Abstract
Purpose – The purpose of this paper is to consider the numerical implementation of the Euler semi-implicit scheme for three-dimensional non-stationary magnetohydrodynamics (MHD) equations. The Euler semi-implicit scheme is used for time discretization and (P 1b , P 1, P 1) finite element for velocity, pressure and magnet is used for the spatial discretization. Design/methodology/approach – Several numerical experiments are provided to show this scheme is unconditional stability and unconditional L2−H2 convergence with the L2−H2 optimal error rates for solving the non-stationary MHD flows. Findings – In this paper, the authors mainly focus on the numerical investigation of the Euler semi-implicit scheme for MHD flows. First, the unconditional stability and the L2−H2 unconditional convergence with optimal L2−H2 error rates of this scheme are validated through our numerical tests. Some interesting phenomenons are presented. Originality/value – The Euler semi-implicit scheme is used to simulate a practical physics model problem to investigate the interaction of fluid and induced magnetic field. Some interesting phenomenons are presented.
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