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Robust and efficient adjoint solver for complex flow conditions. (English) Zbl 1410.76274
Summary: A key step in gradient-based aerodynamic shape optimisation using the Reynolds-averaged Navier-Stokes equations is to compute the adjoint solution. Adjoint equations inherit the linear stability and the stiffness of the nonlinear flow equations. Therefore for industrial cases with complex geometries at off-design flow conditions, solving the resulting stiff adjoint equation can be challenging. In this paper, Krylov subspace solvers enhanced by subspace recycling and preconditioned with incomplete lower-upper factorisation are used to solve the stiff adjoint equations arising from typical design and off-design conditions. Compared to the baseline matrix-forming adjoint solver based on the generalized minimal residual method, the proposed algorithm achieved memory reduction of up to a factor of two and convergence speedup of up to a factor of three, on industry-relevant cases. These test cases include the DLR-F6 and DLR-F11 configurations, a wing-body configuration in pre-shock buffet and a large civil aircraft with mesh sizes ranging from 3 to 30 million. The proposed method seems to be particularly effective for the more difficult flow conditions.

76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65M22 Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
76G25 General aerodynamics and subsonic flows
Full Text: DOI
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