Astrophysical Weighted Particle Magnetohydrodynamics

TL;DR

This paper introduces a meshless weighted particle scheme for magnetohydrodynamics that automatically handles dissipation and divergence cleaning, validated through various tests including modeling magneto-rotational instability in accretion disks.

Contribution

It presents a novel meshless scheme for MHD that requires no free parameters for physics control and can be implemented with existing SPH codes.

Findings

Successfully models magneto-rotational instability in accretion disks.

Automatically adds necessary dissipation through Riemann problem formulation.

Maintains divergence constraint with a new meshless cleaning procedure.

Abstract

This paper presents applications of weighted meshless scheme for conservation laws to the Euler equations and the equations of ideal magnetohydrodynamics. The divergence constraint of the latter is maintained to the truncation error by a new meshless divergence cleaning procedure. The physics of the interaction between the particles is described by an one-dimensional Riemann problem in a moving frame. As a result, necessary diffusion which is required to treat dissipative processes is added automatically. As a result, our scheme has no free parameters that controls the physics of inter-particle interaction, with the exception of the number of the interacting neighbours which control the resolution and accuracy. The resulting equations have the form similar to SPH equations, and therefore existing SPH codes can be used to implement the weighed particle scheme. The scheme is validated in several hydrodynamic and MHD test cases. In particular, we demonstrate for the first time the ability of a meshless MHD scheme to model magneto-rotational instability in accretion disks.