Implicit Solution of the Four-field Extended-magnetohydroynamic Equations using High-order High-continuity Finite Elements
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 (C{sup 1} 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.
- Research Organization:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC) (US)
- DOE Contract Number:
- AC02-76CH03073
- OSTI ID:
- 836487
- Report Number(s):
- PPPL-4031; TRN: US0500618
- Resource Relation:
- Other Information: PBD: 17 Dec 2004
- Country of Publication:
- United States
- Language:
- English
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