Computation of moving boundaries and interfaces and stabilization parameters

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. Copyright © 2003 John Wiley & Sons, Ltd.