Comparative study of finite difference approaches in simulation of magnetohydrodynamic turbulence at low magnetic Reynolds number

Abstract

Two approaches to finite difference approximation of turbulent flows of electrically conducting incompressible fluids in the presence of a steady magnetic field are analyzed. One is based on high-order approximations and upwind-biased discretization of the nonlinear term. Another is consistently of the second order and nearly fully conservative in regard of mass, momentum, kinetic energy, and electric charge conservation principles. The analysis is conducted using comparison with high-accuracy spectral direct numerical simulations of channel flows with wall-normal and spanwise magnetic fields. Focus of the analysis is on the quality of finite difference approximation in the situation when the magnetic field leads to significant transformation of the flow structure. In the case of turbulent flows at moderate magnetic fields, the conservative scheme approach offers better stability and equal or higher accuracy than the approach based on the upwind discretization. The conservation property is expected to become increasingly important and even indispensable at stronger magnetic fields.