NEWTON-KRYLOV METHODS FOR LOW-MACH-NUMBER COMPRESSIBLE COMBUSTION

Fully coupled numerical techniques are used to compute steady-state so lutions to a combusting, low-Mach-number compressible flow through a c hannel. The nonlinear governing equations are discretized on a stagger ed mesh via integration over discrete finite volumes. The resulting no nlinear algebraic equations are linearized with Newton's method and so lved with a preconditioned Krylov algorithm. The selected Krylov solve r is the generalized minimum residual algorithm. A matrix-free Newton- Krylov method and a modified Newton-Krylov method are employed as a me ans of reducing the required number of expensive Jacobian evaluations. The matrix-free implementation is shown to be superior to the modifie d Newton-Krylov method when starting from a poor initial guess. The te chnique of mesh sequencing is shown to provide significant CPU savings for fine grid calculations. Additionally, the domain-based multiplica tive Schwarz preconditioning strategy was found to be more effective t han incomplete lower-upper factorization type preconditioning at lower Mach numbers.