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Adjoint complement to viscous finite-volume pressure-correction methods. (English) Zbl 1349.76391
Summary: A hybrid-adjoint Navier-Stokes method for the pressure-based computation of hydrodynamic objective functional derivatives with respect to the shape is systematically derived in three steps: The underlying adjoint partial differential equations and boundary conditions for the frozen-turbulence Reynolds-averaged Navier-Stokes equations are considered in the first step. In step two, the adjoint discretisation is developed from the primal, unstructured finite-volume discretisation, such that adjoint-consistent approximations to the adjoint partial differential equations are obtained following a so-called hybrid-adjoint approach. A unified, discrete boundary description is outlined that supports high- and low-Reynolds number turbulent wall-boundary treatments for both the adjoint boundary condition and the boundary-based gradient formula. The third component focused in the development of the industrial adjoint CFD method is the adjoint counterpart to the primal pressure-correction algorithm. The approach is verified against the direct-differentiation method and an application to internal flow problems is presented.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
Software:
TAF
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