Unconditional stability of a partitioned IMEX method for magnetohydrodynamic flows

Abstract Magnetohydrodynamic (MHD) flows are governed by Navier–Stokes equations coupled with Maxwell equations through coupling terms. We prove the unconditional stability of a partitioned method for the evolutionary full MHD equations, at high magnetic Reynolds number, written in the Elsasser variables. The method we analyze is a first-order one-step scheme, which consists of implicit discretization of the subproblem terms and explicit discretization of the coupling terms.

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