An adjoint view on flux consistency and strong wall boundary conditions to the Navier–Stokes equations

Journal Article · Sun Nov 15 04:00:00 EST 2015 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2015.08.022· OSTI ID:22570196

Stück, Arthur

Inconsistent discrete expressions in the boundary treatment of Navier–Stokes solvers and in the definition of force objective functionals can lead to discrete-adjoint boundary treatments that are not a valid representation of the boundary conditions to the corresponding adjoint partial differential equations. The underlying problem is studied for an elementary 1D advection–diffusion problem first using a node-centred finite-volume discretisation. The defect of the boundary operators in the inconsistently defined discrete-adjoint problem leads to oscillations and becomes evident with the additional insight of the continuous-adjoint approach. A homogenisation of the discretisations for the primal boundary treatment and the force objective functional yields second-order functional accuracy and eliminates the defect in the discrete-adjoint boundary treatment. Subsequently, the issue is studied for aerodynamic Reynolds-averaged Navier–Stokes problems in conjunction with a standard finite-volume discretisation on median-dual grids and a strong implementation of noslip walls, found in many unstructured general-purpose flow solvers. Going out from a base-line discretisation of force objective functionals which is independent of the boundary treatment in the flow solver, two improved flux-consistent schemes are presented; based on either body wall-defined or farfield-defined control-volumes they resolve the dual inconsistency. The behaviour of the schemes is investigated on a sequence of grids in 2D and 3D.

• OSTI ID: 22570196
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 301; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCURACY
ADVECTION
BOUNDARY CONDITIONS
CONTROL
DIFFUSION
FUNCTIONALS
IMPLEMENTATION
NAVIER-STOKES EQUATIONS
OSCILLATIONS
REYNOLDS NUMBER
WALLS