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 differential equations. The proposed scheme combines a new analytical method for strongly non‐linear problems, namely the homotopy analysis method, with the multigrid techniques. A family of formulas at different orders is given. At the lowest order, the current approach is the same as the traditional multigrid methods. However, our high‐order scheme needs a fewer number of iterations and less CPU time than the classical ones.