Abstract
A two-dimensional simulation model of the “magnetohydrodynamic (MHD)” vortex method, current-vortex method, is developed. The concept is based on the previously developed current-vortex filament model in three-dimensional space. It is assumed that electric current and vorticity have discontinuous filamentary (point) distributions on the two-dimensional plane, and both the point electric current and the point vortex are confined in a filament. In other words, they share the same point on the two-dimensional plane, which is called the “current-vortex filament.” The spatial profiles of the electric current and the vorticity are determined by the sum of such filaments. Time development equations for a filament are obtained by integrating the two-dimensional MHD equations around the filament. It is found that a special-purpose computer, MDGRAPE-2, is capable not only of molecular dynamics simulations but also of MHD simulations, because MDGRAPE-2 accelerates calculations of the Biot–Savart integral. The current-vortex method on MDGRAPE-2 reproduces the result obtained by the traditional MHD code on a general-purpose computer.
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