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A direct Eulerian GRP scheme for relativistic hydrodynamics: One-dimensional case. (English) Zbl 1408.76597
Summary: 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 et al., J. Comput. Phys. 218, No. 1, 19–43 (2006; Zbl 1158.76375)]. 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 [M. Ben-Artzi und J. Falcovitz, J. Comput. Phys. 55, 1–32 (1984; Zbl 0535.76070)] can be avoided. Several numerical examples are given to demonstrate the accuracy and effectiveness of the proposed GRP scheme.

76Y05 Quantum hydrodynamics and relativistic hydrodynamics
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