Gerbeau, J., Le Bris, C. and Lelievre, T. (2006) Mathematical Methods for the Magnetohydrodynamics of Liquid Metals. Numerical Mathematics and Scientic Computation. Oxford University Press, Oxford. https://doi.org/10.1093/acprof:oso/9780198566656.001.0001

has been cited by the following article:

• TITLE: Convergence Analysis of the Fully Decoupled Linear Scheme for Magnetohydrodynamic Equations

  AUTHORS: Zeyu Xia, Qian Xu

  KEYWORDS: MHD Equations, Zero-Energy-Contribution, Unique Solvability, Unconditional Energy Stability, Optimal Error Estimates

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.11, November 30, 2022

  ABSTRACT: In this paper, we propose a fully decoupled and linear scheme for the magnetohydrodynamic (MHD) equation with the backward differential formulation (BDF) and finite element method (FEM). To solve the system, we adopt a technique based on the “zero-energy-contribution” contribution, which separates the magnetic and fluid fields from the coupled system. Additionally, making use of the pressure projection methods, the pressure variable appears explicitly in the velocity field equation, and would be computed in the form of a Poisson equation. Therefore, the total system is divided into several smaller sub-systems that could be simulated at a significantly low cost. We prove the unconditional energy stability, unique solvability and optimal error estimates for the proposed scheme, and present numerical results to verify the accuracy, efficiency and stability of the scheme.