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

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.