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Stabilisation of discrete steady adjoint solvers. (English) Zbl 1351.76131
Summary: A new implicit time-stepping scheme which uses Runge-Kutta time-stepping and Krylov methods as a smoother inside FAS-cycle multigrid acceleration is proposed to stabilise the flow solver and its discrete adjoint counterpart. The algorithm can fully converge the discrete adjoint solver in a wide range of cases where conventional point-implicit methods fail due to either physical or numerical instability. This enables the discrete adjoint to be applied to a much wider range of flow regimes. In addition, the new algorithm offers improved efficiency when applied to stable cases for which the conventional Block-Jacobi solver can fully converge. Both stable and unstable cases are presented to demonstrate the improved robustness and performance of the new scheme. Eigen-analysis is presented to outline the mechanism of the adjoint stabilisation effect.

76M12 Finite volume methods applied to problems in fluid mechanics
65M22 Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
Full Text: DOI
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