Fast vortex method calculation using a special-purpose computer

A mathematical formulation for the 3D vortex method has been developed for calculation using a special-purpose computer MDGRAPE-2 that was originally designed for molecular dynamics simulations. We made an assessment of this hardware for a few representative problems and compared the results with and without it. It is found that the generation of appropriate function tables, which are used to call libraries, embedded in MDGRAPE-2 is of primary importance in order to retain accuracy. The error arising from the approximation is evaluated by calculating a pair of vortex rings impinging to themselves. Consequently, acceleration about 50 times greater is achieved by MDGRAPE-2 while the error in the statistical quantities such as kinetic energy and enstrophy remain negligible.