On high-order numerical schemes for viscous relativistic hydrodynamics through the Kelvin–Helmholtz instability

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dc.contributor.authorTownsend, Jamie F.
dc.contributor.authorInutsuka, Shu-ichiro
dc.contributor.authorKönözsy, László Z.
dc.contributor.authorJenkins, Karl W.
dc.date.accessioned2022-08-03T10:49:02Z
dc.date.available2022-08-03T10:49:02Z
dc.date.issued2022-06-24
dc.description.abstractThis work assesses the dissipative properties of high-order numerical methods for relativistic hydrodynamics. A causal theory of physical dissipation is included within a finite volume high-resolution shock-capturing framework based on the Israel–Stewart theory to study high-order WENO (weighted-essentially non-oscillatory) schemes for simulating the relativistic Kelvin–Helmholtz instability. We provide an estimation of the numerical dissipation of high-order schemes based on results obtained both with and without physically resolved dissipation and determine an empirical relationship between the numerical dissipation and the grid resolution. We consider the appearance of secondary flow features within the evolution of the Kelvin–Helmholtz instability and determine that they are numerical artifacts — this is partly based on arguments presented in terms of a frame-dependent form of the relativistic Reynolds number. There is a potential advantage of using high-order schemes in terms of their accuracy and computational cost on coarser grid resolutions when directly compared to low-order schemes on a fine grid in the presence of physical viscosity. It is possible to find reasonable agreement between numerical results that employ lower-order schemes using a finer grid resolution and results that employ higher order schemes at a coarser grid resolution when sufficient viscosity is present. Overall, the present analysis gives an insight into the numerical dissipation of high-order shock-wave capturing schemes which can be relevant to computational studies of astrophysical phenomena in the relativistic regime. The results presented herein are problem and scheme-dependent and serve to highlight the different roles of numerical and physical dissipation.en_UK
dc.description.sponsorshipCranfield University: EEB6001Ren_UK
dc.identifier.citationTownsend JF, Inutsuka S, Könözsy L, Jenkins KW. (2022) On high-order numerical schemes for viscous relativistic hydrodynamics through the Kelvin–Helmholtz instability, Monthly Notices of the Royal Astronomical Society, Volume 515, Issue 1, September 2022, pp. 451-472en_UK
dc.identifier.eissn1365-2966
dc.identifier.issn0035-8711
dc.identifier.urihttps://doi.org/10.1093/mnras/stac1741
dc.identifier.urihttps://dspace.lib.cranfield.ac.uk/handle/1826/18270
dc.language.isoenen_UK
dc.publisherOxford University Pressen_UK
dc.rightsAttribution-NonCommercial 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by-nc/4.0/*
dc.subjecthydrodynamicsen_UK
dc.subjectinstabilitiesen_UK
dc.subjectrelativistic processesen_UK
dc.subjectmethods: numericalen_UK
dc.titleOn high-order numerical schemes for viscous relativistic hydrodynamics through the Kelvin–Helmholtz instabilityen_UK
dc.typeArticleen_UK

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