Multiphase computations using sharp and continuous interface techniques for micro-gravity applications

The Eulerian–Lagrangian method is a popular and effective approach for handling multi-fluid problems involving substantial shape variations. Specifically, one can consider the interface either as a sharp discontinuity, consistent with the fundamental continuum theory, or as a smooth transition zone, reducing numerical difficulties in tracking distinct regions. In this article, we highlight the performance characteristics of both techniques. Computationally, both approaches can be devised using similar concepts, namely, the interface is represented by marker points and advected in a Lagrangian framework, and the mass, momentum, and energy conservation equations are solved on a fixed (Eulerian) Cartesian grid using a second-order projection method. The main difference lies in the way of accounting for the interfacial conditions and communication across the interface. The sharp interface method is more demanding computationally because the field equations in each zone need to be coupled with those in other materials/phases, by explicitly tracking the interfacial conditions via matching procedures. In return, second-order accuracy can be attained as compared to the first-order accuracy in the continuous interface method. Nevertheless, in physical applications, both approaches can be highly effective in handling a variety of multi-fluid problems involving moving boundaries. Several examples are presented to highlight the various performance characteristics of the two techniques.