A Decoupled Structure-preserving Scheme for the Incompressible Ideal MHD System

Numerical simulations of incompressible ideal magnetohydrodynamics (MHD) equations cover multiple coupled physical fields, including the flow filed, the magnetic field, and the electric field. And classic methods are not able to accurately preserve conservation laws at the discrete level. In this paper we propose a high order, mass-conserving mixed finite element discretization for the incompressible ideal MHD equations. We use the velocity-vorticity-magnetic formulation, employ the implicit midpoint method to establish staggered grids in time, and obtain a completely decoupled system by applying some explicit-implicit treatments for coupling terms. In the 3D convergence test, optimal spatial convergence rate is obtained. In the 2D Orszag-Tang vortex test, conservation of mass to the machine precision is shown.