Optimal Control for Two-Phase Flows
We consider an optimal control problem with respect to the two-phase Navier–Stokes equations. Different numerical schemes are presented, in particular a level-set method, as well as an approach based an Allen-Cahn phase field model. We also consider a geometrical approach to treat the interface and address the question of convergence of a numerical scheme.
KeywordsTwo-phase Optimal control Stabilized finite elements Level set Allen-Cahn
Mathematics Subject Classification (2010)49Q10 76D55 76M10 76T05 93C20
The authors acknowledge the support by the German Research Association (DFG) under grant SPP-1253, BR-3391/4-1 and PR-548/8-1.
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