Unconditional convergence of the Euler semi-implicit scheme for the 3D incompressible MHD equations: Numerical implementation
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 2 November 2015
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.
Keywords
Acknowledgements
This work is supported by the NSF of China (No. 11271298) and the NSF of China (No. 11371289).
Citation
Zhang, G.-D. and He, Y. (2015), "Unconditional convergence of the Euler semi-implicit scheme for the 3D incompressible MHD equations: Numerical implementation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 25 No. 8, pp. 1912-1923. https://doi.org/10.1108/HFF-08-2014-0257
Publisher
:Emerald Group Publishing Limited
Copyright © 2015, Emerald Group Publishing Limited