Some Properties of the M3D-C1 Form of the 3D Magnetohydrodynamics Equations
Authors: J. Breslau, N. Ferraro, S. Jardin
Abstract:
We introduce a set of scalar variables and projection operators for the vector momentum and magnetic field evolution equations that have several unique and desirable properties, making them a preferred system for solving the magnetohydrodynamics equations in a torus with a strong toroidal magnetic field. We derive a "weak form" of these equations that explicitly conserves energy and is suitable for a Galerkin finite element formulation provided the basis elements have C1 continuity. Systems of reduced equations are discussed, along with their energy conservation properties. An implicit time advance is presented that adds diagonally dominant self-adjoint energy terms to the mass matrix to obtain numerical stability.
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Submitted to: Physics of Plasmas (July 2009)
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Download PPPL-4425 (pdf 714 KB 16 pp)
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