Physical Constraint Preserving Higher Order Finite Volume Schemes for Divergence-Free Astrophysical MHD and RMHD
arXiv:2506.11181 · doi:10.3847/1538-4357/ade397
Abstract
Higher order finite volume schemes for magnetohydrodynamics (MHD) and relativistic magnetohydrodynamics (RMHD) are very valuable because they allow us to carry out astrophysical simulations with very high accuracy. However, astrophysical problems sometimes have unusually large Mach numbers, exceptionally high Lorentz factors and very strong magnetic fields. All these effects cause higher order codes to become brittle and prone to code crashes. In this paper we document physical constraint preserving (PCP) methods for treating numerical MHD and RMHD. While unnecessary for standard problems, for stringent astrophysical problems these methods show their value. We describe higher order methods that allow divergence-free evolution of the magnetic field. We present a novel two-dimensional Riemann solver. This two-dimensional Riemann solver plays a key role in the design of PCP schemes for MHD and RMHD. We present a very simple PCP formulation and show how it is amalgamated with the evolution of face-centered magnetic fields. The methods presented here are time-explicit and do not add much to the computational cost. We show that the methods meet their design accuracies and work well on problems that would otherwise be considered too extreme for typical higher order Godunov methods of the type used in computational astrophysics.
Accepted in "The Astrophysical Journal (ApJ)"
References in corpus (27)
- HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics
- ECHO: an Eulerian Conservative High Order scheme for general relativistic magnetohydrodynamics and magnetodynamics
- Second Order Accurate Schemes for Magnetohydrodynamics With Divergence-Free Reconstruction
- Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics
- Efficient, High Accuracy ADER-WENO Schemes for Hydrodynamics and Divergence-Free Magnetohydrodynamics
- Positivity-preserving flux limiters for high-order conservative schemes
- Numerical Magnetohydrodynamics in Astrophysics: Algorithm and Tests for One-Dimensional Flow
- A Divergence-Free Upwind Code for Multidimensional Magnetohydrodynamic Flows
- Multidimensional HLLE Riemann solver; Application to Euler and Magnetohydrodynamic Flows
- A Two-dimensional HLLC Riemann Solver for Conservation Laws : Application to Euler and MHD Flows
- Divergence-Free Reconstruction of Magnetic Fields and WENO Schemes for Magnetohydrodynamics
- An HLLC Solver for Relativistic Flows -- II. Magnetohydrodynamics
- WHAM: A WENO-based general relativistic numerical scheme I: Hydrodynamics
- The Exact Solution of the Riemann Problem in Relativistic MHD
- A five-wave HLL Riemann solver for relativistic MHD
- A general framework to construct schemes satisfying additional conservation relations. Application to entropy conservative and entropy dissipative schemes
- Provably Positive Discontinuous Galerkin Methods for Multidimensional Ideal Magnetohydrodynamics
- Relativistic Magnetohydrodynamics: Renormalized eigenvectors and full wave decomposition Riemann solver
- Improved Accuracy of High-Order WENO Finite Volume Methods on Cartesian Grids
- Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes: Application to Structure Preserving Discretization
- A Subluminal Relativistic Magnetohydrodynamics Scheme with ADER-WENO Predictor and Multidimensional Riemann Solver-Based Corrector
- Entropy Symmetrization and High-Order Accurate Entropy Stable Numerical Schemes for Relativistic MHD Equations
- A finite-volume scheme for modeling compressible magnetohydrodynamic flows at low Mach numbers in stellar interiors
- Efficient Finite Difference WENO Scheme for Hyperbolic Systems with Non-Conservative Products
- HOW-MHD: A High-Order WENO-Based Magnetohydrodynamic Code with a High-Order Constrained Transport Algorithm for Astrophysical Applications
- Efficient Alternative Finite Difference WENO Schemes for Hyperbolic Conservation Laws
- Efficient Alternative Finite Difference WENO Schemes for Hyperbolic Systems with Non-Conservative Products