The HFD method for large eddy simulation of MHD turbulence decay

Abstract

This work deals with the modelling of  the Magnetohydrodynamic (MHD) turbulence decay  by hybrid finite-difference method (HFDM) combining two different numerical methods: finite-difference and spectral methods. The numerical algorithm of hybrid method solves the Navier-Stokes equations and equation for magnetic field  by a finite-difference method in combination with cyclic penta-diagonal matrix, which yields fourth-order accuracy in space and second-order accuracy in time. The pressure Poisson equation is solved by the spectral method. For validation of the developed algorithm the classical problem of the 3-D Taylor and Green vortex flow is considered without considering the magnetic field, and the simulated time-dependent turbulence characteristics of this flow were found to be in excellent agreement with the corresponding analytical solution valid for short times. We also demonstrate that the developed efficient numerical algorithm can be used to simulate the magnetohydrodynamic turbulence decay at different magnetic Reynolds numbers.