Finite-volume method for the calculation of compressible chemically reacting flows

The time-dependent Euler and Navier-Stokes equations including the effects of finite-rate chemistry are numerically integrated forward in time to predict the steady-state behavior of compressible chemically reacting flows. An efficient acceleration technique is developed based on preconditioning the conservation equations. One possible choice for the preconditioner leads to a procedure which is equivalent to treating the convection and diffusion terms explicitly and species source terms implicitly. These methods can be viewed as ways of rescaling the equations in time so that all chemical and convective phenomena evolve on comparable pseudotime scales. For the steady-state solution in this paper, the number of iterations needed to solve reacting problems is approximately the same as for nonreacting problems. The methods are applied to a quasi-one-dimensional dissociation model problem, a quasi-one-dimensional H2-air combustion problem, and to two-dimensional inviscid and viscous premixed H2-air problems.