diffusion2d

Description

This small Python project solves the two-dimensional diffusion (heat) equation on a square plate using a finite-difference scheme.

Key points about the model and the code:

• The computational domain is a square plate of size w x h (units in mm in the example).
• The plate is initialized at a base temperature T_cold and contains a circular region in the centre at a higher temperature T_hot.
• The time integration is performed with an explicit forward-difference scheme, while spatial derivatives are approximated with central differences.
• The code computes a stable timestep dt for the explicit scheme from the grid spacings dx, dy and the thermal diffusivity D.
• Parameters such as dx, dy, D and the number of timesteps can be changed by the user.

Code layout and functions (current repository state):

• diffusion2d/diffusion2d/diffusion2d.py – main solver module. It defines solve(w,h,dx,dy,D,T_cold,T_hot) and also can be executed as a script (it calls solve(...) in the if __name__ == "__main__" guard).
• diffusion2d/diffusion2d/output.py – plotting helper functions that the solver uses to create and finalize subplots.

Output:

The script produces four snapshots of the temperature distribution at selected timesteps and arranges them in a single figure with a shared colorbar so the diffusion of heat is easy to observe.

Installing the package

To run the example you only need Python (>= 3.6) and the required libraries (NumPy and Matplotlib).

Recommended steps (macOS / Linux / WSL):

1. Check Python version:

python3 --version

2. If your Python is older than 3.6, update it (for example via Homebrew on macOS):

brew install python

3. (Optional) Create and activate a virtual environment:

python3 -m venv .venv
source .venv/bin/activate

5. Install dependencies:

python3 -m pip install numpy matplotlib

6. Install the package:

pip install -i https://test.pypi.org/simple/ schoenan-diffusion2d==0.0.10

Running this package

Run the script from the repository root. Note: in this repository the solver script is placed in the diffusion2d/ subfolder, so run:

python3 diffusion2d/diffusion2d/diffusion2d.py

Alternatively you can import and call the solver from Python:

from diffusion2d.diffusion2d import solve
# call with default example parameters
solve(10., 10., 0.1, 0.1, 4., 300, 700)

What to expect:

• The script prints the computed timestep dt.
• A plotting window opens showing four subplots (temperature fields at different times) and a shared colorbar.

Notes about plotting helpers:

• diffusion2d/diffusion2d/output.py provides two convenience functions used by the solver:
  • create_plot(fig_counter, T_cold, T_hot, dt, u, n, fig) – creates and configures a single subplot for time index n and returns the AxesImage (im).
  • output_plots(im, fig) – finalizes the figure (adds shared colorbar and shows the plot window).

Tips:

• Try changing dx, dy and D inside diffusion2d.py and observe how dt and runtime change. Smaller dx/dy increase the grid size and therefore the computation time.
• The script computes dt to satisfy the stability condition for the explicit scheme; if you change parameters, check dt to ensure stability.

Citing

If you reuse this example in teaching or publications, please cite the book chapter and the scipython example page:

• "Learning Scientific Programming with Python", chapter 7 (two-dimensional diffusion example).
• scipython.com: The two-dimensional diffusion equation (https://scipython.com/book/chapter-7-matplotlib/examples/the-two-dimensional-diffusion-equation/)