标题： 有限圆柱中的极向-环向分解。 I. 磁流体力学方程的影响矩阵 显示英文标题

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

摘要： 纳维-斯托克斯方程和磁流体力学方程以有限圆柱中的位势形式书写。 这种表述方式保证了速度场和磁场从构造上是散度自由的，但导致了更高阶偏微分方程组，其边界条件是耦合的。 影响矩阵技术被用来将这些方程组转化为解耦的抛物型和椭圆型问题。 通过Dirichlet到Neumann映射，感应方程中的磁场与外部真空中的磁场相匹配，从而消除了对外部区域进行离散化的需要。 影响矩阵按比例缩放以达到可接受的条件数。 显示英文摘要

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.