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	A direct Eulerian GRP scheme for relativistic hydrodynamics: Two-dimensional case
	Yang, Zhicheng ; Tang, Huazhong
	2012
关键词	Generalized Riemann problem scheme Riemann problem Riemann invariant Rankine-Hugoniot jump condition Relativistic hydrodynamics GENERALIZED RIEMANN PROBLEM GAS-DYNAMICS CONSERVATION-LAWS FLUID-DYNAMICS FLOWS SOLVER
英文摘要	This paper develops a direct Eulerian generalized Riemann problem (GRP) scheme for two-dimensional (2D) relativistic hydrodynamics (RHD). It is an extension of the GRP scheme for one-dimensional (1D) RHDs [Z.C. Yang, P. He, H.Z. Tang, J. Comput. Phys. 230 (2011) 7964-7987] and the GRP scheme for the non-relativistic hydrodynamics [M. Ben-Artzi, J.Q. Li, G. Warnecke, J. Comput. Phys. 218 (2006) 19-43]. In order to derive the direct Eulerian GRP scheme, the (local) GRP of the split 2D RHD equations in the Eulerian formulation has to be directly resolved by using corresponding Riemann invariants and Rankine-Hugoniot jump conditions so that the crucial and delicate Lagrangian treatment in the original GRP scheme [M. Ben-Artzi, J. Falcovitz, J. Comput. Phys. 55 (1984) 1-32] may be avoided. An important difference of resolving the GRP of the split 2D RHD equations from the GRP of the 1D RHD equations or the non-relativistic hydrodynamical equations is coming from the fact that the flow regions across the shock or rarefaction wave in the GRP of the split 2D RHD equations are nonlinearly coupled through the Lorentz factor which is also built in terms of the tangential velocities. It is a purely multi-dimensional relativistic feature. Several numerical examples are given to demonstrate the accuracy and effectiveness of the proposed 2D GRP scheme. (C) 2011 Elsevier Inc. All rights reserved.; Computer Science, Interdisciplinary Applications; Physics, Mathematical; SCI(E); 8; ARTICLE; 4; 2116-2139; 231
语种	英语
出处	SCI
出版者	计算物理学杂志
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/234567]
专题	数学科学学院 工学院
推荐引用方式 GB/T 7714	Yang, Zhicheng,Tang, Huazhong. A direct Eulerian GRP scheme for relativistic hydrodynamics: Two-dimensional case. 2012-01-01.

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