TY - JOUR
T1 - Gradient-Robust Hybrid DG Discretizations for the Compressible Stokes Equations
AU - Lederer, P.L.
AU - Merdon, C.
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/8
Y1 - 2024/8
N2 - 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.
AB - 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.
KW - UT-Hybrid-D
KW - Gradient-robustness
KW - Hybrid discontinuous Galerkin methods
KW - Well-balanced schemes
KW - Compressible Stokes equations
UR - http://www.scopus.com/inward/record.url?scp=85197509147&partnerID=8YFLogxK
U2 - 10.1007/s10915-024-02605-2
DO - 10.1007/s10915-024-02605-2
M3 - Article
AN - SCOPUS:85197509147
SN - 0885-7474
VL - 100
JO - Journal of scientific computing
JF - Journal of scientific computing
IS - 2
M1 - 54
ER -