inverse square root of the number of vortices N. If the initial vorticity inside the region is constant, the number A new method is proposed for simulating diffusion in vortex methods for two-dimensional incompressible flows. The method of vortices must be increased with the Reynolds number resolves length scales up to the spacing of the vortices. The gridto keep the relative error in change in size constant at free nature of vortex methods is fully retained and the distribution finite times. Roberts [50] showed that if the relative error of the vortices can be irregular. It is shown for the Stokes equations in size itself is of importance, higher Reynolds numbers that in principle, the method can have any order of accuracy. It also do not require additional vortices. In fact, the number of conserves circulation, linear, and angular momentum. The method is based on exchanging a conserved quantity between arbitrary vortices can be reduced if the initial data represent the computational points. This suggests that extensions to more geninitial mean size accurately. eral flows may be possible. For the two-dimensional incompressible Marchioro and Pulvirenti [41], Goodman [28], and Long flows studied, circulation is exchanged between vortices to simulate [40] have shown the convergence of the method. Chang diffusion. The amounts of circulation exchanged must satisfy a lin-[13] discusses how to incorporate the random walk in ear system of equations. Based on stability considerations, the exchanged amounts should further be positive. A procedure to find Runge-Kutta time-stepping schemes. a solution to this problem is formulated using linear programming Ghoniem and Sherman [27] studied ways of handling techniques. To test the method, the decay processes of a single point boundary conditions. Sethian and Ghoniem [53] studied vortex and of a counterrotating pair of point vortices are computed. convergence for a backward-facing step numerically. Current limitations of the method are discussed. แฎ 1996 Academic Cheer [14] has implemented the random vortex-sheet/blob Press, Inc.
method for the flow due to an impulsively started cylinder at Re ฯญ 9500.
Fogelson and Dillon [24] have used a simplified one-88