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Poloidal–toroidal decomposition in a finite cylinder. I: Influence matrices for the magnetohydrodynamic equations
Authors:Piotr Boronski  Laurette S. Tuckerman
Affiliation:aLIMSI-CNRS, BP 133, 91403 Orsay, France
Abstract:The Navier–Stokes equations and magnetohydrodynamics equations are written in terms of poloidal and toroidal potentials in a finite cylinder. This formulation insures that the velocity and magnetic fields are divergence-free by construction, but leads to systems of partial differential equations of higher order, whose boundary conditions are coupled. The influence matrix technique is used to transform these systems into decoupled parabolic and elliptic problems. The magnetic field in the induction equation is matched to that in an exterior vacuum by means of the Dirichlet-to-Neumann mapping, thus eliminating the need to discretize the exterior. The influence matrix is scaled in order to attain an acceptable condition number.
Keywords:Poloidal–  toroidal   Influence matrix   Magnetohydrodynamics   Divergence-free   Finite cylinder   Dirichlet-to-Neumann mapping   Compatibility conditions   Matrix conditioning
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