A gradient-robust well-balanced scheme for the compressible isothermal Stokes problem
Abstract
A novel notion for constructing a well-balanced scheme - a gradient-robust scheme - is introduced and a showcase application for a steady compressible, isothermal Stokes equations is presented. Gradient-robustness means 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. The scheme is asymptotic-preserving in the sense that it degenerates for low Mach numbers to a recent inf-sup stable and pressure-robust discretization for the incompressible Stokes equations. The convergence of the coupled FEM-FVM scheme for the nonlinear, isothermal Stokes equations is proved by compactness arguments. Numerical examples illustrate the numerical analysis, and show that the novel approach can lead to a dramatically increased accuracy in nearly-hydrostatic low Mach number flows. Numerical examples also suggest that a straight-forward extension to barotropic situations with nonlinear equations of state is feasible.
Keywords
Cite
@article{arxiv.1911.01295,
title = {A gradient-robust well-balanced scheme for the compressible isothermal Stokes problem},
author = {Mine Akbas and Thierry Gallouet and Almut Gassmann and Alexander Linke and Christian Merdon},
journal= {arXiv preprint arXiv:1911.01295},
year = {2020}
}