Sensitivity computation for ducted flows using adjoint of implicit pressure-velocity coupled solver based on Foam

Adjoint based methods have become the focus of research in CFD optimization pertaining to their low computational cost compared to other traditional methods. In principle, adjoints are computed via two methods: Continuous and Discrete. In the continuous method, adjoints are computed by deriving the adjoint equations of corresponding state variables and boundary conditions and then are solved using similar schemes as that of the primal. The discrete approach using Algorithmic Differentiation (AD) [9] is implemented either by source transformation or by an operator overloading tool. For an object-oriented code in C++ like OpenFOAM [10], the use of an operator overloading tool becomes imperative. Discrete adjoints based on operator overloading have the distinct advantage of robustness and stability while computing accurate gradients. Our experience however shows that adjoints of traditional SIMPLE (semi implicit method for pressure linked equations) [13] like algorithms have high computational cost even after employing standard performance improvement techniques such as binomial checkpointing [4] and analytic treatment of the linear solver [3]. Thus in this paper we present the discrete adjoint solver based on puCoupledFoam [7], an implicit pressure-velocity coupled incompressible steady state solver in Foam-extend(v3.1) [14].The objective is to exploit the faster rate of convergence of the flow equations in terms of runtime and number of non-linear solves to compute fast gradients. The solver is tested on related test problems to demonstrate significant performance improvement