A Python Module for the Heat Equation

A Python implementation of the 2D heat equation for simulating temperature diffusion with optional heat sources.

Table of Contents

• Overview
• Sources
• Installation
• Dependencies
• Usage
• License

Overview

This is a Python module developed during MSc studies. It is a simple implementation of the heat equation in 2D. It can be used to simulate the spread of heat in a 2D domain, with two different types of optional sources of heat.

Sources

Type 1 holds a location at a fixed value,

$$ \tag{type 1} T[I_s, J_s] = K,$$

Type 2 applies an additional fixed forcing of K

$$ \tag{type 2} T[I_s, J_s] = T[I_s, J_s] + K $$

Installation

pip install -r requirements.txt

conda env create -f environment.yml

or

pip install -r requirements.txt

Dependencies

• NumPy >= 1.20.0
• Matplotlib >= 3.4.0

The easiest way to install the dependencies is to use the requirements.txt file or create a new environment with the dependencies using the environment.yml file.

Usage

The heat equation solver can be used as follows:

from heat_equation import State, Model, Source

# Initialize the environment
state = State(
    initial_value=30.0,
    boundary_value=10.0,
    lx=1.0,
    ly=1.0,
    dx=0.1,
    dtype=np.float64
)

# Optional: Add sources
sources = [
    Source(i_index=5, j_index=5, value=50.0, source_type=1),
    Source(i_index=2, j_index=2, value=50.0, source_type=2)
]

# Initialize the model
model = Model(
    state=state,
    kappa=0.1,
    sources=sources
)

# run the model
model.run(
    dt=0.01,
    n_steps=5,
    filename="run_1",
    plot_steps=1,
    show=True
)

The result of this implementation is shown on the gif attached at the top of the README.

or use the command line interface:

python main.py --help

python main.py --lx 1.0 --ly 1.0 --dx 0.1 --kappa 0.1 --dt 0.0005 --n-steps 100

License

This project is licensed under the MIT License - see the LICENSE file for details.