Low-effort stabilization for compressible Euler-Equations for volcanic plume simulation

A stabilization method for a discontinuous Galerkin discretization of the compressible Euler equations is presented, based on the idea of balancing the equations discretely. This method is very cost efficient with regards to computational effort while still effective in stabilizing the discrete numerical scheme. We apply the new numerical scheme to standard test cases as well as to a simplified volcanic plume model within an adaptive mesh refinement simulation framework. Comparisons with different adaptive mesh refinement environments (i.e. amatos and deal.II) are perfomed and demonstrate the applicability in particular in triangular adaptive meshes. Tests show that this method generates reliable and computationally efficient results.