13th International Workshop on Variational Multiscale and Stabilized Finite Elemements (VMS 18) - Abstract

Merdon, Christian

Well-balanced discretisation of the compressible Stokes problem

This talk suggest a novel well-balanced discretization of the stationary compressible Stokes problem that has a number of interesting properties. First, the upwind-stabilisation discretization of the continuity equation and a pseudo time integration for the density ensures existence of a discrete solution and non-negativity of the discrete density. Second, a reconstruction operator is used in the discretization of the right-hand side functional(s) that maps discretely divergence-free testfunctions to divergence-free ones. This ensures a certain well-balanced property in the sense that arbitrary gradient forces are balanced by the discrete pressure as long as there is enough mass to compensate them. Moreover, if the Mach number converges to zero, the scheme converges to a pressure-robust discretization of the incompressible Stokes problem. All properties are demonstrated in several numerical examples.