An Explicit Variable-Density Projection Method for Low-Mach Reacting Flows on Structured Uniform Grids

Low-Mach reacting flows belong to a category of fluid dynamics where acoustic perturbations have negligible influence on the thermodynamics of the flow. They are used to model flares, combustors, reactors, supernovae, and other variable-density flows. However, solving the full equations of gas dynamics in the low-Mach regime is notoriously inefficient due to the presence of acoustic timescales which dictate stability requirements on the timestep size. Pressure projection methods provide a means of excluding these acoustic timescales and allowing one to march in time at the much more attainable convective timescales. In this study, a consistent, explicit projection method is developed for low-Mach reacting flows on structured uniform grids. The approach is based on predicting a dilatation field that is consistent with the thermodynamic state of the flow. The method is fully explicit, first-order in time and requires the solution of a variable coefficient Poisson equation for the pressure. The method has been formally verified and validated against analytical and MMS solutions of variable density flows with mixing and reactions. It has been shown to be robust over a very high range of density ratios up to 1000 and is capable of recovering the incompressible limit.