Fully Decoupled and Unconditionally Energy Stable Scheme for Incompressible MHD Equations
In this paper,we propose a first order linear,unconditional energy stable and fully decoupled scheme to solve coupled,nonlinear magnetohydrodynamics equations.The scheme is based on the pressure projection method of saddle point system,the implicit-explicit treatment of nonlinear coupling terms and the introduction of stable terms to stabilize the decoupling calculation of magnetic field with velocity field.The scheme transforms the MHD dynamic system into several linear elliptic problems,which is efficient,easy-to-implement and stable.We prove that the time semi-discrete form and the fully discrete form of the scheme are unconditionally energy stable.Final-ly,the stability and convergence of the scheme are verified by several numerical experiments.
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