A comparison of approximate non-linear Riemann solvers for Relativistic MHD
We compare a particular selection of approximate solutions of the Riemann problem in the context of ideal relativistic magnetohydrodynamics. In particular, we focus on Riemann solvers not requiring a full eigenvector structure. Such solvers recover the solution of the Riemann problem by solving a si...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2022
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| In: |
Monthly notices of the Royal Astronomical Society
Year: 2022, Volume: 510, Issue: 1, Pages: 481-499 |
| ISSN: | 1365-2966 |
| DOI: | 10.1093/mnras/stab3373 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1093/mnras/stab3373 Verlag, lizenzpflichtig, Volltext: https://www.webofscience.com/api/gateway?GWVersion=2&SrcAuth=DOISource&SrcApp=WOS&KeyAID=10.1093%2Fmnras%2Fstab3373&DestApp=DOI&SrcAppSID=EUW1ED0E40TRwfzoQVMG1L5M6shBs&SrcJTitle=MONTHLY+NOTICES+OF+THE+ROYAL+ASTRONOMICAL+SOCIETY&DestDOIRegistrantName=Oxford+University+Press 
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| Author Notes: | G. Mattia and A. Mignone |
| Summary: | We compare a particular selection of approximate solutions of the Riemann problem in the context of ideal relativistic magnetohydrodynamics. In particular, we focus on Riemann solvers not requiring a full eigenvector structure. Such solvers recover the solution of the Riemann problem by solving a simplified or reduced set of jump conditions, whose level of complexity depends on the intermediate modes that are included. Five different approaches - namely the HLL, HLLC, HLLD, HLLEM, and GFORCE schemes - are compared in terms of accuracy and robustness against one - and multidimensional standard numerical benchmarks. Our results demonstrate that - for weak or moderate magnetizations - the HLLD Riemann solver yields the most accurate results, followed by HLLC solver(s). The GFORCE approach provides a valid alternative to the HLL solver being less dissipative and equally robust for strongly magnetized environments. Finally, our tests show that the HLLEM Riemann solver is not cost-effective in improving the accuracy of the solution and reducing the numerical dissipation. |
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| Item Description: | Advance Access publication 2021 November 24 Gesehen am 07.10.2022 |
| Physical Description: | Online Resource |
| ISSN: | 1365-2966 |
| DOI: | 10.1093/mnras/stab3373 |