Efficient and Stable Schemes for the Magnetohydrodynamic Potential Model

Abstract

In this paper, we consider the numerical approximations of a magnetohy-drodynamic potential model that was developed in [15]. Several decoupled, linear, unconditionally energy stable schemes are developed by combining some subtle implicit-explicit treatments for nonlinear coupling terms and the projection-type method for the Navier-Stokes equations. The divergence-free condition for the magnetic field is preserved in the fully-discrete level. We further establish the well-posedness and unconditional energy stabilities of the proposed schemes and present a series of numerical examples in 3D, including accuracy/stability tests, benchmark simulations of driven cavity flow and hydromagnetic Kelvin-Helmholtz instability.