Derivation of an adjoint high-Reynolds number model for thermally driven flows

This paper presents a high-Reynolds number (high-Re) approach to the adjoint Navier-Stokes-Fourier equations based upon modified high-Re boundary conditions for buoyancy-driven flows. For reasons of efficiency, the computational framework adheres to the continuous adjoint method using a frozen-turbulence assumption. Opposed to the state of the art, the present model uses a high-Re model for the primal equations and a high-Re model for the adjoint equations. The adjoint high-Re model can easily be implemented and be used for flow problems where wall functions are needed. The impact of this approach is an improved consistency of primal and adjoint equations which leads to stable and realistic shape optimisation results for industrial flows. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)