A Second Order Godunov Method for Multidimensional Relativistic Magnetohydrodynamics

Abstract

We describe a new Godunov algorithm for relativistic magnetohydrodynamics (RMHD) that combines a simple, unsplit second order accurate integrator with the constrained transport (CT) method for enforcing the solenoidal constraint on the magnetic field. A variety of approximate Riemann solvers are implemented to compute the fluxes of the conserved variables. The methods are tested with a comprehensive suite of multidimensional problems. These tests have helped us develop a hierarchy of correction steps that are applied when the integration algorithm predicts unphysical states due to errors in the fluxes, or errors in the inversion between conserved and primitive variables. Although used exceedingly rarely, these corrections dramatically improve the stability of the algorithm. We present preliminary results from the application of these algorithms to two problems in RMHD: the propagation of supersonic magnetized jets, and the amplification of magnetic field by turbulence driven by the relativistic Kelvin-Helmholtz instability (KHI). Both of these applications reveal important differences between the results computed with Riemann solvers that adopt different approximations for the fluxes. For example, we show that use of Riemann solvers which include both contact and rotational discontinuities can increase the strength of the magnetic field within the cocoon by a factor of ten in simulations of RMHD jets, and can increase the spectral resolution of three-dimensional RMHD turbulence driven by the KHI by a factor of 2. This increase in accuracy far outweighs the associated increase in computational cost. Our RMHD scheme is publicly available as part of the Athena code.

75 pages, 28 figures, accepted for publication in ApJS. Version with high resolution figures available from http://jila.colorado.edu/~krb3u/Athena_SR/rmhd_method_paper.pdf

References in corpus (8)

• PLUTO: a Numerical Code for Computational Astrophysics
• Athena: A New Code for Astrophysical MHD
• An Unsplit Godunov Method for Ideal MHD via Constrained Transport in Three Dimensions
• ECHO: an Eulerian Conservative High Order scheme for general relativistic magnetohydrodynamics and magnetodynamics
• The Influence of Magnetic Field Geometry on the Evolution of Black Hole Accretion Flows: Similar Disks, Drastically Different Jets
• Equation of State in Relativistic Magnetohydrodynamics: variable versus constant adiabatic index
• An HLLC Solver for Relativistic Flows -- II. Magnetohydrodynamics
• Three-Dimensional Relativistic MHD Simulations of the Kelvin-Helmholtz Instability: Magnetic Field Amplification by a Turbulent Dynamo

Cited by in corpus (77)

