NUMERICAL-METHOD FOR INCOMPRESSIBLE VORTICAL FLOWS WITH 2 UNBOUNDED DIRECTIONS

A new, efficient, and accurate method has been developed for computing unsteady, incompressible, viscous flows in a domain where two dimensi ons are unbounded, the third dimension is periodic and the vorticity i s rapidly decaying in the unbounded directions. We use the term unboun ded to mean doubly infinite (no boundaries of any kind). This is an ex tension of the methods described by others for flows with two periodic and one unbounded direction, where the irrotational velocities outsid e the vortical domain are treated analytically. The new method is show n to be both accurate and efficient. The method presented here has fin ite, but arbitrarily high order, formal accuracy, and incurs substanti al additional cost for a given mesh. However, this increased cost is m ore than offset by the reduction in the number of mesh points required for a given accuracy. The result is that for accurate computations, t he present method can be orders of magnitude more efficient than other s currently in use. This paper presents the method, discusses implemen tation issues, validates its accuracy, and presents sample calculation s. (C) 1997 Academic Press.