tvddg2d
General purpose high-order Discontinunous Galerkin 2D solver for hyperbolic conservation laws problems.
Features:
- Solves homogenous hyperbolic systems with any number of equations. User needs to define the variable vector and the flux computation routines
- Riemmann problem based. Used needs to provide an (approximate) generalized Riemmann solver. Generalized means that not only state variables have a discontinuity but also may have the parameters. If parameters are constant then this problem reduces to regular Riemmann problem.
- High order DG approximation. Each cell is subdivided into several subcells (up to 6x6) to raise the order of the spatial discretization
- Strong stability preserving Runge-Kutta integrators (orders 1-3).
- The scheme is monotonized with a flux limiter technique and is total variation diminishing. It is nessesary to provide routines to define the complete eigendecomposition for the Jacobi matrix of the system.
Here's an example of a droplet simulation inside a basin (left - low order, right - high order TVD). A version without limiting is
not shown since it breaks when water height is negative due to spurious numerical oscillations.
