A decoupled Crank-Nicolson time-stepping scheme for thermally coupled magneto-hydrodynamic system

Abstract

Thermally coupled magneto-hydrodynamics (MHD) studies the dynamics ofelectro-magnetically and thermally driven flows, involving MHD equations cou-pled with heat equation. We introduce a partitioned method that allows oneto decouple the MHD equations from the heat equation at each time step andsolve them separately. The extrapolated Crank-Nicolson time-stepping schemeis used for time discretization while mixed finite element method is used forspatial discretization.We derive optimal order error estimates in suitable normswithout assuming any stability condition or restrictions on the time step size.We prove the unconditional stability of the scheme. Numerical experiments areused to illustrate the theoretical results.