On high order positivity-preserving well-balanced finite volume methods for the Euler equations with gravitation
This paper studies three high-order structure-preserving finite volume weighted essentially non-oscillatory (WENO) methods, which are not only well balanced (WB) for a general known hydrostatic equilibrium state but also preserve the positivity of density and pressure, for the compressible Euler equations under gravitational fields. These methods are built on a simple local scaling positivity-preserving (PP) limiter and a modified WENO-ZQ reconstruction exactly preserving the cell average value and scaling invariance. The WB properties of these three methods are achieved based on suitable numerical fluxes and approximation to the gravitational source terms. Based on some convex decomposition techniques as well as several critical properties of the admissible states and numerical flux, we carry out rigorous positivity-preserving analyses for these three WB schemes. We rigorously prove that the three WB methods, coupled with the PP limiter and a strong-stability-preserving time discretization, are always PP under suitable Courant-Friedrichs-Lewy conditions. Extensive numerical examples are provided to confirm WB and PP properties of three methods.
National Natural Science Foundation of China;National Natural Science Foundation of China;National Key Research and Development Program of China[2022YFA1004501];National Science Foundation[DMS-1753581];National Science Foundation[DMS-2309590];
|WOS Research Area|
Computer Science ; Physics
Computer Science, Interdisciplinary Applications ; Physics, Mathematical
|WOS Accession No|
|ESI Research Field|
Cited Times [WOS]:0
|Document Type||Journal Article|
|Department||Department of Mathematics|
1.Beijing Computational Science Research Center,Beijing,100193,China
2.Department of Mathematics & SUSTech International Center for Mathematics,Southern University of Science and Technology,National Center for Applied Mathematics Shenzhen (NCAMS),Shenzhen,Guangdong,518055,China
3.School of Mathematical Sciences,Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing,Xiamen University,Xiamen,Fujian,361005,China
4.Department of Mathematics,The Ohio State University,Columbus,43210,United States
Ren，Yupeng,Wu，Kailiang,Qiu，Jianxian,et al. On high order positivity-preserving well-balanced finite volume methods for the Euler equations with gravitation[J]. Journal of Computational Physics,2023,492.
Ren，Yupeng,Wu，Kailiang,Qiu，Jianxian,&Xing，Yulong.(2023).On high order positivity-preserving well-balanced finite volume methods for the Euler equations with gravitation.Journal of Computational Physics,492.
Ren，Yupeng,et al."On high order positivity-preserving well-balanced finite volume methods for the Euler equations with gravitation".Journal of Computational Physics 492(2023).
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