Perspective on Eulerian Finite Volume Methods for Incompressible Interfacial Flows
volume 391 of CISM Courses and Lectures IV, Springer, Wien, (1998)Abstract
Incompressible interfacial flows here refer to those incompressible flows possessing multiple distinct, immiscible fluids separated by interfaces of arbitrarily complex topology. A prototypical example is free surface flows, where fluid properties across the interface vary by orders of magnitude. Interfaces present in these flows possess topologies that are not only irregular but also dynamic, undergoing gross changes such as merging, tearing, and lamenting as a result of the flow and interface physics such as surface tension and phase change. The interface topology requirements facing an algorithm tasked to model these flows inevitably leads to an underlying Eulerian methodology. The discussion herein is confined therefore to Eulerian schemes, with further emphasis on finite volume methods of discretization for the partial differential 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 difficult to select or devise algorithms whose shortcomings are not manifested while modeling the problem at hand. In the following, many algorithms are reviewed briefly 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 flow algorithms continues and the future looks very promising. This perspective will hopefully provide "field guidance" useful in devising algorithms whose weaknesses are not magnified when applied to your problem.