SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Optimal control of incompressible two-phase flows

M. Braack and B. Tews

Abstract
We consider an optimal control problem of two incompressible and immiscible Newtonian fluids. The motion of the interface between these fluids can be captured by a phase field model or level set model. Both methods are subject of this talk. The state equation includes surface tension and is discretized by a discontinuous Galerkin scheme in time and a continuous Galerkin scheme in space. In order to resolve the interface propagation we also apply adaptive finite elements in space and time. We derive first order optimality conditions including the adjoint equation which is also formulated in a strong sense. The optimality system on the discrete level is solved by Newton's method. In the numerical example we compare level sets with a phase field model.

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