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Volume 34, Issue 4
Genuinely Multidimensional Physical-Constraints-Preserving Finite Volume Schemes for the Special Relativistic Hydrodynamics

Dan Ling & Huazhong Tang

DOI: 10.4208/cicp.OA-2023-0065

Commun. Comput. Phys., 34 (2023), pp. 955-992.

Published online: 2023-11

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  • Abstract

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.

  • Keywords

Genuinely multidimensional schemes, HLL, physical-constraint-preserving property, high order accuracy, special relativistic hydrodynamics.

  • AMS Subject Headings

65M08, 35L02, 76Y05, 83A05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-34-955, author = {Ling , Dan and Tang , Huazhong}, title = {Genuinely Multidimensional Physical-Constraints-Preserving Finite Volume Schemes for the Special Relativistic Hydrodynamics}, journal = {Communications in Computational Physics}, year = {2023}, volume = {34}, number = {4}, pages = {955--992}, abstract = {

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} }
TY - JOUR T1 - Genuinely Multidimensional Physical-Constraints-Preserving Finite Volume Schemes for the Special Relativistic Hydrodynamics AU - Ling , Dan AU - Tang , Huazhong JO - Communications in Computational Physics VL - 4 SP - 955 EP - 992 PY - 2023 DA - 2023/11 SN - 34 DO - http://doi.org/10.4208/cicp.OA-2023-0065 UR - https://global-sci.org/intro/article_detail/cicp/22128.html KW - Genuinely multidimensional schemes, HLL, physical-constraint-preserving property, high order accuracy, special relativistic hydrodynamics. AB -

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.

Dan Ling & Huazhong Tang. (2023). Genuinely Multidimensional Physical-Constraints-Preserving Finite Volume Schemes for the Special Relativistic Hydrodynamics. Communications in Computational Physics. 34 (4). 955-992. doi:10.4208/cicp.OA-2023-0065
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