MINIMUM PRINCIPLE ON SPECIFIC ENTROPY AND HIGH-ORDER ACCURATE INVARIANT-REGION-PRESERVING NUMERICAL METHODS FOR RELATIVISTIC HYDRODYNAMICS

Wu, Kailiang

2021

10.1137/21M1397994

SIAM JOURNAL ON SCIENTIFIC COMPUTING   影响因子和分区

1064-8275

1095-7197

This paper first explores Tadmor's minimum entropy principle for the special relativistic hydrodynamics (RHD) equations and incorporates this principle into the design of robust proposed schemes are rigorously proven to preserve numerical solutions in a global invariant region constituted by all the known intrinsic constraints: minimum entropy principle, the subluminal constraint on fluid velocity, the positivity of pressure, and the positivity of rest-mass density. Relativistic effects lead to some essential difficulties in the present study which are not encountered in the nonrelativistic case. Most notably, in the RHD case the specific entropy is a highly nonlinear implicit function of the conservative variables, and, moreover, there is also no explicit formula of the flux in terms of the conservative variables. In order to overcome the resulting challenges, we first propose a novel equivalent form of the invariant region by skillfully introducing two auxiliary variables. As a notable feature, all the constraints in the novel form are explicit and linear with respect to the conservative variables. This provides a highly effective approach to theoretically analyze the invariant-region-preserving (IRP) property of numerical schemes for RHD, without any assumption on the IRP property of the exact Riemann solver. Based on this, we prove the convexity of the invariant region and establish the generalized Lax-Friedrichs splitting properties via technical estimates, laying the foundation for our rigorous IRP analyses. It is rigorously shown that the first-order Lax-Friedrichs type scheme for the RHD equations satisfies a local minimum entropy principle and is IRP under a CFL condition. Provably IRP high-order accurate DG and finite volume methods are then developed for the RHD with the help of a simple scaling limiter, which is designed by following the bound-preserving type limiters in the literature. Several numerical examples demonstrate the effectiveness and robustness of the proposed schemes.

minimum entropy principle invariant region bound-preserving relativistic hydro-dynamics discontinuous Galerkin finite volume high-order accuracy

SCI ; EI

英语

第一 ; 通讯

National Natural Science Foundation of China[12171227]

Mathematics

Mathematics, Applied

WOS:000736742800003

SIAM PUBLICATIONS

20221912089777

Entropy ; Galerkin methods ; Hydrodynamics ; Numerical methods

Thermodynamics:641.1 ; Numerical Methods:921.6

MATHEMATICS

Web of Science

Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, Peoples R China

Wu, Kailiang. MINIMUM PRINCIPLE ON SPECIFIC ENTROPY AND HIGH-ORDER ACCURATE INVARIANT-REGION-PRESERVING NUMERICAL METHODS FOR RELATIVISTIC HYDRODYNAMICS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2021,43(6):B1164-B1197.

Wu, Kailiang.(2021).MINIMUM PRINCIPLE ON SPECIFIC ENTROPY AND HIGH-ORDER ACCURATE INVARIANT-REGION-PRESERVING NUMERICAL METHODS FOR RELATIVISTIC HYDRODYNAMICS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,43(6),B1164-B1197.

Wu, Kailiang."MINIMUM PRINCIPLE ON SPECIFIC ENTROPY AND HIGH-ORDER ACCURATE INVARIANT-REGION-PRESERVING NUMERICAL METHODS FOR RELATIVISTIC HYDRODYNAMICS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 43.6(2021):B1164-B1197.