2D DG code

Discontinuous Galerkin code that can be used to simulate conservation laws. The time-integration solver is explicit, and uses Runge-Kutta methods.

The assumptions are the following:

• 2D mesh, coming from a .msh file (using gmsh);
• the elements edges are straight (constant normal vector over it);
• the conservation law take the form of a simple transport case f=au, with a a constant and homogeneous velocity.

This last assumption can be easily removed, by introducing manually another flux in the code. Simulations have shown that the code was working for both a non-constant as well as an inhomogeneous velocity field. Non-linear fluxes (e.g. f=au²/2) are also supported, thanks to the general formulation of the DG method.

Furthermore, the code could eventually be extended to 1D and 3D cases.