Acceleration of Vortex Methods Calculation Using FMM and Mdgrape-3

Abstract

Abstract-The present study discusses some numerical techniques on the simultaneous use of the Fast Multipole Method (FMM) and special-purpose computer (MDGRAPE-3) to make the impractically expensive calculation feasible without the loss of numerical accuracy. In the present calculations, the impingement of two identical inclined vortex rings has been studied, and the computation time has been reduced by a factor of 1000 at N = 1.18×10 6 where N is the number of vortex elements. The direct and MDGRAPE-3 calculations both have a scaling of O(N 2 ), and the use of the FMM brings them both down to O(N ). The global kinetic energy, enstrophy and energy spectra have been investigated to address the numerical accuracy and have good agreement with other similar works.