GSMAC-FEM for Incompressible Viscous Flow Analysis : A Modified GSMAC Method

Abstract

The GSMAC-FEM (generalized simplified marker and cell FEM), which is an extension of the SMAC-FDM, is a stable and fast scheme for an incompressible viscous flow. The rotational form of the Navier-Stokes equations in which velocity and the Bernoulli function are variables is used in the GSMAC method. Velocity components and Bernoulli function are interpolated as a linear function and a constant function, respectively. This interpolation is simple and convenient for creating the mesh system. However, the approximation which is mentioned above makes it difficult to analyze inlet-outlet flows including the Neumann boundary conditions. The present paper shows a new modified GSMAC method which is applicable to high Reynolds flows with Neumann boundary condition (especially the pressure boundary). The modified scheme consists of an algorithm which satisfies the continuity equation much better than the previous GSMAC method.