DGax: Discontinuous Galerkin Solver for 2D Euler Equations

Overview

This project implements a Discontinuous Galerkin (DG) solver for 2D Euler equations. This is based on the matlab code https://github.com/tcew/nodal-dg It includes modules for mesh generation, boundary condition handling, and numerical flux computation.

Requirements

To run this project, you need the following Python packages installed:

• numpy
• scipy

You can install the required packages using the following command:

pip install numpy scipy

Project Structure

• Mesh.py: Contains the Elements class for mesh geometric computations.
• Euler2D.py: Implements the 2D Euler solver using the DG method.
• euler_BC_IC.py: Defines boundary and initial conditions for the Euler equations.
• utils.py: Utility functions for reading mesh files and comparing results with MATLAB outputs.
• constants.py: Contains constants used throughout the project.

Usage

1. Solve 2D Euler Equations

To solve the 2D Euler equations using the DG method, run:

python Euler2D.py

2. Compare Results with MATLAB

If you have MATLAB .mat files for comparison, ensure they are in the same directory and run the corresponding scripts to compare results.

Notes

• Ensure the mesh file (e.g., vortexA04.neu) is in the same directory as the scripts.
• The project is designed to work with Gambit .neu mesh files.

License

This project is licensed under the MIT License.