Abstract
We study two-phase and free surface flows with soluble and insoluble surfactants. A numerical analysis of the contained convection-diffusion equations is carried out. The surface equation is stabilized by Local Projection Stabilization. The benefit of Local Projection Stabilization on surfaces is shown by a numerical example. An advanced finite element method that allow for a robust and accurate numerical simulation is presented. The arbitrary Langrangian-Eulerian framework is utilized to capture the moving surface. This allows the usage of a fitted finite element mesh. A decoupling strategy is used to divide the origin problem into subproblems easier to solve. Different time discretizations are considered and the problem of spurious velocities for the spatial discretization is discussed. Numerical examples in 2d and 3d illustrate the potential of the proposed algorithm. The comparison to mathematical predicted values validates the obtained results.
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