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Interface-tracking and interface-capturing techniques for finite element computation of moving boundaries and interfaces. (English) Zbl 1176.76076

Summary: We provide an overview of some of the interface-tracking and interface-capturing techniques we developed for finite element computation of flow problems with moving boundaries and interfaces. This category of flow problems includes fluid-particle, fluid-object and fluid-structure interactions; free-surface and two-fluid flows; and flows with moving mechanical components. Both classes of techniques are based on stabilized formulations. 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 primarily for free-surface and two-fluid interface flows, are formulated typically over non-moving meshes, using an advection equation in addition to the flow equations. The advection equation governs the evolution of an interface function that marks the location of the interface. We also highlight some of the 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
76D05 Navier-Stokes equations for incompressible viscous fluids
76D27 Other free boundary flows; Hele-Shaw flows
76D50 Stratification effects in viscous fluids
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