Poloidal toroidal decomposition in a finite cylinder. I: Influence matrices for the magnetohydrodynamic equations
Abstract
The NavierStokes 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 divergencefree 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 DirichlettoNeumann mapping, thus eliminating the need to discretize the exterior. The influence matrix is scaled in order to attain an acceptable condition number.
 Publication:

Journal of Computational Physics
 Pub Date:
 December 2007
 DOI:
 10.1016/j.jcp.2007.08.023
 arXiv:
 arXiv:0705.0785
 Bibcode:
 2007JCoPh.227.1523B
 Keywords:

 Mathematics  Numerical Analysis;
 Physics  Computational Physics
 EPrint:
 Journal of Computational Physics 227, 15441566 (2007)