{"title":"可压缩斯托克斯方程的梯度-稳健混合 DG 离散法","authors":"P. L. Lederer, C. Merdon","doi":"10.1007/s10915-024-02605-2","DOIUrl":null,"url":null,"abstract":"<p>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 <span>\\(H(\\textrm{div})\\)</span>-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.</p>","PeriodicalId":50055,"journal":{"name":"Journal of Scientific Computing","volume":"25 1","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Gradient-Robust Hybrid DG Discretizations for the Compressible Stokes Equations\",\"authors\":\"P. L. Lederer, C. Merdon\",\"doi\":\"10.1007/s10915-024-02605-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>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 <span>\\\\(H(\\\\textrm{div})\\\\)</span>-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.</p>\",\"PeriodicalId\":50055,\"journal\":{\"name\":\"Journal of Scientific Computing\",\"volume\":\"25 1\",\"pages\":\"\"},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2024-07-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Scientific Computing\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10915-024-02605-2\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Scientific Computing","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10915-024-02605-2","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Gradient-Robust Hybrid DG Discretizations for the Compressible Stokes Equations
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 \(H(\textrm{div})\)-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.
期刊介绍:
Journal of Scientific Computing is an international interdisciplinary forum for the publication of papers on state-of-the-art developments in scientific computing and its applications in science and engineering.
The journal publishes high-quality, peer-reviewed original papers, review papers and short communications on scientific computing.