Dynamical Low-Rank Solver for the Boltzmann Equation

This project is a simplified Python implementation of the numerical methods described in the academic paper: "Asymptotic-preserving dynamical low-rank method for the stiff nonlinear Boltzmann equation".

[Link to the paper on ScienceDirect]

The code was personally refactored from the original MATLAB research code into a structured and more accessible Python application.

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Project Structure

The monolithic research script was reorganized into a clean, modular structure that separates distinct functionalities for improved clarity and maintainability.

dlr-boltzmann-solver/
├── src/
│   ├── collision.py          # The Boltzmann collision operator
│   ├── initial_conditions.py # Functions to set up problem scenarios
│   ├── numerics.py           # Core numerical schemes (e.g., MUSCL)
│   ├── solvers.py            # Main solver functions (Full and DLR)
│   └── visualization.py      # Plotting and results visualization
│
├── tests/
│   ├── test_initial_conditions.py
│   └── test_numerics.py
│
├── main.py                     # Main script with CLI to run simulations
├── requirements.txt            # Project dependencies
└── README.md                   # This file

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Setup and Installation

1. Clone the repository:

   git clone <your-repo-url>
   cd dlr-boltzmann-solver

2. Create and activate a virtual environment (recommended):

   python -m venv venv
   source venv/bin/activate  # On Windows, use `venv\Scripts\activate`

3. Install the required dependencies:

   pip install -r requirements.txt

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How to Run a Simulation

The simulation is controlled via the command line from the project's root directory.

Example 1: Run both the Full and the DLR solvers with default settings.

python main.py --methods full dlr

Example 2: Run only the DLR solver with a specific rank of 8 and a max time of 0.2.

python main.py --methods dlr --rank 8 --tmax 0.2

Example 3: Run the simulation for the 'shock' problem instead of the default 'sin' problem.

python main.py --problem shock

Output plots will be saved in the simulation_results/ directory.

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Testing 🧪

This project uses pytest for unit testing to ensure the reliability of core numerical and setup functions.

To run the test suite, execute the following command from the root directory:

python -m pytest -v

All tests should pass, confirming that the fundamental components of the code are working as expected.

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Sample Output

The script generates plots comparing the macroscopic quantities (density, velocity, temperature) calculated by the different methods.