = sqrt(
74 | (particle_1.x_pos - particle_2.x_pos) ** 2
75 | + (particle_1.y_pos - particle_2.y_pos) ** 2
76 | )
77 | if distance < R:
78 | # normal distance is between 0 and 1
79 | normal_distance = 1 - distance / R
80 | density += normal_distance**2
81 | density_near += normal_distance**3
82 | particle_2.rho += normal_distance**2
83 | particle_2.rho_near += normal_distance**3
84 | particle_1.neighbors.append(particle_2)
85 | particle_1.rho += density
86 | particle_1.rho_near += density_near
87 |
88 |
89 | def create_pressure(particles: list[Particle]) -> None:
90 | """
91 | Calculates pressure force of particles
92 | Neighbors list and pressure have already been calculated by calculate_density
93 | We calculate the pressure force by summing the pressure force of each neighbor
94 | and apply it in the direction of the neighbor
95 |
96 | Args:
97 | particles (list[Particle]): list of particles
98 | """
99 | for particle in particles:
100 | press_x = 0.0
101 | press_y = 0.0
102 | for neighbor in particle.neighbors:
103 | particle_to_neighbor = [
104 | neighbor.x_pos - particle.x_pos,
105 | neighbor.y_pos - particle.y_pos,
106 | ]
107 | distance = sqrt(particle_to_neighbor[0] ** 2 + particle_to_neighbor[1] ** 2)
108 | normal_distance = 1 - distance / R
109 | total_pressure = (
110 | particle.press + neighbor.press
111 | ) * normal_distance**2 + (
112 | particle.press_near + neighbor.press_near
113 | ) * normal_distance**3
114 | pressure_vector = [
115 | particle_to_neighbor[0] * total_pressure / distance,
116 | particle_to_neighbor[1] * total_pressure / distance,
117 | ]
118 | neighbor.x_force += pressure_vector[0]
119 | neighbor.y_force += pressure_vector[1]
120 | press_x += pressure_vector[0]
121 | press_y += pressure_vector[1]
122 | particle.x_force -= press_x
123 | particle.y_force -= press_y
124 |
125 |
126 | def calculate_viscosity(particles: list[Particle]) -> None:
127 | """
128 | Calculates the viscosity force of particles
129 | Force = (relative distance of particles)*(viscosity weight)*(velocity difference of particles)
130 | Velocity difference is calculated on the vector between the particles
131 |
132 | Args:
133 | particles (list[Particle]): list of particles
134 | """
135 |
136 | for particle in particles:
137 | for neighbor in particle.neighbors:
138 | particle_to_neighbor = [
139 | neighbor.x_pos - particle.x_pos,
140 | neighbor.y_pos - particle.y_pos,
141 | ]
142 | distance = sqrt(particle_to_neighbor[0] ** 2 + particle_to_neighbor[1] ** 2)
143 | normal_p_to_n = [
144 | particle_to_neighbor[0] / distance,
145 | particle_to_neighbor[1] / distance,
146 | ]
147 | relative_distance = distance / R
148 | velocity_difference = (particle.x_vel - neighbor.x_vel) * normal_p_to_n[
149 | 0
150 | ] + (particle.y_vel - neighbor.y_vel) * normal_p_to_n[1]
151 | if velocity_difference > 0:
152 | viscosity_force = [
153 | (1 - relative_distance)
154 | * SIGMA
155 | * velocity_difference
156 | * normal_p_to_n[0],
157 | (1 - relative_distance)
158 | * SIGMA
159 | * velocity_difference
160 | * normal_p_to_n[1],
161 | ]
162 | particle.x_vel -= viscosity_force[0] * 0.5
163 | particle.y_vel -= viscosity_force[1] * 0.5
164 | neighbor.x_vel += viscosity_force[0] * 0.5
165 | neighbor.y_vel += viscosity_force[1] * 0.5
166 |
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9 | 
35 |