Validity of Pressure-Velocity Correction Algorithm (C-HSMAC method) for Incompressible Fluids with Passive Scalar Convection

Abstract

In the computations of incompressible fluids, it is essentially important to obtain accurately the velocity components that satisfy the incompressible condition (∇・u = 0) as well as the pressure variables which are consistent with the velocity fields. For this purpose, a pressure-velocity correction method (C-HSMAC method) has been proposed by Ushijima et al. (2002) with a finite volume method (FVM) for incompressible fluids. The purpose of this paper is to estimate the effects of the unsatisfied incompressible condition on the passive scalar convection and to confirm that the C-HSMAC method is able to suppress them. The C-HSMAC and usual SMAC methods were applied to the passive scalar convection in the cavity having an oscillating top wall. It was concluded that the unsatisfied incompressible condition may cause the unphysical scalar overshoots in the SMAC method. In contrast, the C-HSMAC method enables us to control |∇・u| with the given threshold ϵD and to suppress such overshoots. In addition, it was demonstrated that the C-HSMAC method allows us to obtain reasonable results without overshoots even in combination with a higher-order scheme for convection terms with finer cell divisions.