有限圆柱中的极向-环向分解. I. 磁流体动力学方程的影响矩阵
Poloidal-toroidal decomposition in a finite cylinder. I. Influence matrices for the magnetohydrodynamic equations
AI总结：
本文在有限圆柱中利用极向-环向势函数表述磁流体动力学方程，通过影响矩阵技术解耦高阶偏微分方程组，并利用Dirichlet-to-Neumann映射匹配外部真空磁场，避免外部区域离散化。
摘要：
Navier-Stokes方程和磁流体动力学方程在有限圆柱中用极向和环向势函数表示。这种表述确保速度和磁场自动无散，但导致高阶偏微分方程组，其边界条件耦合。采用影响矩阵技术将这些系统转化为解耦的抛物型和椭圆型问题。感应方程中的磁场通过Dirichlet-to-Neumann映射与外部真空中的磁场匹配，从而无需对外部区域进行离散化。对影响矩阵进行缩放以获得可接受的条件数。
英文摘要：
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.
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