Journal
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
Volume 25, Issue -, Pages -Publisher
EDP SCIENCES S A
DOI: 10.1051/cocv/2018006
Keywords
Optimal control; boundary control; initial value control; two-phase flow; Cahn-Hilliard; Navier-Stokes; diffuse-interface models
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Funding
- Deutsche Forschungsgemeinschaft (DFG) [GA695/6-2, HI689/7-1]
- DFG through the International Research Training Group [IGDK 1754]
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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.
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