Poloidal-toroidal decomposition in a finite cylinder. I: Influence matrices for the magnetohydrodynamic equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:227

Article

Boronski, Piotr¹  Tuckerman, Laurette S.¹ 

[1] LIMSI CNRS, F-91403 Orsay, France

关键词: poloidal-toroidal;    influence matrix;    magnetohydrodynamics;    divergence-free;    finite cylinder;    Dirichlet-to-Neumann mapping;    compatibility conditions;    matrix conditioning;   

DOI  :  10.1016/j.jcp.2007.08.023

来源: Elsevier

【 摘 要 】

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. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free