The Exact Solution of the Riemann Problem in Relativistic MHD

Abstract

We discuss the procedure for the exact solution of the Riemann problem in special relativistic magnetohydrodynamics (MHD). We consider both initial states leading to a set of only three waves analogous to the ones in relativistic hydrodynamics, as well as generic initial states leading to the full set of seven MHD waves. Because of its generality, the solution presented here could serve as an important test for those numerical codes solving the MHD equations in relativistic regimes.

arXiv comment36 pages, 13 figures. Minor changes to match published version

References in corpus (16)

• HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics
• Three-dimensional relativistic simulations of rotating neutron-star collapse to a Kerr black hole
• An efficient shock-capturing central-type scheme for multidimensional relativistic flows. I. Hydrodynamics
• Relativistic Magnetohydrodynamics In Dynamical Spacetimes: Numerical Methods And Tests
• GENESIS: A high-resolution code for 3D relativistic hydrodynamics
• General relativistic MHD simulations of monopole magnetospheres of black holes
• The runaway instability of thick discs around black holes. I. The constant angular momentum case
• The Exact Solution of the Riemann Problem in Relativistic MHD
• Three-dimensional simulations of stellar core collapse in full general relativity: Nonaxisymmetric dynamical instabilities
• The runaway instability of thick discs around black holes. II. Non constant angular momentum discs
• Relativistic Hydrodynamic Evolutions with Black Hole Excision
• An Improved Exact Riemann Solver for Relativistic Hydrodynamics
• General Relativistic Magnetohydrodynamic Simulations of Collapsars
• New Relativistic Effects in the Dynamics of Nonlinear Hydrodynamical Waves
• The exact solution of the Riemann problem in relativistic MHD with tangential magnetic fields
• Quasi-Periodic Oscillations in Relativistic Tori

Cited by in corpus (79)

