Leibniz MMS Days 2022 - Abstract

Merdon, Christian

A novel gradient-robust, well-balanced discretisation for the compressible Stokes problem

This talk presents a recent well-balanced discretisation of the stationary compressible isothermal Stokes problem based on the concept of gradient-robustness. Gradient-robustness ensures that arbitrary gradient fields in the momentum balance are well-balanced by the discrete pressure gradient, if there is enough mass in the system to compensate the force, which is relevant e.g. in an atmosphere-at-rest scenario over non-flat bottom topography. The scheme is also provably convergent and asymptotic-preserving in the sense that it degenerates for low Mach numbers to a recent inf-sup stable and pressure-robust modified Bernardi--Raugel finite element method for the incompressible Stokes equations. All properties are demonstrated in numerical examples.