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Computation of moving boundaries and interfaces and stabilization parameters. (English) Zbl 1032.76605

Summary: The interface-tracking and interface-capturing techniques we developed in recent years for computation of flow problems with moving boundaries and interfaces rely on stabilized formulations such as the streamline-upwind/Petrov-Galerkin (SUPG) and pressure-stabilizing/Petrov-Galerkin (PSPG) methods. The interface-tracking techniques are based on the deforming-spatial-domain/stabilized space-time formulation, where the mesh moves to track the interface. The interface-capturing techniques, typically used with non-moving meshes, are based on a stabilized semi-discrete formulation of the Navier-Stokes equations, combined with a stabilized formulation of the advection equation governing the time-evolution of an interface function marking the interface location. We provide an overview of the interface-tracking and interface-capturing techniques, and highlight how we determine the stabilization parameters used in the stabilized formulations.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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