Gradient-robust hybrid DG discretizations for the compressible Stokes equations
Abstract
This paper studies two hybrid discontinuous Galerkin (HDG) discretizations for the velocity-density formulation of the compressible Stokes equations with respect to several desired structural properties, namely provable convergence, the preservation of non-negativity and mass constraints for the density, and gradient-robustness. The later property dramatically enhances the accuracy in well-balanced situations, such as the hydrostatic balance where the pressure gradient balances the gravity force. One of the studied schemes employs an H(div)-conforming velocity ansatz space which ensures all mentioned properties, while a fully discontinuous method is shown to satisfy all properties but the gradient-robustness. Also higher-order schemes for both variants are presented and compared in three numerical benchmark problems. The final example shows the importance also for non-hydrostatic well-balanced states for the compressible Navier-Stokes equations.
Cite
@article{arxiv.2311.06098,
title = {Gradient-robust hybrid DG discretizations for the compressible Stokes equations},
author = {Philip L. Lederer and Christian Merdon},
journal= {arXiv preprint arXiv:2311.06098},
year = {2023}
}