A new resolution method for solving linear systems resulting from the discrete adjoint approach in aerodynamic shape optimization with a single objective and multiple constraint functions is presented. The steady flow is governed by the three-dimensional compressible Favre-averaged Navier–Stokes equations combined with a two-equation turbulence model. Block flexible variants of the generalized minimal residual method are Krylov methods designed for the solution of linear systems with multiple right-hand sides allowing variable preconditioning. Then, they can be applied to the discrete adjoint equations of Favre-averaged Navier–Stokes equations for all objective and constraint functions as a right-hand side. The paper focuses on the development of a new algorithm combining the three following features: flexibility, multiple right-hand-side concurrent processing, and spectral deflation. This latter property enables to recycle approximate spectral information from one restart to the next one in order to avoid generalized minimal residual stagnation when short restart recurrences are performed. This novel block method is named block flexible generalized minimal residual with deflated restarting. It is evaluated on two aerodynamic configurations showing its capabilities to reduce computational times over standard Krylov methods.
Block Krylov Methods to Solve Adjoint Problems in Aerodynamic Design Optimization
AIAA Journal ; 51 , 9 ; 2183-2191
2013-09-01
Article (Journal)
Electronic Resource
English
Block Krylov Methods to Solve Adjoint Problems in Aerodynamic Design Optimization
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