A Fourth-Order Finite Volume Scheme for Resistive Relativistic Magnetohydrodynamics

Fuente: arXiv
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Main Authors: Mignone, Andrea, Berta, Vittoria, Rossazza, Marco, Bugli, Matteo, Mattia, Giancarlo, Del Zanna, Luca, Pareschi, Lorenzo
Format: Preprint
Published: 2024
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_version_ 1866914866524061696
author Mignone, Andrea
Berta, Vittoria
Rossazza, Marco
Bugli, Matteo
Mattia, Giancarlo
Del Zanna, Luca
Pareschi, Lorenzo
author_facet Mignone, Andrea
Berta, Vittoria
Rossazza, Marco
Bugli, Matteo
Mattia, Giancarlo
Del Zanna, Luca
Pareschi, Lorenzo
contents We present a finite-volume, genuinely 4th-order accurate numerical method for solving the equations of resistive relativistic magnetohydrodynamics (Res-RMHD) in Cartesian coordinates. In our formulation, the magnetic field is evolved in time in terms of face-average values via the constrained-transport method while the remaining variables (density, momentum, energy and electric fields) are advanced as cell volume-averages. Spatial accuracy employs 5th-order accurate WENO-Z reconstruction from point values (as described in a companion paper) to obtain left and right states at zone interfaces. Explicit flux evaluation is carried out by solving a Riemann problem at cell interfaces, using the Maxwell-Harten-Lax-van Leer with contact wave resolution (MHLLC). Time stepping is based on the implicit-explicit (IMEX) Runge-Kutta (RK) methods, of which we consider both the 3rd-order strong stability preserving SSP3(4,3,3) and a recent 4th-order additive RK scheme, to cope with the stiffness introduced by the source term in Ampere's law. Numerical benchmarks are presented in order to assess the accuracy and robustness of our implementation.
format Preprint
id arxiv_https___arxiv_org_abs_2407_08519
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A Fourth-Order Finite Volume Scheme for Resistive Relativistic Magnetohydrodynamics
Mignone, Andrea
Berta, Vittoria
Rossazza, Marco
Bugli, Matteo
Mattia, Giancarlo
Del Zanna, Luca
Pareschi, Lorenzo
High Energy Astrophysical Phenomena
We present a finite-volume, genuinely 4th-order accurate numerical method for solving the equations of resistive relativistic magnetohydrodynamics (Res-RMHD) in Cartesian coordinates. In our formulation, the magnetic field is evolved in time in terms of face-average values via the constrained-transport method while the remaining variables (density, momentum, energy and electric fields) are advanced as cell volume-averages. Spatial accuracy employs 5th-order accurate WENO-Z reconstruction from point values (as described in a companion paper) to obtain left and right states at zone interfaces. Explicit flux evaluation is carried out by solving a Riemann problem at cell interfaces, using the Maxwell-Harten-Lax-van Leer with contact wave resolution (MHLLC). Time stepping is based on the implicit-explicit (IMEX) Runge-Kutta (RK) methods, of which we consider both the 3rd-order strong stability preserving SSP3(4,3,3) and a recent 4th-order additive RK scheme, to cope with the stiffness introduced by the source term in Ampere's law. Numerical benchmarks are presented in order to assess the accuracy and robustness of our implementation.
title A Fourth-Order Finite Volume Scheme for Resistive Relativistic Magnetohydrodynamics
topic High Energy Astrophysical Phenomena
url https://arxiv.org/abs/2407.08519