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A Third-Order Accurate Direct Eulerian GRP Scheme for One-Dimensional Relativistic Hydrodynamics

Published online by Cambridge University Press:  28 May 2015

Kailiang Wu ,
Zhicheng Yang  and
Huazhong Tang
Kailiang Wu*
Affiliation:
HEDPS, CAPT & LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, PR., China
Zhicheng Yang*
Affiliation:
HEDPS, CAPT & LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, PR., China
Huazhong Tang*
Affiliation:
HEDPS, CAPT & LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, PR., China
*
Corresponding author. Email Address: wukl@pku.edu.cn
Corresponding author. Email Address: yangzhicheng@foxmail.com
Corresponding author. Email Address: hztang@math.pku.edu.en
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Abstract

A third-order accurate direct Eulerian generalised Riemann problem (GRP) scheme is derived for the one-dimensional special relativistic hydrodynamical equations. In our GRP scheme, the higher-order WENO initial reconstruction is employed, and the local GRPs in the Eulerian formulation are directly and analytically resolved to third-order accuracy via the Riemann invariants and Rankine-Hugoniot jump conditions, to get the approximate states in numerical fluxes. Unlike a previous second-order accurate GRP scheme, for the non-sonic case the limiting values of the second-order time derivatives of the fluid variables at the singular point are also needed for the calculation of the approximate states; while for the sonic case, special attention is paid because the calculation of the second-order time derivatives at the sonic point is difficult. Several numerical examples are given to demonstrate the accuracy and effectiveness of our GRP scheme.

Keywords

65M0676M1276Y05Godunov-type schemeWENOgeneralised Riemann problemRiemann invariantRankine-Hugoniot jump conditionrelativistic hydrodynamics
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 4 , Issue 2 , May 2014 , pp. 95 - 131
Copyright
Copyright © Global-Science Press 2014

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