Gradient-Robust Hybrid DG Discretizations for the Compressible Stokes Equations

P.L. Lederer*, C. Merdon

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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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.

Original languageEnglish
Article number54
JournalJournal of scientific computing
Volume100
Issue number2
DOIs
Publication statusPublished - Aug 2024

Keywords

  • UT-Hybrid-D
  • Gradient-robustness
  • Hybrid discontinuous Galerkin methods
  • Well-balanced schemes
  • Compressible Stokes equations

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