A multigrid approach for steady state laminar viscous flows

In this paper, we use the laminar viscous flow in a lid-driven cavity as an example to describe and verify a numerical scheme for non-linear partial d ifferential equations. The proposed scheme combines a new analytical method for strongly non-linear problems, namely the homotopy analysis method, wit h the multigrid techniques. A family of formulas at different orders is giv en. At the lowest order, the current approach is the same as the traditiona l multigrid methods. However, our high-order scheme needs a fewer number of iterations and less CPU time than the classical ones. Copyright (C) 2001 J ohn Wiley & Sons, Ltd.