README.md

Diffusion Simulation

Numerical solutions of the diffusion equation in 1-D and 2-D, with comparison to analytical results.

Structure

diffusion_simulation/
├── src/
│   ├── 1d_diffusion_fipy.py       # Explicit FiPy solver (Notebook 1)
│   └── diffusion_analysis.py      # Crank–Nicholson + 2-D Laplace (Notebook 2)
├── results/
│   └── RESULTS.txt                # Detailed description of physics & outputs
└── requirements.txt

Setup

pip install -r requirements.txt

Note: fipy is only required for 1d_diffusion_fipy.py. diffusion_analysis.py needs only numpy, scipy, and matplotlib.

Run

# FiPy explicit scheme (1-D diffusion, script 1)
python src/1d_diffusion_fipy.py

# Crank–Nicholson + 2-D Laplace (script 2)
python src/diffusion_analysis.py

Physics overview

Script	Equation	Method
1d_diffusion_fipy.py	∂φ/∂t = D ∂²φ/∂x²	Explicit FV (FiPy)
diffusion_analysis.py §2	Same, analytical	Error function (erf)
diffusion_analysis.py §3–4	Same	Crank–Nicholson FV
diffusion_analysis.py §5	∂²c/∂x² + ∂²c/∂y² = 0	Implicit FV (2-D)

See results/RESULTS.txt for a full description of each simulation, boundary conditions, and the bug-fixes applied from the original notebooks.