Application of mosaic-skeleton approximations in the simulation of three-dimensional vortex flows by vortex segments

The computations in a vortex method for three-dimensional fluid dynamics simulation are accelerated by applying mosaic-skeleton approximations of matrices in the velocity computations. A modified vortex segment method is proposed in which mosaic-skeleton matrix approximations are effectively used to solve the problem of a vorticity field developing in an unbounded three-dimensional domain and in separated flow problems. Examples of the numerical solution of model fluid dynamic problems, such as the motion of a pair of vortex rings, the flow past a hemisphere, and the flow past an octahedral cylinder, are given that illustrate the capability of accelerating the computations while preserving the qualitative and quantitative description of the flow.