Lederer P L, Merdon C
Department of Applied Mathematics, University of Twente, Hallenweg 19, 7522NH Enschede, Netherlands.
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany.
J Sci Comput. 2024;100(2):54. doi: 10.1007/s10915-024-02605-2. Epub 2024 Jul 4.
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 -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.
本文针对可压缩斯托克斯方程的速度-密度公式，研究了两种混合间断伽辽金（HDG）离散化方法，涉及几个期望的结构特性，即可证明的收敛性、密度的非负性和质量约束的保持以及梯度鲁棒性。后一种特性显著提高了在诸如压力梯度平衡重力的静水压力平衡等平衡情况下的精度。所研究的方案之一采用了一个符合(H^1)的速度试探空间，该空间确保了所有上述特性，而一种完全间断方法被证明满足除梯度鲁棒性之外的所有特性。此外，还给出了两种变体的高阶格式，并在三个数值基准问题中进行了比较。最后一个例子表明，这对于可压缩纳维-斯托克斯方程的非静水压力平衡状态也很重要。
