GSMAC-A New Finite Element Method for Unsteady Incompressible Viscous Flow Problems : 1st Report, A Stable Method at High Reynolds Numbers

Abstract

We present a new fast finite element method which is called the generalized-simplified marker and cell method (GSMAC) as an extention of the SMAC finite difference method of Amsden and Harlow. There are several new features of the GSMAC method, which is distinguished from other iterative finite element methods. We use two important concepts, orthogonal decomposition and cycle-to-cycle self-adjustment, which allow a stable and accurate calculation of unsteady flow fields at high Reynolds numbers without any artificial modification. As a result, the GSMAC method has proved to be faster than the other finite element methods and to require only the same amount of CPU time and storage as the standard finite difference method. The results of calculation in a square cavity agree very well with those of Ghia et al.. Especially for R_e=5000 and 10000, the same degree of accuracy can be obtained with 1/26.4 of mesh points.