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15 changes: 15 additions & 0 deletions README.md
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Expand Up @@ -7,13 +7,28 @@ Please follow the instructions in [pypi_exercise.md](https://github.com/Simulati
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/).

## 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.

## Installing the package

### Using pip3 to install from PyPI

```bash
pip install -i https://test.pypi.org/simple/ luosg-diffusion2d==0.0.1
```

### Required dependencies

- **Python** >= 3.6
- **NumPy**
- **Matplotlib**

## Running this package
Following Commands could be run in python Shell:
```python
>>> from luosg_diffusion2d import diffusion2d
>>> diffusion2d.solve()
```

## Citing
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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73 changes: 73 additions & 0 deletions luosg_diffusion2d/diffusion2d.py
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"""
Solving the two-dimensional diffusion equation

Example acquired from https://scipython.com/book/chapter-7-matplotlib/examples/the-two-dimensional-diffusion-equation/
"""

import numpy as np
import matplotlib.pyplot as plt
from luosg_diffusion2d.output import create_plot, output_plots


def solve(dx = 0.1, dy = 0.1, D = 4):
# plate size, mm
w = h = 10.


# Initial cold temperature of square domain
T_cold = 300

# Initial hot temperature of circular disc at the center
T_hot = 700

# Number of discrete mesh points in X and Y directions
nx, ny = int(w / dx), int(h / dy)

# Computing a stable time step
dx2, dy2 = dx * dx, dy * dy
dt = dx2 * dy2 / (2 * D * (dx2 + dy2))

print("dt = {}".format(dt))

u0 = T_cold * np.ones((nx, ny))
u = u0.copy()

# 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


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)

u_nm1 = u.copy()
return u_nm1, u


# Number of timesteps
nsteps = 101
# Output 4 figures at these timesteps
n_output = [0, 10, 50, 100]
fig_counter = 0
fig = plt.figure()

# Time loop
for n in range(nsteps):
u0, u = do_timestep(u0, u, D, dt, dx2, dy2)

# Create figure
if n in n_output:
im, fig_counter = create_plot(T_cold, T_hot, dt, u, fig_counter, fig, n)

# Plot output figures
output_plots(fig, im)
16 changes: 16 additions & 0 deletions luosg_diffusion2d/output.py
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import matplotlib.pyplot as plt

def create_plot(T_cold, T_hot, dt, u, fig_counter, fig, n):
fig_counter += 1
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, fig_counter

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()
28 changes: 28 additions & 0 deletions pyproject.toml
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[build-system]
requires = ["setuptools", "wheel"]

[project]
name = "luosg_diffusion2d"
version = "0.0.1"
authors = [
{name="Luo, Shiting", email="[email protected]"}
]
description = "2D diffusion equation simulation"
readme = "README.md"
requires-python = ">=3.6"
license = { file = "LICENSE" }
keywords = ["sse", "2D diffusion"]
classifiers = [
"Programming Language :: Python :: 3",
]
dependencies = [
"numpy",
"matplotlib",
]

[project.urls]
Homepage = "https://github.com/Simulation-Software-Engineering/diffusion2D"


[project.entry-points."simulation"]
solve = "luosg_diffusion2d:solve"
4 changes: 4 additions & 0 deletions setup.py
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from setuptools import setup

if __name__ == "__main__":
setup()
3 changes: 3 additions & 0 deletions test.py
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from luosg_diffusion2d.diffusion2d import solve

solve(dx = 0.1, dy = 0.1, D = 4)