Comparative Study of Inner-Outer Krylov Solvers for Linear Systems in Structured and High-Order Unstructured CFD Problems

Abstract

Advanced Krylov subspace methods are investigated for the solution of linear systems arising from an adjoint-based aerodynamic shape optimization problem. A special attention is paid for the flexible inner-outer GMRES strategy combined with most relevant preconditioning strategies and deflation techniques. The choice of this specific class of Krylov solvers for solving challenging problems is based on its outstanding convergence properties. Moreover, parallel scalability is improved by globalizing the preconditioning phase through an additive domain decomposition technique. However, maintaining the performance of the preconditioner may be challenging since scalability and efficiency of a preconditioning technique are properties often antagonistic to each other. We demonstrate how flexible inner-outer Krylov methods are able to overcome this critical issue. A numerical comparative study is provided on the supercritical OAT15A airfoil in turbulent flow under transonic regime conditions using a Finite Volume method (FV) and a High-Order Discontinuous Galerkin (DG) one. Based on this representative problem a discussion of the recommended numerical practices is proposed.

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