Optimal control of time-discrete two-phase flow driven by a diffuse-interface model

Abstract

We propose a general control framework for two-phase flows with variable densities in the diffuse interface formulation, where the distribution of the fluid components is described by a phase field. The flow is governed by the diffuse interface model proposed in Abelset al.[M3AS22(2012) 1150013]. On the basis of the stable time discretization proposed in Garckeet al.[Appl. Numer. Math.99(2016) 151] we derive necessary optimality conditions for the time-discrete and the fully discrete optimal control problem. We present numerical examples with distributed and boundary controls, and also consider the case, where the initial value of the phase field serves as control variable.