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arXiv · 2311.06098

Gradient-robust hybrid DG discretizations for the compressible Stokes equations

Philip L. Lederer·Christian Merdon
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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.

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Philip L. Lederer, Christian Merdon. 2023-11-10. Gradient-robust hybrid DG discretizations for the compressible Stokes equations. https://arxiv.org/abs/2311.06098

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