A deferred correction coupling strategy for low Mach number flow with complex chemistry

Abstract

We present a new thermodynamic coupling strategy for complex reacting flow in a low Mach number framework. In such flows, the advection, diffusion and reaction processes span a broad range of time scales. In order to reduce splitting errors inherent in Strang splitting approaches, we couple the processes with a multi-implicit spectral deferred correction strategy. Our iterative scheme uses a series of relatively simple correction equations to reduce the error in the solution. The new method retains the efficiencies of Strang splitting compared to a traditional method-of-lines approach in that each process is discretised sequentially using a numerical method well suited for its particular time scale. We demonstrate that the overall scheme is second-order accurate and provides increased accuracy with less computational work compared to Strang splitting for terrestrial and astrophysical flames. The overall framework also sets the stage for higher-order coupling strategies.