Preconditioned Multigrid Methods for Two-Dimensional Combustion Calculations at All Speeds

The development of an effective implicit integration strategy for two-dimensional (axisymmetric) combustion calculations at all speeds is presented. A time-derivative preconditioning technique is first combined with an implicit line relaxation algorithm to yield an approach capable of removing the acoustic time step restriction at low flow speeds while handling stiff chemical kinetics in a fully implicit fashion. Numerical performance is further improved through the addition of a full multigrid/full approximation storage (FMG-FAS) convergence acceleration strategy. Numerical simulations of a subsonic reacting shear layer (finite rate hydrogen-air chemistry), a subsonic bluff-body stabilized flame (mixing-limited methane-air chemistry), and a supersonic jet diffusion flame (finite rate hydrogen-air chemistry) are presented to test the basic attributes of the algorithm. Comparisons with experimental data are presented for all cases, and a detailed examination of the computational efficiency of the new procedure is conducted. The strengths and weaknesses of multigrid ideas for fully coupled combustion calculations are particularly highlighted.