Finite-Element Method for Three-Dimensional Incompressible Viscous Flow Using Simultaneous Relaxation of Velocity and Bernoulli Function : Flow in a Lid-Driven Cubic Cavity at Re=5000

Abstract

A simple finite-element method for unsteady incompressible viscous flow is presented. This method is a simplified version of the GSMAC (generalized simplified marker and cell) finite-element method, and it is applicable to large systems. Navier-Stokes equations in rotational form and the equation of continuity are employed as the governing equations. A time-dependent solution is obtained by the following procedures. (1) Prediction of velocity field by explicit time advancement. (2) Correction of both velocity and the Bernoulli function by simultaneous relaxation satisfying the equation of continuity. Unsteady flow in a lid-driven cubic cavity at the Reynolds number of 5000 is numerically investigated to verify the present method. Velocity profiles in the cavity are in good agreement with the experimental results of Prasad and Koseff. The present method is stable in three-dimensional analysis, and nonphysical pressure oscillations are not observed.