A SEMIIMPLICIT NUMERICAL SCHEME FOR REACTING FLOW - I - STIFF CHEMISTRY

An additive semi-implicit projection scheme for the simulation of unst eady combustion in two dimensions is constructed. The scheme relies on a zero-Mach number formulation of the compressible conservation equat ions with detailed chemistry. The governing equations are discretized in space using second-order differences and integrated in time using a semi-implicit approach. Time integration of the evolution equations f or species mass fraction, thermodynamic pressure, and density is perfo rmed using a semi-implicit, nonsplit scheme that combines a second-ord er predictor-corrector treatment of convection and diffusion terms, an d a stiff integrator for the reaction source terms. Meanwhile, the mom entum equations are integrated using a second-order projection scheme. The projection scheme is based on a predictor-corrector approach that couples the evolution of the Velocity and density fields in order to stabilize computations of reacting flows with large density variations . A pressure Poisson equation is inverted following both the predictor and corrector steps using a fast solver. The advantages of the stiff integration of reaction source terms are analyzed by comparing the per formance of the scheme to that of a predictor-corrector scheme in whic h reaction and diffusion are integrated in a similar nonstiff fashion. The comparison in based on both one-dimensional (1D) unsteady tests o f a premixed methane-air flame, and unsteady two-dimensional tests of the same flame interacting with a counterrotating Vortex pair. In both cases, the GRImech 1.2 reaction mechanism with 32 species and 177 ele mentary reactions is used. Computed results show that the stiff reacti on scheme enables selection of larger time steps and thus leads to sub stantial improvement in the performance of the computations. For the p resent reaction mechanism and flame conditions, speedup factors of abo ut 10 are achieved in the 1D tests and about five in two dimensions. P ossible extensions of the present scheme to further improve efficiency are also discussed. (C) 1998 Academic Press.