Abstract
This paper presents a second-order semi-implicit Crank-Nicolson scheme for a hybrid magnetohydrodynamics system coupled by the nonstationary Navier-Stokes equations and the stationary Maxwell equations. Main features of proposed scheme are two-fold. One is that it is a decoupled scheme and the magnetic field and velocity field can be solved independently at the same time discrete level. Another is that two subproblems both are linear and are easy to be solved numerically. A rigorous temporal-spatial error analysis is done and we prove that the proposed scheme is of second-order convergence rate O((Δt)2) for approximations of the magnetic field, the velocity field and the pressure under the condition Δt=O(h1/2). Finally, a numerical result is displayed to illustrate the theoretical results.
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