Time-accurate calculation of variable density flows with strong temperature gradients and combustion

A time-accurate algorithm is proposed for low Mach number, variable density flows with or without chemical reactions. 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 fully satisfy the continuity equation at each time step. Spatial discretization is performed on a collocated grid system that offers computational simplicity and straightforward 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 series of numerical experiments. In particular, we present simulations of non-isothermal, turbulent channel flow as well as simulations of a premixed flame–vortex interaction.