Interface-Tracking and Interface-Capturing Techniques for Computation of Moving Boundaries and Interfaces

As a category of challenging flow problems, flows with moving boundaries and interfaces, includes fluid–particle, fluid–object and fluid–structure interactions; free-surface and two-fluid flows; and flows with moving mechanical components. To address the challenges involved in computation of this category of problems, we developed a number of interface-tracking and interface-capturing techniques. Both classes of techniques are based on stabilized formulations. The interface-tracking techniques are based on the DeformingSpatial-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 describe some of the methods we developed to increase the scope and accuracy of these two classes of techniques.