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.
MSC:
| 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 |
Software:
TAPENADEReferences:
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