Schwarz-preconditioned Newton-Krylov algorithm for low speed combustion problems

Newton-Krylov-Schwarz algorithms solve a system of equations describing low Mach number combustion. Two model problems are considered. The first is a low speed, combusting flow through a channel, representing an idealized laminar diffusion flame. The second problem consists of an expansion channel, representing an idealized combustion chamber. Both problems include three chemical species and one kinetic reaction. Finite-volume discretization on a staggered mesh converts the continuous system of governing equations into a discrete system of nonlinear algebraic equations, which are subsequently linearized using Newton's method. The resulting linearized systems are solved using the preconditioned Generalized Minimal RESidual (GMRES) algorithm. The effectiveness of domainbased additive and multiplicative Schwarz preconditioned is studied with respect to partitioning strategy and subdomain solver selection. Block incomplete factorizations of the subdomain matrices yield effective Schwarz preconditioners with comparatively moderate computer memory requirements. In comparison, point-wise incomplete factorizations are unreliable at low Mach numbers, while complete factorizations often require excessive computer memory. Multiplicative Schwarz preconditioning outperforms additive Schwarz, but not sufficiently so to outweigh the parallel advantages of additive Schwarz. Preconditionng with a low-order discretization reduces both computer memory and CPU time for the Reynolds number of interest.