High order accurate vortex methods with explicit velocity kernels

Vortex methods of high order accuracy are developed for inviscid, incompressible fluid flow in two or three space dimensions. The velocity kernels are smooth functions given by simple, explicit formulas. Numerical results are given for test problems with exact solutions in two dimensions. It is found that the higher order methods yield a considerably more accurate representation of the velocity field than those of lower order for moderate integration times. On the other hand, the velocity field computed by the point vortex method has very poor accuracy at locations other than the particle trajectories.