• The PLUTO Code for Adaptive Mesh Computations in Astrophysical Fluid Dynamics
• ECHO: an Eulerian Conservative High Order scheme for general relativistic magnetohydrodynamics and magnetodynamics
• The Black Hole Accretion Code
• Very High Order $\PNM$ Schemes on Unstructured Meshes for the Resistive Relativistic MHD Equations
• Accurate evolutions of inspiralling and magnetized neutron-stars: equal-mass binaries
• Beyond ideal MHD: towards a more realistic modeling of relativistic astrophysical plasmas
• Semi-implicit scheme for treating radiation under M1 closure in general relativistic conservative fluid dynamics codes
• General-relativistic resistive magnetohydrodynamics in three dimensions: Formulation and tests
• WhiskyMHD: a new numerical code for general relativistic magnetohydrodynamics
• Numerical magneto-hydrodynamics for relativistic nuclear collisions
• GRHydro: A new open source general-relativistic magnetohydrodynamics code for the Einstein Toolkit
• WHAM: A WENO-based general relativistic numerical scheme I: Hydrodynamics
• Impulsive Acceleration of Strongly Magnetized Relativistic Flows
• The Exact Solution of the Riemann Problem in Relativistic MHD
• Analytic Bjorken flow in one-dimensional relativistic magnetohydrodynamics
• A five-wave HLL Riemann solver for relativistic MHD
• Can magnetic fields be detected during the inspiral of binary neutron stars?
• A Particle Module for the PLUTO code: II - Hybrid Framework for Modeling Non-thermal emission from Relativistic Magnetized flows
• Bjorken flow in one-dimensional relativistic magnetohydrodynamics with magnetization
• Relativistic MHD with Adaptive Mesh Refinement
• Solving the relativistic magnetohydrodynamics equations with ADER discontinuous Galerkin methods, a posteriori subcell limiting and adaptive mesh refinement
• High Order Lagrangian ADER-WENO Schemes on Unstructured Meshes - Application of Several Node Solvers to Hydrodynamics and Magnetohydrodynamics
• Hydrodynamics in full general relativity with conservative AMR
• Effect of intense magnetic fields on reduced-MHD evolution in $\sqrt{s_{\mathrm{NN}}}$ = 200 GeV Au+Au collisions
• ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics
• Relativistic Magnetohydrodynamics: Renormalized eigenvectors and full wave decomposition Riemann solver
• A multidimensional grid-adaptive relativistic magnetofluid code
• Magnetohydrodynamic Effects in Propagating Relativistic Jets: Reverse Shock and Magnetic Acceleration
• On the dynamic efficiency of internal shocks in magnetized relativistic outflows
• Admissible state and physical constraints preserving schemes for relativistic magnetohydrodynamic equations
• A Subluminal Relativistic Magnetohydrodynamics Scheme with ADER-WENO Predictor and Multidimensional Riemann Solver-Based Corrector
• Simulating gamma-ray binaries with a relativistic extension of RAMSES
• A New numerical scheme for resistive relativistic MHD using method of characteristics
• On Arbitrary-Lagrangian-Eulerian One-Step WENO Schemes for Stiff Hyperbolic Balance Laws
• A Constrained Transport Method for the Solution of the Resistive Relativistic MHD Equations
• Relativistic MHD and black hole excision: Formulation and initial tests
• CAFE: A New Relativistic MHD Code
• Implementation of advanced Riemann solvers in a neutrino-radiation magnetohydrodynamics code in numerical relativity and its application to a binary neutron star merger
• General relativistic smoothed particle hydrodynamics
• High Order Cell-Centered Lagrangian-Type Finite Volume Schemes with Time-Accurate Local Time Stepping on Unstructured Triangular Meshes
• Runge-Kutta discontinuous Galerkin methods for the special relativistic magnetohydrodynamics
• Entropy Symmetrization and High-Order Accurate Entropy Stable Numerical Schemes for Relativistic MHD Equations
• Exact solution of the hydrodynamical Riemann problem with nonzero tangential velocities and the ultrarelativistic equation of state
• Spritz: a new fully general-relativistic magnetohydrodynamic code
• The structure of steady, relativistic, magnetised jets with rotation
• Three Dimensional Magneto Hydrodynamical Simulations of Gravitational Collapse of a 15Msun Star
• An HLLC Riemann Solver for Resistive Relativistic Magnetohydrodynamics
• GRaM-X: A new GPU-accelerated dynamical spacetime GRMHD code for Exascale computing with the Einstein Toolkit
• The Role of the Equation of State in Resistive Relativistic Magnetohydrodynamics
• Charge diffusion in relativistic resistive second-order dissipative magnetohydrodynamics
• An extension of Gmunu: General-relativistic resistive magnetohydrodynamics based on staggered-meshed constrained transport with elliptic cleaning
• Effect of Interacting Rarefaction Waves on Relativistically Hot Jets
• 3D RMHD simulations of jet-wind interactions in High Mass X-ray Binaries
• On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state
• Evolution of 3-dimensional Relativistic Current Sheets and Development of Self-Generated Turbulence
• Inflationary Universe with a Viscous Fluid Avoiding Self-Reproduction
• Relativistic resistive magneto-hydrodynamics code for high-energy heavy-ion collisions
• Simulating magnetized neutron stars with discontinuous Galerkin methods
• Richtmyer-Meshkov Type Instability of a Current Sheet in a Relativistically Magnetized Plasma
• Performance-Portable Binary Neutron Star Mergers with AthenaK
• Thermal conductivity of evolving quark-gluon plasma in the presence of a time-varying magnetic field
• Lorentz transformation in Maxwell equations for slowly moving media
• A high-order shock capturing discontinuous Galerkin-finite-difference hybrid method for GRMHD
• A Multidimensional Relativistic Hydrodynamics Code with a General Equation of State
• Scaling of the Anomalous Boost in Relativistic Jet Boundary Layer
• AsterX: a new open-source GPU-accelerated GRMHD code for dynamical spacetimes
• 1+1 dimensional relativistic magnetohydrodynamics with longitudinal acceleration
• Linear Wave Propagation for Resistive Relativistic Magnetohydrodynamics
• A comparison of approximate non-linear Riemann solvers for Relativistic MHD
• Implementing a new recovery scheme for primitive variables in the general relativistic magnetohydrodynamic code Spritz
• Numerical general relativistic MHD with magnetically polarized matter
• Resistive and multi-fluid RMHD on graphics processing units
• Relativistic oblique shocks with ordered or random magnetic fields: tangential field governs
• Quadrature-based Lattice Boltzmann Model for Relativistic Flows
• Reverse shock forming condition for magnetized relativistic outflows: reconciling theories and simulations
• A general relativistic extension to mesh-free methods for hydrodynamics
• General relativistic hydrodynamics code for dynamical spacetimes with curvilinear coordinates, tabulated equations of state, and neutrino physics
• A general relativistic magnetohydrodynamics extension to mesh-less schemes in the code GIZMO
• Physical Constraint Preserving Higher Order Finite Volume Schemes for Divergence-Free Astrophysical MHD and RMHD