This thesis is concerned with the simulation of clouds using the ExaHyPE framework.ExaHyPE is an engine for hyperbolic partial differential equations that uses theader-dgscheme.We use the compressible Navier-Stokes equations for computational fluid dynamics.Due to the diffusive components, the Navier-Stokes equations are not hyperbolic. Wethus need to modify parts of the numerical scheme. In addition, we extend the equationset to the reactive compressible Navier-Stokes equations which include a source termthat models chemical reactions.We develop a gradient-based, global adaptive mesh refinement (amr) indicator thatfinds cells with unusually large gradients.Our implementation is evaluated for standard two and three dimensional fluiddynamics test cases, for flows over a realistic background atmosphere and for a reactivedetonation wave. Additionally, we perform a convergence test and a time-to-solutionbenchmark that evaluates our proposed AMR criterion.     «

This thesis is concerned with the simulation of clouds using the ExaHyPE framework.ExaHyPE is an engine for hyperbolic partial differential equations that uses theader-dgscheme.We use the compressible Navier-Stokes equations for computational fluid dynamics.Due to the diffusive components, the Navier-Stokes equations are not hyperbolic. Wethus need to modify parts of the numerical scheme. In addition, we extend the equationset to the reactive compressible Navier-Stokes equations which include a...     »