Study On Decoupling Fractional-step Method For A Coupled System Arising In Magnetohynamic Problem

This article mainly considers a kind of mixed MHD system coupled by the nonstationary Navier-Stokes equations and the steady Maxwell equations.The physical meaning of this system is that the speed at which the magnetic field reaches the steady state is much faster than the speed at which the fluid reaches the steady state.For this mixed MHD system,this paper mainly studies a fully discrete fractional step finite element scheme for solving the system.The research content is divided into following two parts:1.Construct a fractional step scheme for solving mixed MHD equations,the scheme is a decoupled scheme,which means the magnetic field and velocity field can be solved independently at the same time discrete level.The nonlinearity and the divergence-free of the NavierStokes equations are splitted by introducing an intermediate velocity field.2.Through rigorous error analysis of the magnetic field and velocity field,we have obtained the optimal H1 convergence order O(?t+h)for the magnetic and the velocity under the time step condition ?t=O(h),where h is the mesh size.Numerical results are shown to illustrate the theoretical convergence analysis.