Model Predictive Control of Variable Density Multiphase Flows Governed by Diffuse Interface Models

We present a nonlinear model predictive framework for closed-loop control of two-phase flows governed by Cahn-Hilliard Navier-Stokes system with variable density. The control goal consists in achieving a prescribed concentration distribution in the Cahn-Hilliard part through distributed and/or boundary control of the flow part. Special emphasis is taken on quick control responses which are achieved through the inexact solution of the optimal control problems appearing in the model predictive control strategy. The resulting control concept is known as instantaneous control and is applied to feedback control of the Navier-Stokes system in e.g. Choi et al. (1999); Hinze (2005a); Hinze and Volkwein (2002). We provide numerical investigations which indicate that instantaneous wall parallel boundary control of the flow part is well suited to achieve a prescribed concentration distribution in the variable density Cahn-Hilliard Navier-Stokes system.