A three-dimensional numerical method for modelling weakly ionized plasmas

Abstract

Astrophysical fluids under the influence of magnetic fields are often subjected to single-fluid or two-fluid approximations. In the case of weakly ionized plasmas however, this can be inappropriate due to distinct responses from the multiple constituent species to both collisional and non-collisional forces. As a result, in dense molecular clouds and proto-stellar accretion discs for instance, the conductivity of the plasma may be highly anisotropic leading to phenomena such as Hall and ambipolar diffusion strongly influencing the dynamics. Diffusive processes are known to restrict the stability of conventional numerical schemes which are not implicit in nature. Furthermore, recent work establishes that a large Hall term can impose an additional severe stability limit on standard explicit schemes. Following a previous paper which presented the one-dimensional case, we describe a fully three-dimensional method which relaxes the normal restrictions on explicit schemes for multifluid processes. This is achieved by applying the little known Super TimeStepping technique to the symmetric (ambipolar) component of the evolution operator for the magnetic field in the local plasma rest-frame, and the new Hall Diffusion Scheme to the skew-symmetric (Hall) component.

13 pages, 9 figures, accepted for publication in MNRAS

References in corpus (11)

• The Balbus-Hawley instability in weakly ionised discs
• The conductivity of dense molecular gas
• 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
• Magnetorotational instability in protoplanetary discs
• An explicit scheme for multifluid magnetohydrodynamics
• Direct simulations of helical Hall-MHD turbulence and dynamo action
• A numerical scheme for multifluid magnetohydrodynamics
• Dust grains and the structure of steady C-type magnetohydrodynamic shock waves in molecular clouds
• 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 (38)

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• Partially Ionized Plasmas in Astrophysics
• Hall-effect Controlled Gas Dynamics in Protoplanetary Disks: I. Wind Solutions at the Inner Disk
• 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
• The transport of cosmic rays in self-excited magnetic turbulence
• Incorporating Ambipolar and Ohmic Diffusion in the AMR MHD code RAMSES
• Turbulent magnetic field amplification driven by cosmic-ray pressure gradients
• 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
• MHDSTS: a new explicit numerical scheme for simulations of partially ionised solar plasma
• Nonequilibrium ionization and ambipolar diffusion in solar magnetic flux emergence processes
• Hall Effect in Protostellar Disc Formation and Evolution
• Ambipolar diffusion in the Bifrost code
• The effect of extreme ionisation rates during the initial collapse of a molecular cloud core
• Dust segregation in Hall-dominated turbulent protoplanetary disks
• Scalable explicit implementation of anisotropic diffusion with Runge-Kutta-Legendre super-time-stepping
• Direct Evidence for Two-Fluid Effects in Molecular Clouds
• A Two-Fluid Method for Ambipolar Diffusion
• Driven Multifluid MHD Molecular Cloud Turbulence
• Multifluid simulations of the Magnetorotational Instability in protostellar disks
• A class of high-order Runge-Kutta-Chebyshev stability polynomials
• 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
• Advancing parabolic operators in thermodynamic MHD models: Explicit super time-stepping versus implicit schemes with Krylov solvers
• 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
• Thermal instability in ionized plasma
• Multifluid magnetohydrodynamic turbulent decay
• Non-ideal MHD turbulent decay in molecular clouds
• Global multifluid simulations of the magnetorotational instability in radially stratified protoplanetary disks
• Two-dimensional partially ionized magnetohydrodynamic turbulence
• Efficient numerical treatment of ambipolar and Hall drift as hyperbolic system
• An Implicit Scheme for Ohmic Dissipation with Adaptive Mesh Refinement
• Factorized Runge-Kutta-Chebyshev Methods
• Ambipolar diffusion: Self-similar solutions and MHD code testing. Cylindrical symmetry
• Spectral Analysis of Non-Ideal MRI Modes: The effect of Hall diffusion
• Effects of ambipolar diffusion on waves in the solar chromosphere