Implicit Solution of the Four-field Extended-magnetohydroynamic Equations using High-order High-continuity Finite Elements
Authors: S.C. Jardin and J.A. Breslau
Date of PPPL Report: December 2004
Published in: Physics of Plasmas 12:5 (May 2005) Article No. 056101 (10 pages). Invited paper at the 46th Annual Meeting of the APS Division of Plasma Physics (15-19 November 2004, Savannah, Georgia).
Here we describe a technique for solving the four-field extended-magnetohydrodynamic (MHD) equations in two dimensions. The introduction of triangular high-order finite elements with continuous first derivatives (C1 continuity) leads to a compact representation compatible with direct inversion of the associated sparse matrices. The split semi-implicit method is introduced and used to integrate the equations in time, yielding unconditional stability for arbitrary time step. The method is applied to the cylindrical tilt mode problem with the result that a non-zero value of the collisionless ion skin depth will increase the growth rate of that mode. The effect of this parameter on the reconnection rate and geometry of a Harris equilibrium and on the Taylor reconnection problem is also demonstrated. This method forms the basis for a generalization to a full extended-MHD description of the plasma with six, eight, or more scalar fields.