Parallel implicit Newton-Krylov-Schwarz method for predicting compressible turbomachinery flows

A parallel Newton-Krylov-Schwarz (NKS) algorithm is presented for solving two-dimensional steady compressible flows in turbomachinery. The spatial discretization of the governing equations is carried out on multiblock quadrilateral mesh using an upwind finite-volume formulation with limited linear reconstruction and Riemann-solver-based flux functions. A matrix-free inexact Newton method is used to solve the system of nonlinear equations arising from the finite-volume discretization procedure and a preconditioned GMRES method is used to solve the resulting linear system of equations. A Schwarz global preconditioner is used in conjunction with block incomplete LU (BILU) preconditioners based on the Jacobian of the first-order scheme for the mesh sub-domains. The preconditioning and multiblock mesh structure allow efficient and scalable parallel implementation of the implicit algorithm. Numerical results are described for several flow cases, demonstrating both the effectiveness of the algorithm and parallel implementation. Influences of the global and local preconditioning are also investigated and discussed.