The design and numerical analysis of vortex methods

A description is presented of some recent progress in the design and numerical analysis of vortex methods for incompressible fluid flow in two or three space dimensions. These methods have been developed for the simulation of high Reynolds number or inviscid fluid flows. Vortex methods have a number of attractive computational advantages when compared to conventional finite difference or finite element methods for this class of problems. Since vortex methods are neither finite difference nor finite element methods, a different point of view and different techniques are required for the numerical analysis of these methods. Chorin (1980) has developed a new three-dimensional (3-D) vortex algorithm with applications to a numerical study of boundary layer stability and the inertial range of 3-D turbulence. Another new 3-D vortex method is described in connection with the present investigation. Particular attention is given to the formulation of these methods, their flexibility, higher order accuracy, and nonlinear stability.