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**Stabilized finite element methods for flows with moving boundaries and interfaces.**
*(English)*
Zbl 1309.76135

Summary: We highlight some of the finite element methods we developed for computation of flows with moving boundaries and interfaces. The methods developed can be classified into two main categories: interface-tracking and interface-capturing techniques. Both classes of techniques are based on stabilized formulations, and determination of the stabilization parameters used in these formulations is also highlighted here. The interface-tracking techniques are based on the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation, where the mesh moves to track the interface. The interface-capturing techniques, developed for two-fluid flows, are formulated typically over non-moving meshes, using an advection equation in addition to the flow equations. The advection equation governs the time-evolution of an interface function marking the interface location. We also highlight some of the additional methods we developed to increase the scope and accuracy of these two classes of techniques.

### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |