An efficient inexact-Newton-Krylov algorithm is presented for the computation of steady aerodynamic flows. The algorithm uses preconditioned, restarted GMRES in matrix-free form to solve the linear system arising at each Newton iteration. The preconditioner is formed using an ILU(2) factorization of an approximate Jacobian matrix after applying the Reverse Cuthill-McKee reordering. The algorithm has been successfully applied to a wide range of test cases which include inviscid, laminar, and turbulent aerodynamic flows. In all cases except one, convergence of the residual to 10^-12 is achieved with a CPU cost equivalent to fewer than 1200 function evaluations. The sole exception is a low Mach number case where some form of local preconditioning is needed. Several other efficient implicit solvers have been applied to the same test cases, and the matrix-free inexact-Newton-GMRES algorithm is seen to be the fastest and most robust of the methods studied. Hence this strategy is an excellent option for flow computations in which memory use is not critical, such as two-dimensional applications.

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An efficient Newton-GMRES algorithm is presented for computing steady compressible aerodynamic flows on structured grids. The algorithm uses preconditioned restarted GMRES in matrix-free form to solve the linear system arising at each Newton iteration. The preconditioner is formed using an ILU(2) factorization of an approximate Jacobian matrix after applying the Reverse CuthillMcKee reordering. Studies are presented which show the optimum choices of various parameters and strategies for the class of flows of interest. Finally, the algorithm developed is applied to a range of test cases and compared with a Newton-GMRES algorithm using an approximate Jacobian matrix and a well-known approximatelyfactored implicit algorithm. The new algorithm is shown to offer substantial reductions in the CPU time required to achieve a steady state. Introduction Computational methods for simulating aerodynamic flows have an important role in aircraft design. A great effort has been made to develop code...

The prediction of unsteady flow field in turbine blades as well as in the turbomachinery stages is now an affordable item, and is required by the reduced margin for increasing efficiency, stability and life of propulsion components. The numerical tools are now capable to run within reasonable time 3D unsteady calculation for full stage, and the new techniques on the computation and parallel computer allow the improvements of results in terms of cost and accuracy. Despite these advantages many questions remain open and the physical modelling joint with the numerical improvements is still a challenge if it has to produce usable results, compared with the experiments. On the other side the huge amount of data extracted from experiments require care and skinless to become useful tools for design. The two activities interact and support each other in the attempt to improve design quality. Aim of this paper is the report on some experience and the attempt to give some answer on that challenge, presenting results of a recent activity on modelling side compared with experiments as well. A full-3D unstructured solver based on an upwind TVD finite volume scheme has been developed and applied to the simulation of an unsteady turbine stage. The development of the numerical strategy is discussed with particular concern on the validation of the unsteady model through a comparison against experiments, NISRE approach and a 3D steady stage computation. The present work considers the application of the fully unstructured hybrid solver for internal viscous flows, as well. The multiblock version of the solver developed for turbine is considered, because of the highly improved performance as compared to the single domain version of the code. Moreover, the high numerical costs involved in 3D unsteady computations required the development of a new parallel single program multiple-data version of the numerical solver. The results compare favourably with a set of time averaged and unsteady experimental data available for the turbine stage under investigation, which is representative of a wide class of aero-engines.