A physical-constraint-preserving finite volume WENO method for special relativistic hydrodynamics on unstructured meshes

Chen, Yaping1; Wu, Kailiang2

2022-10-01

10.1016/j.jcp.2022.111398

JOURNAL OF COMPUTATIONAL PHYSICS   影响因子和分区

0021-9991

1090-2716

This paper presents a highly robust third-order accurate finite volume weighted essentially non-oscillatory (WENO) method for special relativistic hydrodynamics on unstructured triangular meshes. We rigorously prove that the proposed method is physical-constraintpreserving (PCP), namely, always preserves the positivity of the pressure and the rest-mass density as well as the subluminal constraint on the fluid velocity. The method is built on a highly efficient compact WENO reconstruction on unstructured meshes, a simple PCP limiter, the provably PCP property of the Harten-Lax-van Leer flux, and third-order strong-stability-preserving time discretization. Due to the relativistic effects, the primitive variables (namely, the rest-mass density, velocity, and pressure) are highly nonlinear implicit functions in terms of the conservative variables, making the design and analysis of our method nontrivial. To address the difficulties arising from the strong nonlinearity, we adopt a novel quasilinear technique for the theoretical proof of the PCP property. Three provable convergence-guaranteed iterative algorithms are also introduced for the robust recovery of primitive quantities from admissible conservative variables. We also propose a slight modification to an existing WENO reconstruction to ensure the scaling invariance of the nonlinear weights and thus to accommodate the homogeneity of the evolution operator, leading to the advantages of the modified WENO reconstruction in resolving multi-scale wave structures. Extensive numerical examples are presented to demonstrate the robustness, expected accuracy, and high resolution of the proposed method.

Physical -constraint -preserving Special relativistic hydrodynamics WENO Finite volume High -order accuracy Unstructured mesh

SCI

英语

通讯

National Natural Science Foundation of China["11901460","12171227"]

Computer Science ; Physics

Computer Science, Interdisciplinary Applications ; Physics, Mathematical

WOS:000841979000014

ACADEMIC PRESS INC ELSEVIER SCIENCE

PHYSICS

Web of Science

1.Northwestern Polytech Univ, Sch Math & Stat, Xian Key Lab Sci Computat & Appl Stat, NPU UoG Int Cooperat Lab Computat & Applicat Cardi, Xian 710129, Shaanxi, Peoples R China
2.Southern Univ Sci & Technol, Dept Math & SUSTech Int Ctr Math, Natl Ctr Appl Math Shenzhen NCAMS, Shenzhen 518055, Guangdong, Peoples R China

Chen, Yaping,Wu, Kailiang. A physical-constraint-preserving finite volume WENO method for special relativistic hydrodynamics on unstructured meshes[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2022,466.

Chen, Yaping,&Wu, Kailiang.(2022).A physical-constraint-preserving finite volume WENO method for special relativistic hydrodynamics on unstructured meshes.JOURNAL OF COMPUTATIONAL PHYSICS,466.

Chen, Yaping,et al."A physical-constraint-preserving finite volume WENO method for special relativistic hydrodynamics on unstructured meshes".JOURNAL OF COMPUTATIONAL PHYSICS 466(2022).