渦糸近似法の数理的研究の一動向について

抄録

The vortex methods are applied to various complicated problems of high Reynolds number flows of inviscid incompressible flows. These numerical simulations have been proved to be reasonable in point of view of the features of flow behavior, comparing with experiments or results given by other numerical methods. In the point vortex method, the local induced velocities are permitted to be arbitray large. To avoid them, the idea of using a finite vortex core has been proposed and a large number of successful simulations of two-dimensional flow problems have been carried out. However, in the practical numerical simulations, there are many choices such as time step, smoothing function, setting additional condition at the boundary, and simulation model on the viscous effect, and numerical results seem to be sensitive to the choice of paramenters mentioned above. From these circumstances, in the present paper, we pick up some analytical works which the present authors are interesting in and we survey the theoretical analysis of the vortex method of a two-dimensional fluid flow in order to know the theoretical background of the vortex methods.