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A multigrid approach for steady state laminar viscous flows
Author(s) -
Liao ShiJun,
Mashayek F.
Publication year - 2001
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.170
Subject(s) - multigrid method , laminar flow , mathematics , partial differential equation , flow (mathematics) , scheme (mathematics) , computational fluid dynamics , mathematical optimization , computer science , mathematical analysis , mechanics , geometry , physics
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. Copyright © 2001 John Wiley & Sons, Ltd.