Volume 25, 2019
|Number of page(s)||31|
|Published online||17 June 2019|
Optimal control of time-discrete two-phase flow driven by a diffuse-interface model*
Fakultät für Mathematik, Universität Regensburg,
2 Fachbereich Mathematik, Universität Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany.
3 Zentrum Mathematik, Technische Universität München, Garching bei München, Germany.
** Corresponding author: Christian.Kahle@ma.tum.de
Accepted: 13 January 2018
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 Abels et al. [M3AS 22 (2012) 1150013]. On the basis of the stable time discretization proposed in Garcke et 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.
Mathematics Subject Classification: 35Q35 / 49N45 / 49M05 / 65K10
Key words: Optimal control / boundary control / initial value control / two-phase flow / Cahn–Hilliard / Navier–Stokes / diffuse-interface models
The authors gratefully acknowledge the financial support by the Deutsche Forschungsgemeinschaft (DFG) through the grants GA695/6-2 (first author) and HI689/7-1 (second and third author) within the priority program SPP1506 “Transport processes at fluidic interfaces”. The third author additionally gratefully acknowledges the support by the DFG through the International Research Training Group IGDK 1754 “Optimization and Numerical Analysis for Partial Differential Equations with Nonsmooth Structures”.
© EDP Sciences, SMAI 2019
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