A direct Eulerian GRP scheme for relativistic hydrodynamics: One-dimensional case

The paper proposes a direct Eulerian generalized Riemann problem (GRP) scheme for one-dimensional relativistic hydrodynamics. It is an extension of the Eulerian GRP scheme for compressible non-relativistic hydrodynamics proposed in [M. Ben-Artzi, J.Q. Li, G. Warnecke, A direct Eulerian GRP scheme for compressible fluid flows, J. Comput. Phys. 218 (2006) 19-43]. Two main ingredients, the Riemann invariant and the Rankine-Hugoniot jump condition, are directly used to resolve the local GRP in the Eulerian formulation, and thus the crucial and delicate Lagrangian treatment in the original GRP scheme [3] can be avoided. Several numerical examples are given to demonstrate the accuracy and effectiveness of the proposed GRP scheme.