An explicit scheme for ohmic dissipation with smoothed particle magneto-hydrodynamics

TL;DR

This paper introduces an explicit, second-order accurate scheme for modeling Ohmic dissipation in smoothed particle magneto-hydrodynamics, utilizing supertime-stepping to enable larger time steps and improve computational efficiency.

Contribution

The authors develop a novel SPH discretization of Ohmic dissipation combined with supertime-stepping, enhancing stability and efficiency in SPMHD simulations.

Findings

The scheme achieves second-order spatial accuracy and first-order temporal accuracy.

Optimal supertime-stepping parameters for Ohmic dissipation are identified as ν_sts ~ 0.01 and N_sts ~ 5.

Numerical experiments demonstrate improved stability and efficiency of the proposed method.

Abstract

In this paper, we present an explicit scheme for Ohmic dissipation with smoothed particle magneto-hydrodynamics (SPMHD). We propose a SPH discretization of Ohmic dissipation and solve Ohmic dissipation part of induction equation with the supertime-stepping method (STS) which allows us to take a longer time-step than Courant-Friedrich-Levy stability condition. Our scheme is second-order accurate in space and first-order accurate in time. Our numerical experiments show that optimal choice of the parameters of STS for Ohmic dissipation of SPMHD is {\nu}sts ~ 0.01 and Nsts ~ 5.