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venv | ||
__pycache__/ | ||
dist/ | ||
*.egg-info/ |
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# diffusion2D | ||
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## Instructions for students | ||
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Please follow the instructions in [pypi_exercise.md](https://github.com/Simulation-Software-Engineering/Lecture-Material/blob/main/03_building_and_packaging/pypi_exercise.md). | ||
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The code used in this exercise is based on [Chapter 7 of the book "Learning Scientific Programming with Python"](https://scipython.com/book/chapter-7-matplotlib/examples/the-two-dimensional-diffusion-equation/). | ||
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## Project description | ||
## Project Description | ||
This code solves the diffusion equation in 2D over a square domain which is at a certain temperature and a circular disc at the center which is at a higher temperature. This code solves the diffusion equation using the Finite Difference Method. The thermal diffusivity and initial conditions of the system can be changed by the user. The code produces four plots at various timepoints of the simulation. The diffusion process can be clearly observed in these plots. | ||
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## Installing the package | ||
To install the `diffusion2D` package from TestPyPI and PyPI, you can use the following `pip` commands: | ||
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### Using pip3 to install from TestPyPI | ||
```bash | ||
pip3 install --index-url https://test.pypi.org/simple/ --extra-index-url https://pypi.org/simple <username>_diffusion2d | ||
``` | ||
### Using pip3 to install from PyPI | ||
```bash | ||
pip3 install <username>_diffusion2d | ||
``` | ||
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### Required dependencies | ||
The following dependencies are required to run the code: | ||
- python >= 3.6 | ||
- numpy: For numerical computations. | ||
- matplotlib: For plotting the diffusion process. | ||
You can install them using: | ||
```bash | ||
pip install numpy matplotlib | ||
``` | ||
Alternatively, if you are installing the package directly, the dependencies will be installed automatically. | ||
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## Running this package | ||
Once the package is installed, you can use the solve() function to simulate the 2D diffusion process. You can run the code either interactively in a Python shell or in a Python script. Simple way is by using Python Shell. Fo that, open Python Shell and run the following command. | ||
```python | ||
>>> from vangasa_diffusion2d import diffusion2d | ||
>>> diffusion2d.solve() | ||
``` | ||
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Or, to customize the parameters (dx, dy, and D), you can pass them like this: | ||
```python | ||
>>> from vangasa_diffusion2d import diffusion2d | ||
>>> diffusion2d.solve(dx=0.05, dy=0.05, D=2.0) | ||
``` | ||
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## Citing | ||
Please follow the instructions in [pypi_exercise.md](https://github.com/Simulation-Software-Engineering/Lecture-Material/blob/main/03_building_and_packaging/pypi_exercise.md). | ||
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If you are interested in the theoretical background of the code, please have a look in Chapter 7 of the book ["Learning Scientific Programming with Python"](https://scipython.com/book/chapter-7-matplotlib/examples/the-two-dimensional-diffusion-equation/) |
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[build-system] | ||
requires = ["setuptools","wheel","build"] | ||
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[project] | ||
name = "vangasa_diffusion2d" | ||
description = "A Python package for 2D heat diffusion simulation" | ||
version = "0.0.2" | ||
authors = [ | ||
{name="Saranya Vanga", email="vangasaranya1289@gmail.com"} | ||
] | ||
readme = "README.md" | ||
requires-python = ">=3.6" | ||
keywords = ["solver" ,"diffusion2D"] | ||
classifiers = [ | ||
"Programming Language :: Python :: 3", | ||
"Operating System :: OS Independent", | ||
] | ||
dependencies = [ | ||
"numpy", | ||
"matplotlib", | ||
] |
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from setuptools import setup | ||
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if __name__ == "__main__": | ||
setup() |
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""" | ||
Solving the two-dimensional diffusion equation | ||
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Example acquired from https://scipython.com/book/chapter-7-matplotlib/examples/the-two-dimensional-diffusion-equation/ | ||
""" | ||
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import numpy as np | ||
import matplotlib.pyplot as plt | ||
from output import create_plot, output_plots | ||
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def solve(dx=0.1, dy=0.1, D=4.0): | ||
# plate size, mm | ||
w = h = 10 | ||
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# Initial cold temperature of square domain | ||
T_cold = 300 | ||
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# Initial hot temperature of circular disc at the center | ||
T_hot = 700 | ||
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# Number of discrete mesh points in X and Y directions | ||
nx, ny = int(w / dx), int(h / dy) | ||
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# Computing a stable time step | ||
dx2, dy2 = dx * dx, dy * dy | ||
dt = dx2 * dy2 / (2 * D * (dx2 + dy2)) | ||
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print("dt = {}".format(dt)) | ||
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u0 = T_cold * np.ones((nx, ny)) | ||
u = u0.copy() | ||
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# Initial conditions - circle of radius r centred at (cx,cy) (mm) | ||
r = min(h, w) / 4.0 | ||
cx = w / 2.0 | ||
cy = h / 2.0 | ||
r2 = r ** 2 | ||
for i in range(nx): | ||
for j in range(ny): | ||
p2 = (i * dx - cx) ** 2 + (j * dy - cy) ** 2 | ||
if p2 < r2: | ||
u0[i, j] = T_hot | ||
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def do_timestep(u_nm1, u, D, dt, dx2, dy2): | ||
# Propagate with forward-difference in time, central-difference in space | ||
u[1:-1, 1:-1] = u_nm1[1:-1, 1:-1] + D * dt * ( | ||
(u_nm1[2:, 1:-1] - 2 * u_nm1[1:-1, 1:-1] + u_nm1[:-2, 1:-1]) / dx2 | ||
+ (u_nm1[1:-1, 2:] - 2 * u_nm1[1:-1, 1:-1] + u_nm1[1:-1, :-2]) / dy2) | ||
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u_nm1 = u.copy() | ||
return u_nm1, u | ||
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# Number of timesteps | ||
nsteps = 101 | ||
# Output 4 figures at these timesteps | ||
n_output = [0, 10, 50, 100] | ||
fig_counter = 0 | ||
fig = plt.figure() | ||
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# Time loop | ||
for n in range(nsteps): | ||
u0, u = do_timestep(u0, u, D, dt, dx2, dy2) | ||
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# Create figure | ||
if n in n_output: | ||
fig_counter += 1 | ||
im = create_plot(fig,fig_counter,T_cold,T_hot,u,n,dt) | ||
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# Finalize and show plots | ||
output_plots(fig, im) | ||
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import matplotlib.pyplot as plt | ||
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def create_plot(fig, fig_counter, T_cold, T_hot,u,n,dt): | ||
ax = fig.add_subplot(220 + fig_counter) | ||
im = ax.imshow(u.copy(), cmap=plt.get_cmap('hot'), vmin=T_cold, vmax=T_hot) # image for color bar axes | ||
ax.set_axis_off() | ||
ax.set_title('{:.1f} ms'.format(n * dt * 1000)) | ||
return im | ||
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def output_plots(fig, im): | ||
fig.subplots_adjust(right=0.85) | ||
cbar_ax = fig.add_axes([0.9, 0.15, 0.03, 0.7]) | ||
cbar_ax.set_xlabel('$T$ / K', labelpad=20) | ||
fig.colorbar(im, cax=cbar_ax) | ||
plt.show() | ||
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On running this command I got:
perhaps a relative import of
output
intodiffusion2d.py
works.