A comparison of approximate non-linear Riemann solvers for Relativistic MHD

• Verfasst von: Mattia, Giancarlo [VerfasserIn]
• Verfasst von: Mignone, Andrea [VerfasserIn]
• Titel: A comparison of approximate non-linear Riemann solvers for Relativistic MHD
• Verf.angabe: G. Mattia and A. Mignone
• Jahr: 2022
• Umfang: 19 S.
• Fussnoten: Advance Access publication 2021 November 24 ; Gesehen am 07.10.2022
• Titel Quelle: Enthalten in: Royal Astronomical SocietyMonthly notices of the Royal Astronomical Society
• Ort Quelle: Oxford : Oxford Univ. Press, 1827
• Jahr Quelle: 2022
• Band/Heft Quelle: 510(2022), 1, Seite 481-499
• ISSN Quelle: 1365-2966
• DOI: doi:10.1093/mnras/stab3373
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: central-type scheme
• Sach-SW: code
• Sach-SW: flows
• Sach-SW: godunov-type methods
• Sach-SW: magnetohydrodynamics
• Sach-SW: methods: numerical
• Sach-SW: mhd
• Sach-SW: relativistic processes
• Sach-SW: shock waves
• Sach-SW: waves
• K10plus-PPN: 1818242621

Abstract

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.