Newton-Krylov Methods for Low-Mach-Number Compressible Combustion

Fully coupled numerical techniques are used to compute steady-state solutions to a combusting, low-Mach-number compressible flow through a channel. The nonlinear governing equations are discretized on a staggered mesh via integration over discrete finite volumes. The resulting nonlinear algebraic equations are linearized with Newton's method and solved with a preconditioned Krylov algorithm. The selected Krylov solver is the generalized minimum residual algorithm. A matrix-free Newton-Krylov method and a modified Newton-Krylov method are employed as a means of reducing the required number of expensive Jacobian evaluations. The matrix-free implementation is shown to be superior to the modified Newton-Krylov method when starting from a poor initial guess. The technique of mesh sequencing is shown to provide significant CPU savings for fine grid calculations. Additionally, the domain-based multiplicative Schwarz preconditioning strategy was found to be more effective than incomplete lower-upper factorization type preconditioning at lower Mach numbers.

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