Extension of SMAC Scheme for Variable Density Flows Under Strong Temperature Gradient

An extension of SMAC scheme is proposed for variable density flows under low Mach number approximation. The algorithm is based on a predictor-corrector time integration scheme that employs a projection method for the momentum equation. A constant-coefficient Poisson equation is solved for the pressure following both the predictor and corrector steps to satisfy the continuity equation at each time step. Spatial discretization is performed on a collocated grid system that offers computational simplicity and straight forward extension to curvilinear coordinate systems. To avoid the pressure odd-even decoupling that is typically encountered in such grids, a flux interpolation technique is introduced for the equations governing variable density flows. An important characteristic of the proposed algorithm is that it can be applied to flows in both open and closed domains. Its robustness and accuracy are illustrated with a non-isothermal, turbulent channel flow at temperature ratio of 1.01 and 2.