Heat Diffusion Simulator

A Python project for simulating heat diffusion in 1D materials.

Project Overview

This project aims to implement a numerical simulation of heat diffusion using the heat equation:

∂T/∂t = α * ∂²T/∂x²

where:

• T is temperature
• t is time
• x is position
• α is thermal diffusivity

Project Structure

Heat Diffusion Simulator/
├── src/                    # Source code
├── tests/                  # Unit tests
├── results/                # Output results
├── requirements.txt        # Dependencies
└── README.md              # This file

Dependencies

• Python 3.8+
• NumPy
• Matplotlib
• pytest (for testing)

Installation

pip install -r requirements.txt

Usage

Command-Line Interface

Run simulations using the command-line interface:

cd src
python main.py --alpha 0.01 --L 1.0 --nx 100 --t-end 10.0 --ic gaussian

Available Options

Required Parameters:

• --alpha: Thermal diffusivity (m²/s)
• --L: Length of material (m)
• --nx: Number of grid points
• --t-end: Simulation time (s)

Initial Conditions:

• --ic {gaussian,step}: Initial condition type
• --ic-center: Center position (default: middle)
• --ic-width: Width for Gaussian IC
• --ic-amplitude: Amplitude (default: 1.0)

Boundary Conditions:

• --bc {dirichlet,neumann}: Boundary condition type
• --left-temp: Left boundary temperature
• --right-temp: Right boundary temperature

Output Options:

• --output: Output directory (default: output)
• --csv: Export to CSV format
• --no-plot: Skip plots
• --no-save: Skip saving data
• --quiet: Suppress output

Examples

Gaussian heat pulse:

python main.py --alpha 0.01 --L 1.0 --nx 100 --t-end 10.0 --ic gaussian

Step function with Neumann boundaries:

python main.py --alpha 0.005 --L 2.0 --nx 200 --t-end 20.0 --ic step --bc neumann --csv

Custom output directory:

python main.py --alpha 0.01 --L 1.0 --nx 150 --t-end 15.0 --ic gaussian --output my_results

Features

• ✅ FTCS (Forward-Time Central-Space) finite difference method
• ✅ Multiple initial conditions (Gaussian, step function)
• ✅ Boundary conditions (Dirichlet, Neumann)
• ✅ Stability checking (CFL condition)
• ✅ Temperature profile visualization
• ✅ Temperature evolution plots
• ✅ Data export (NPZ, CSV)
• ✅ Command-line interface

Development Status

This project is being developed incrementally:

• Day 1: Project setup ✓
• Day 2: Core physics implementation ✓
• Day 3: Initial and boundary conditions ✓
• Day 4: Visualization and data output ✓
• Day 5: Command-line interface ✓

Author

Student - Applied Physics Course