Fully decoupled, linear and unconditionally energy stable time discretization scheme for solving the unsteady thermally coupled magnetohydrodynamic equations with variable density

Abstract

In this article, we propose a fully decoupled first-order time discrete scheme for the unsteady thermally coupled magnetohydrodynamics (MHD) equations with variable density, which is a large nonlinear strongly coupled system consisting of incompressible Navier-Stokes equations with variable density, heat equation and Maxwell equations. The proposed scheme is highly efficient because only the linearised subproblems need to be solved at the discrete level. Furthermore, unconditional stability analysis is established which is a vital issue in the field of multiphysics. We also construct and implement a fully discrete scheme based on conforming finite elements in space. Several 2D/3D numerical tests are conducted to confirm the efficiency and accuracy of the developed scheme with large density differences.