Development of GSMAC-FEM Using Cycle-to-Cycle Self-Adjustment Method

Abstract

The conventional GSMAC-FEM (generalized simplified marker and cell finite element method) is based on the cycle-to-cycle self adjustment method. The error of the continuity equation which remains on solving the Navier-Stokes equation makes time marching of the GSMAC-FEM stabilize. However, the effect of the cycle-to-cycle self-adjustment method has not been utilized sufficiently because most of the conventional formulations have neglected the compressible term in the Navier-Stokes equation. In the present paper, a new formulation of the momentum equation was presented, which takes the compressible term into consideration. The flows around a circular cylinder were analyzed at the Reynolds numbers of 550 and 3000 in order to verify the new formulation.