An explicit scheme for multifluid magnetohydrodynamics

Abstract

When modeling astrophysical fluid flows, it is often appropriate to discard the canonical magnetohydrodynamic approximation thereby freeing the magnetic field to diffuse with respect to the bulk velocity field. As a consequence, however, the induction equation can become problematic to solve via standard explicit techniques. In particular, the Hall diffusion term admits fast-moving whistler waves which can impose a vanishing timestep limit. Within an explicit differencing framework, a multifluid scheme for weakly ionised plasmas is presented which relies upon a new approach to integrating the induction equation efficiently. The first component of this approach is a relatively unknown method of accelerating the integration of parabolic systems by enforcing stability over large compound timesteps rather than over each of the constituent substeps. This method, Super Time Stepping, proves to be very effective in applying a part of the Hall term up to a known critical value. The excess of the Hall term above this critical value is then included via a new scheme for pure Hall diffusion.

8 pages; 4 figures; accepted by MNRAS; minor corrections to equations; addition of appendix

References in corpus (5)

• The Effect of the Hall Term on the Nonlinear Evolution of the Magnetorotational Instability: II. Saturation Level and Critical Magnetic Reynolds Number
• The Effect of the Hall Term on the Nonlinear Evolution of the Magnetorotational Instability: I. Local Axisymmetric Simulations
• A numerical scheme for multifluid magnetohydrodynamics
• The Wardle Instability in Interstellar Shocks: I. Nonlinear Dynamical Evolution
• Time-Dependent, Multifluid, Magnetohydrodynamic Shock Waves with Grain Dynamics I. Formulation and Numerical Tests

Cited by in corpus (45)

• PLUTO: a Numerical Code for Computational Astrophysics
• Phantom: A smoothed particle hydrodynamics and magnetohydrodynamics code for astrophysics
• Global simulations of protoplanetary disks with net magnetic flux: I. Non-ideal MHD case
• Radiation Magnetohydrodynamic Simulations of Protostellar Collapse: Protostellar Core Formation
• Effect of Ambipolar Diffusion on the Non-linear Evolution of Magnetorotational Instability in Weakly Ionized Disks
• Partially Ionized Plasmas in Astrophysics
• Hall-effect Controlled Gas Dynamics in Protoplanetary Disks: I. Wind Solutions at the Inner Disk
• Can non-ideal magnetohydrodynamics solve the magnetic braking catastrophe?
• Radiation hydrodynamics with Adaptive Mesh Refinement and application to prestellar core collapse. I Methods
• Turbulence In the Outer Regions of Protoplanetary Disks. I. Weak Accretion with No Vertical Magnetic Flux
• MPI-AMRVAC 3.0: updates to an open-source simulation framework
• Magnetic, thermal and rotational evolution of isolated neutron stars
• Magnetic, thermal and rotational evolution of isolated neutron stars
• The role of magnetic fields in the formation of protostellar discs
• A new code for the Hall-driven magnetic evolution of neutron stars
• Incorporating Ambipolar and Ohmic Diffusion in the AMR MHD code RAMSES
• Turbulent magnetic field amplification driven by cosmic-ray pressure gradients
• A three-dimensional numerical method for modelling weakly ionized plasmas
• Ambipolar diffusion in smoothed particle magnetohydrodynamics
• Simulating hydromagnetic processes in star formation: introducing ambipolar diffusion into an adaptive mesh refinement code
• An Explicit Scheme for Incorporating Ambipolar Diffusion in a Magnetohydrodynamics Code
• A Multi-Fluid Dust Module in Athena++: Algorithms and Numerical Tests
• MHDSTS: a new explicit numerical scheme for simulations of partially ionised solar plasma
• Cloud Formation and Acceleration in a Radiative Environment
• Confirmation of the occurrence of the Hall instability in the non-linear regime
• A Simflowny-based high-performance 3D code for the generalized induction equation
• Direct Evidence for Two-Fluid Effects in Molecular Clouds
• A Two-Fluid Method for Ambipolar Diffusion
• Driven Multifluid MHD Molecular Cloud Turbulence
• A class of high-order Runge-Kutta-Chebyshev stability polynomials
• Multifluid simulations of the Magnetorotational Instability in protostellar disks
• The Kelvin-Helmholtz instability in weakly ionised plasmas: Ambipolar dominated and Hall dominated flows
• Cosmic-ray pressure driven magnetic field amplification: dimensional, radiative and field orientation effects
• The challenges of modelling microphysics: ambipolar diffusion, chemistry, and cosmic rays in MHD shocks
• Observational Diagnostics for Two-Fluid Turbulence in Molecular Clouds As Suggested by Simulations
• The Kelvin-Helmholtz instability in weakly ionised plasmas II: multifluid effects in molecular clouds
• Multifluid magnetohydrodynamic turbulent decay
• Existence and Uniqueness of Strong Solutions for a Compressible Multiphase Navier-Stokes Miscible Fluid-Flow Problem in Dimension n = 1
• Global multifluid simulations of the magnetorotational instability in radially stratified protoplanetary disks
• Non-ideal MHD turbulent decay in molecular clouds
• A Discontinuous Galerkin Method for Viscous Compressible Multifluids
• An Implicit Scheme for Ohmic Dissipation with Adaptive Mesh Refinement
• Factorized Runge-Kutta-Chebyshev Methods
• Spectral Analysis of Non-Ideal MRI Modes: The effect of Hall diffusion
• Effects of ambipolar diffusion on waves in the solar chromosphere