A Time-Accurate Projection Method for Low-Mach Number Variable Density Flows in Curvilinear Grids

Abstract

A time-accurate numerical algorithm is proposed for low Mach number variable density flows in curvilinear coordinate systems. In order to increase the stability of the method, a predictor-corrector time integration scheme, coupled with the projection method, is employed. The projection method results in a constant-coefficient Poisson equation for the pressure in both the predictor and corrector steps. The continuity equation is fully satisfied at each step. To prevent the pressure odd-even decoupling typically encountered in collocated grids, a flux interpolation technique is developed. The spatial discretization method offers computational simplicity and straightforward extension to 3D curvilinear coordinate systems, which are essential in the simulation of turbulent flows in complex geometries. The accuracy and stability of the algorithm are tested with a series of numerical experiments, and the results are validated against the available data in the literature.