Control and Optimization of Interfacial Flows Using Adjoint-Based Techniques

Abstract

The applicability of adjoint-based gradient computation is investigated in the context of interfacial flows. Emphasis is set on the approximation of the transport of a characteristic function in a potential flow by means of an algebraic volume-of-fluid method. A class of optimisation problems with tracking-type functionals is proposed. Continuous (differentiate-then-discretize) and discrete (discretize-then-differentiate) adjoint-based gradient computations are formulated and compared in a one-dimensional configuration, the latter being ultimately used to perform optimisation in two dimensions. The gradient is used in truncated Newton and steepest descent optimisers, and the algorithms are shown to recover optimal solutions. These validations raise a number of open questions, which are finally discussed with directions for future work.