General DG FEM code.
Compared to the 1.0 version, the performance of the code was significantly improved by handling more efficiently the data.
(N.B.: the Travis problems have been fixed.)

General DG FEM code.
Compared to the 1.0 version, the performance of the code was significantly improved by handling more efficiently the data.
(N.B.: still some problems with Travis.)

DG code applied to Shallow Water equations

Extension to shallow water equations, and more generally to systems of (possibly coupled) non-linear hyperbolic equations.

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.

First code that seems to go in the right direction.

First Milestone (unfinished)
What still needs to be done:
• debug the flux vectors φ and ψ (in progress) ;
• take into account the boundary conditions ;
• try the 2D simple transport case and debug the code ;
• display the results using gmsh;
• clean the code (refactoring).