Simulation and Control of a Nonsmooth Cahn-Hilliard Navier-Stokes System

Abstract

We are concerned with the simulation and control of a two phase flow model governed by a coupled Cahn-Hilliard Navier-Stokes system involving a nonsmooth energy potential. We establish the existence of optimal solutions and present two distinct approaches to derive suitable stationarity conditions for the bilevel problem, namely C-and strong stationarity. Moreover, we demonstrate the numerical realization of these concepts at the hands of two adaptive solution algorithms relying on a specifically developed goal-oriented error estimator. In addition, we present a model order reduction approach using proper orthogonal decomposition (POD-MOR) in order to replace highfidelity models by low order surrogates. In particular, we combine POD with space-adapted snapshots and address the challenges which are the consideration of snapshots with different spatial resolutions and the conservation of a solenoidal property.

Optimal Control of Sliding Droplets using the Contact Angle Distribution

“…For results on control and boundary control of the Cahn-Hilliard and Cahn-Hilliard Navier-Stokes equation we refer to [21,24,29,30,39,41,42,46]. Remark 1 (Nonlinear density and viscosity).…”