On high order positivity-preserving well-balanced finite volume methods for the Euler equations with gravitation

Ren，Yupeng1; Wu，Kailiang2; Qiu，Jianxian3; Xing，Yulong4

2023-11-01

10.1016/j.jcp.2023.112429

Journal of Computational Physics   Impact Factor & Quartile

0021-9991

1090-2716

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.

Compressible Euler equations Gravitational field Positivity preserving Weighted essentially non-oscillatory methods Well-balanced

SCI

English

Others

National Natural Science Foundation of China[12071392];National Natural Science Foundation of China[12171227];National Key Research and Development Program of China[2022YFA1004501];National Science Foundation[DMS-1753581];National Science Foundation[DMS-2309590];

Computer Science ; Physics

Computer Science, Interdisciplinary Applications ; Physics, Mathematical

WOS:001072126300001

ACADEMIC PRESS INC ELSEVIER SCIENCE

PHYSICS

2-s2.0-85169837641

Scopus

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).