Some properties of the M3D- C1 form of the three-dimensional magnetohydrodynamics equations

Abstract

A set of scalar variables and projection operators for the vector momentum and magnetic field evolution equations is presented that has several unique and desirable properties, making it a preferred system for solving the magnetohydrodynamic equations in a torus with a strong toroidal magnetic field. A "weak form" of these equations is derived 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. © 2009 American Institute of Physics.