Abstract
Thermally coupled magneto-hydrodynamics (MHD) studies the dynamics of electro-magnetically and thermally driven flows,involving MHD equations coupled with heat equation. We introduce a partitioned method that allows one to decouplethe MHD equations from the heat equation at each time step and solve them separately. The extrapolated Crank-Nicolson time-stepping scheme is used for time discretizationwhile mixed finite element method is used for spatial discretization. We derive optimal order error estimates in suitable norms without assuming any stability condition or restrictions on the time step size. We prove the unconditional stability of the scheme. Numerical experiments are used to illustrate the theoretical results.
Highlights
We introduce a partitioned method that allows one to decouple the MHD equations from the heat equation at each time step and solve them separately
Coupled magneto-hydrodynamics has many applications including in electromagnetic pumping design [35], electromagnetic filtration [4], contact-less electromagnetic stirring [32] and damping convective flow in metal-like melt [34]
We propose and analyze a decoupled time stepping scheme for the thermally coupled MHD equations
Summary
Coupled magneto-hydrodynamics has many applications including in electromagnetic pumping design [35], electromagnetic filtration [4], contact-less electromagnetic stirring [32] and damping convective flow in metal-like melt [34]. Magnetohydrodynamics in general has broad applications including fusion [19], underwater propulsion [18], nuclear reactors [13], metallurgy [1, 2, 11, 31] and astrophysics [30] In all of these applications, qualitative and quantitative understanding of the dynamics is important to achieve optimal operating conditions. We propose and analyze a decoupled time stepping scheme for the thermally coupled MHD equations. It uses a semi-implicit Crank-Nicolson scheme, which combines an implicit treatment of the second derivative terms, a semi-implicit second order extrapolation of the nonlinear convective terms and an explicit treatment of the temperature coupling term in the Navier-Stokes equations. We present a numerical example that illustrates our theoretical results
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