A time-accurate implicit method for chemically reacting flows at all Mach numbers

The objective of this work is to develop a unified solution algorithm capable of treating time-accurate chemically reacting flows at all Mach numbers, ranging from molecular diffusion velocities to supersonic speeds. A rescaled pressure term is used in the momentum equation to circumvent the singular behavior of pressure at low Mach numbers. A dual time-stepping integration procedure is established. The system eigenvalues become well behaved and have the same order of magnitude, even in the very low Mach number regime. The computational efficiency for moderate and high speed flow is competitive with the conventional density-based scheme. The capabilities of the algorithm are demonstrated by applying it to selected model problems including nozzle flows and flame dynamics.