ELLAM for resolving the kinematics of two-dimensional resistive magnetohydrodynamic flows

Authors:
Jiangguo Liu;Simon Tavener;Hongsen Chen
Affiliations:
Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874, USA;Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874, USA;Institute for Scientific Computation, Texas A&M University, College Station, TX 77843-3404, USA
Venue:
Journal of Computational Physics
Year:
2007

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Abstract

We combine the finite element method with the Eulerian-Lagrangian Localized Adjoint Method (ELLAM) to solve the convection-diffusion equations that describe the kinematics of magnetohydrodynamic flows, i.e., the advection and diffusion of a magnetic field. Simulations of three two-dimensional test problems are presented and in each case we analyze the energy of the magnetic field as it evolves towards its equilibrium state. Our numerical results highlight the accuracy and efficiency of the ELLAM approach for convection-dominated problems.