UDG - Upwind Discontinuous Galerkin Method

A minimal python implementation of the upwind discontinuous galerkin method for solving scalar advection equations.

Installation

pip install udg

Or with uv:

uv pip install udg

Quick Start

Step 1: Run the DGSEM solver (Kopriva et al., 2009)

python -m udg.cli sem-dg

Step 2: Run the Nodal-DG solver (Hesthaven et al., 2008)

python -m udg.cli nodal-dg

Step 3: Run the entropy-stable DG solver (Gassner et al., 2013)

python -m udg.cli entropy-dg

Step 4: Run the upwind summation-by-parts DG solver

python -m udg.cli upwind-dg

Development

Setup

# Install uv
curl -LsSf https://astral.sh/uv/install.sh | sh

# Clone and install
git clone https://github.com/jaisw7/udg.git
cd udg
uv sync --all-extras

# Activate virtual environment
source .venv/bin/activate

# Install pre-commit hooks (optional)
pre-commit install

Code Quality

# Format code
make format

# Run linting
make lint

# Type checking
make type-check

# Run all checks
make pre-commit

Contributing

Contributions are welcome! Please:

1. Fork the repository
2. Create a feature branch
3. Make your changes with tests
4. Run make pre-commit to ensure code quality
5. Submit a pull request

License

MIT License - See LICENSE file for details

Disclaimer

This software is for educational and research purposes only.

Support

For issues, questions, or contributions:

• Open an issue on GitHub
• Check documentation
• Review test examples

References

1. Kopriva, David A. Implementing spectral methods for partial differential equations: Algorithms for scientists and engineers. Springer Science & Business Media, 2009.
2. Hesthaven, Jan S., and Tim Warburton. Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications. Springer Science & Business Media, 2008.
3. Gassner, Gregor J. "A skew-symmetric discontinuous Galerkin spectral element discretization and its relation to SBP-SAT finite difference methods." SIAM Journal on Scientific Computing 35.3 (2013): A1233-A1253.

Results

DGSEM

Nodal-DG

Entropy-Stable DG

Upwind DG