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Commun. Comput. Phys., 34 (2023), pp. 955-992.
Published online: 2023-11
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This paper develops the genuinely multidimensional HLL Riemann solver for the two-dimensional special relativistic hydrodynamic equations on Cartesian meshes and studies its physical-constraint-preserving (PCP) property. Based on the resulting HLL solver, the first- and high-order accurate PCP finite volume schemes are proposed. In the high-order scheme, the WENO reconstruction, the third-order accurate strong-stability-preserving time discretizations and the PCP flux limiter are used. Several numerical results are given to demonstrate the accuracy, performance and resolution of the shock waves and the genuinely multi-dimensional wave structures etc. of our PCP finite volume schemes.
}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0065}, url = {http://global-sci.org/intro/article_detail/cicp/22128.html} }This paper develops the genuinely multidimensional HLL Riemann solver for the two-dimensional special relativistic hydrodynamic equations on Cartesian meshes and studies its physical-constraint-preserving (PCP) property. Based on the resulting HLL solver, the first- and high-order accurate PCP finite volume schemes are proposed. In the high-order scheme, the WENO reconstruction, the third-order accurate strong-stability-preserving time discretizations and the PCP flux limiter are used. Several numerical results are given to demonstrate the accuracy, performance and resolution of the shock waves and the genuinely multi-dimensional wave structures etc. of our PCP finite volume schemes.