GSMAC-A New Finite Element Method for Unsteady Incompressible Viscous FIOW problems : 2nd Report. Flow in a Square Cavity at High Reynolds Numbers

Abstract

The unsteady flowfields in a square cavity at high Reynolds numbers are investigated numerically by solving the unsteady Navier-Stokes equation through the GSMAC finite element method which includes two important concepts: orthogonal decomposition and cycle-to-cycle self adjustment. Unsteady flow simulations in terms of streamlines, isobars, equi-vorticity lines and equienergy lines are obtained at Reynolds numbers of 5000 and 10⁴. The conclusions are as follows; (1) The influence of the spiral motion of the main vortex to the shapes and sizes of secondary vortex are explained. (2) It is observed from the results that the flows in a square cavity at a Reynolds number of 10⁴ show turbulent-like behavior. (3) The GSMAC finite element method requires only the same amount of CPU time and storage as a standard finite difference method and shows the great capability of solving unsteady flow problems.