Finite element methods based on a new formulation for the non-stationary incompressible Navier-Stokes equations

Abstract

A new formulation of the Navier-Stokes equations is introduced to solve incompressible flow problems. When finite element methods are used under this formulation there is no need to worry whether Babuska-Brezzi condition is satisfied or not. Both velocity and pressure can be obtained separately and the pressure can be simply obtained by a substitution. Moreover, fully explicit time integration can be applied for easy implementation. Implementation issues are discussed and a couple of flow examples are simulated. Parallel implementation based on domain decomposition is incorporated as well. Copyright © 2004 John Wiley & Sons, Ltd.