Riemann solvers form a crucial component in solving partial differential equations (PDEs) nu- merically using Discontinuous Galerkin (DG) or Finite Volumes methods, which are invoked extensively often in the final code. This thesis implements HLL-type, exact, and augmented Riemann solvers in the open-source software ExaHyPE 2, an engine to generate simulations for hyperbolic PDEs in first-order formulation. Thereby, the solvers are evaluated and veri- fied with the ADER-DG approach applied to the non-homogeneous shallow water and elastic wave equations in various example problems like dam break, lake at rest, and oscillating lake. The work shows that in this context, the choice of Riemann solver influences properties such as accuracy or well-balancedness. However, due to the high order of convergence, the dif- ferences between the solvers are small, in particular, if scenarios with smooth solutions are considered. Furthermore, the necessary adjustments to the solvers to allow for numerically demanding problems like inundation and tsunami simulations are outlined.     «

Riemann solvers form a crucial component in solving partial differential equations (PDEs) nu- merically using Discontinuous Galerkin (DG) or Finite Volumes methods, which are invoked extensively often in the final code. This thesis implements HLL-type, exact, and augmented Riemann solvers in the open-source software ExaHyPE 2, an engine to generate simulations for hyperbolic PDEs in first-order formulation. Thereby, the solvers are evaluated and veri- fied with the ADER-DG approach applied...     »