A consistent splitting scheme for unsteady incompressible viscous flows I. Dirichlet boundary condition and applications

Abstract

AbstractA well‐recognized approach for handling the incompressibility constraint by operating directly on the discretized Navier–Stokes equations is used to obtain the decoupling of the pressure from the velocity field. By following the current developments by Guermond and Shen, the possibilities of obtaining accurate pressure and reducing boundary‐layer effect for the pressure are analysed. The present study mainly reports the numerical solutions of an unsteady Navier–Stokes problem based on the so‐called consistent splitting scheme (J. Comput. Phys. 2003; 192:262–276). At the same time the Dirichlet boundary value conditions are considered. The accuracy of the method is carefully examined against the exact solution for an unsteady flow physics problem in a simply connected domain. The effectiveness is illustrated viz. several computations of 2D double lid‐driven cavity problems. Copyright © 2005 John Wiley & Sons, Ltd.