• The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohydrodynamic Solvers
• The PLUTO Code for Adaptive Mesh Computations in Astrophysical Fluid Dynamics
• An Extension of the Athena++ Code Framework for GRMHD Based on Advanced Riemann Solvers and Staggered-Mesh Constrained Transport
• THC: a new high-order finite-difference high-resolution shock-capturing code for special-relativistic hydrodynamics
• 3D Turbulent Reconnection: Theory, Tests and Astrophysical Implications
• GRHydro: A new open source general-relativistic magnetohydrodynamics code for the Einstein Toolkit
• Testing Convergence for Global Accretion Disks
• SpECTRE: A Task-based Discontinuous Galerkin Code for Relativistic Astrophysics
• General relativistic simulations of black hole-neutron star mergers: Effects of magnetic fields
• Magnetic energy production by turbulence in binary neutron star mergers
• Three-Dimensional Relativistic Magnetohydrodynamic Simulations of Current-Driven Instability. III. Rotating Relativistic Jets
• Relativistic MHD in dynamical spacetimes: Improved EM gauge condition for AMR grids
• Three-Dimensional Simulations of MHD Turbulence Behind Relativistic Shock Waves and Their Implications for GRBs
• Solving the relativistic magnetohydrodynamics equations with ADER discontinuous Galerkin methods, a posteriori subcell limiting and adaptive mesh refinement
• Numerical Simulations of Driven Relativistic MHD Turbulence
• Morphology of Hydrodynamic Winds: A Study of Planetary Winds in Stellar Environments
• Importance of cooling in triggering the collapse of hypermassive neutron stars
• Spatial growth of current-driven instability in relativistic rotating jets and the search for magnetic reconnection
• Spectral and Intermittency Properties of Relativistic Turbulence
• Large-scale magnetic field generation via the kinetic Kelvin-Helmholtz instability in unmagnetized scenarios
• Hydrodynamics in full general relativity with conservative AMR
• Space-time adaptive ADER-DG schemes for dissipative flows: compressible Navier-Stokes and resistive MHD equations
• Spatial Growth of the Current-Driven Instability in Relativistic Jets
• Local Simulations of Instabilities in Relativistic Jets I: Morphology and Energetics of the Current-Driven Instability
• A High-Order Relativistic Two-Fluid Electrodynamic Scheme with Consistent Reconstruction of Electromagnetic Fields and a Multidimensional Riemann Solver for Electromagnetism
• Variability in Active Galactic Nuclei from Propagating Turbulent Relativistic Jets
• PIC Simulation Methods for Cosmic Radiation and Plasma Instabilities
• GRMHD large eddy simulations with gradient subgrid-scale model
• Simulating gamma-ray binaries with a relativistic extension of RAMSES
• Resistive relativistic MHD simulations of astrophysical jets
• Numerical relativity in spherical coordinates: A new dynamical spacetime and general relativistic MHD evolution framework for the Einstein Toolkit
• Gradient sub-grid-scale model for relativistic MHD Large Eddy Simulations
• A Constrained Transport Method for the Solution of the Resistive Relativistic MHD Equations
• CAFE: A New Relativistic MHD Code
• Dissipative Magnetohydrodynamics for Non-Resistive Relativistic Plasmas
• Gamma-ray Bursts Induced by Turbulent Reconnection
• grim: A Flexible, Conservative Scheme for Relativistic Fluid Theories
• Spritz: a new fully general-relativistic magnetohydrodynamic code
• The structure of steady, relativistic, magnetised jets with rotation
• Radiative Relativistic Magnetohydrodynamic Simulations of Neutron Star Column Accretion in Cartesian Geometry
• 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
• Extension of the sub-grid-scale gradient model for compressible magnetohydrodynamics turbulent instabilities
• High-order accurate entropy stable nodal discontinuous Galerkin schemes for the ideal special relativistic magnetohydrodynamics
• A $4^{\mathrm{th}}$-order accurate finite volume method for ideal classical and special relativistic MHD based on pointwise reconstructions
• 3D RMHD simulations of jet-wind interactions in High Mass X-ray Binaries
• Quantifying energetics and dissipation in magnetohydrodynamic turbulence
• Dynamic Fisheye Grids for Binary Black Holes Simulations
• CosmosDG: An hp-Adaptive Discontinuous Galerkin Code for Hyper-Resolved Relativistic MHD
• 2D Relativistic MHD Simulations of the Kruskal-Schwarzschild Instability in a Relativistic Striped Wind
• GenASiS: General Astrophysical Simulation System. I. Refinable Mesh and Nonrelativistic Hydrodynamics
• A resistive extension for ideal MHD
• Simulating magnetized neutron stars with discontinuous Galerkin methods
• Performance-Portable Binary Neutron Star Mergers with AthenaK
• Theory and Applications of Non-Relativistic and Relativistic Turbulent Reconnection
• Radio-loud AGN variability from three-dimensional propagating relativistic jets
• As A Matter of State: The role of thermodynamics in magnetohydrodynamic turbulence
• A Second-order Divergence-constrained Multidimensional Numerical Scheme for Relativistic Two-Fluid Electrodynamics
• Fast Shocks From Magnetic Reconnection Outflows
• A high-order shock capturing discontinuous Galerkin-finite-difference hybrid method for GRMHD
• Radiative MHD Simulations of Photon Bubbles in Radiation-Supported Magnetized Atmospheres of Neutron Stars with Isotropic Thomson Scattering
• On the correction of conserved variables for numerical RMHD with staggered constrained transport
• AsterX: a new open-source GPU-accelerated GRMHD code for dynamical spacetimes
• A comparison of approximate non-linear Riemann solvers for Relativistic MHD
• Blob formation and ejection from the radiative inefficient accretion flow around massive black hole
• On the application of Jacobian-free Riemann solvers for relativistic radiation magnetohydrodynamics under M1 closure
• The Evolution of High Temperature Plasma in Magnetar Magnetospheres and its Implications for Giant Flares
• Divergence-Free Magnetohydrodynamics on Conformally Moving, Adaptive Meshes Using a Vector Potential Method
• Resistive and multi-fluid RMHD on graphics processing units
• Covariant approach to relativistic large-eddy simulations: Lagrangian filtering
• KHARMA: Flexible, Portable Performance for GRMHD
• Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows
• Assessing the role of the Kelvin-Helmholtz instability at the QCD cosmological phase transition
• A general relativistic magnetohydrodynamics extension to mesh-less schemes in the code GIZMO
• Internal shocks in microquasar jets with a continuous Lorentz factor modulation
• Constraints Preserving Lax-Wendroff Flux Reconstruction for Relativistic Hydrodynamics with General Equations of State
• Shock corrugation to the rescue of the internal shock model in microquasars: The single-scale MHD view