Partitioned time-stepping scheme for an MHD system with temperature-dependent coefficients

Abstract

Abstract In this paper, a partitioned time-stepping scheme for transient electromagnetically and thermally driven flow is analysed. The flow is modeled by coupled evolutionary magneto-hydrodynamic (MHD) equations with temperature-dependent coefficients. The partitioned scheme requires solving only one uncoupled MHD equation and one heat transfer equation per time step. It is based on Crank–Nicolson discretization in time and extrapolated treatment of the coupling and nonlinear terms such that skew-symmetry properties of the nonlinear terms are preserved. We prove that the proposed time-stepping scheme is unconditionally stable and derive error estimates for the fully discretized scheme using finite element spatial discretization in suitable norms. Numerical examples are presented that illustrate the accuracy and efficiency of the scheme.