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 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.
Keywords
Cite
@article{arxiv.1907.04285,
title = {Simulation and Control of a Nonsmooth Cahn-Hilliard Navier-Stokes System},
author = {Carmen Gräßle and Michael Hintermüller and Michael Hinze and Tobias Keil},
journal= {arXiv preprint arXiv:1907.04285},
year = {2019}
}