Perspective on Eulerian Finite Volume Methods for Incompressible Interfacial Flows

Incompressible interfacial ows here refer to those incompressible ows possessing multiple distinct, immiscible uids separated by interfaces of arbitrarily complex topology. A prototypical example is free surface ows, where uid properties across the interface vary by orders of magnitude. Interfaces present in these ows possess topologies that are not only irregular but also dynamic, undergoing gross changes such as merging, tearing, and lamenting as a result of the ow and interface physics such as surface tension and phase change. The interface topology requirements facing an algorithm tasked to model these ows inevitably leads to an underlying Eulerian methodology. The discussion herein is connned therefore to Eulerian schemes, with further emphasis on nite volume methods of discretization for the partial diierential equations manifesting the physical model. Numerous algorithm choices confront users and developers of simulation tools designed to model the time-unsteady incompressible Navier-Stokes (NS) equations in the presence of interfaces. It remains diicult to select or devise algorithms whose shortcomings are not manifested while modeling the problem at hand. In the following, many algorithms are reviewed brieey and commented on, but special attention is paid to projection methods for the incompressible NS equations, volume tracking methods for interface kinematics, and immersed interface methods for interface dynamics such as surface tension. At present, the quest for improved interfacial ow algorithms continues and the future looks very promising. This perspective will hopefully provide \\eld guidance" useful in devising algorithms whose weaknesses are not magniied when applied to your problem.