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Author: Hintermüller, Michael × End date: 2019 × Start date: 2010 × Type: Text × Subject: adaptivity × Subject: optimal control × WGL Institute: WIAS ×

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    Simulation and control of a nonsmooth Cahn--Hilliard Navier--Stokes system with variable fluid densities
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Gräßle, Carmen; Hintermüller, Michael; Hinze, Michael; Keil, Tobias
    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 high-fidelity 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.