A FAST VORTEX METHOD FOR COMPUTING 2D VISCOUS-FLOW

We present a fast version of the random vortex method for computing incompressible, viscous flow at large Reynolds numbers. The basis of this method is Anderson's method of local corrections and similar ideas for handling the potential and boundary layer flows. The goal of these ideas is to reduce the cost involved in computing the velocity field at each time step from being quadratic to linear as a function of the number of vortex elements. We present the results of a numerical study of the flow in a closed box due to a vortex fixed at its center. Our results demonstrate that the addition of the viscous portions of the random vortex method to the method of local corrections does not add appreciably to the cost. Furthermore, the cost of the resulting method is linear when O(104) vortex elements are used, in spite of the fact that the majority of these elements lie in a thin band adjacent to the boundary. © 1990.