Adjoint-based optimisation of interfacial flows in the sharp interface limit. Application to the Stefan problem.

The flows encountered in energy conversion systems consist of a wealth of complex phenomena. While computational fluid dynamics has now become a present tool in describing and predicting such multi-physics flows, these state-of-the-art computational resources still provide limited insight towards a robust optimization framework. Targeted manipulation of such flows by enhanced designs or active control strategies is however crucial for improvements in performance and robustness and venturing beyond standard operating conditions. The transition from model-based numerical simulations to model-based optimal control requires an alternative approach, which allows access to inverse information. As far as two-phase flows are concerned, to date, inverse information has been extracted from simulations of simplified configurations with additional unrealistic assumptions, or from low-fidelity models. In this work, on the other hand, the one-fluid formulation is used, where the sharp interface representation is captured by a level set method. We focus our study on the Stefan problem, where the motion of the interface is a function of the jump in gradient of temperature. The gradient extraction strategy differentiate-then-discretize is then used to minimize tracking-type objective functions.