Fast Projection Methods for Variable Density and low-Mach Reacting Flows.*

In this work, we report on the progress we made at developing a theory of fast projection methods for high-order (in time) variable density and low-Mach reacting flows. Fast-projection methods aim at eliminating the computationally expensive pressure-solve in Navier-Stokes simulations, while retaining formal accuracy and stability. These methods replace the pressure Poisson equation by rationally derived approximations for the pressure that are much cheaper to calculate than solving for the pressure itself. When compared to their conventional counterparts, where a pressure-solve is required at each stage of a high-order integrator, these methods can achieve up to 40% speedup for the same target accuracy. While the projection method has been extended to low-mach and reacting flows, fast projections methods have mainly been exclusive to incompressible flows. When applied to reacting flows, the projection method results in a variable coefficient Poisson equation for the pressure and a dilatation field that is coupled to energy, species, and scalar transport. This in turn complicates the design of fast-projection methods for low-Mach flows. In this work, we report our progress on developing a theory of fast projection methods for reacting flows and demonstrate, surprisingly, that the same pseudo-pressure approximations derived for incompressible flow case remain valid in a low- mach, reacting flow setting.