Discussion of Dynamics and Operator Splitting Techniques for Two-Phase Flow with Gravity

Abstract

We study the dynamics of two-phase flow with gravity and point out three different transport mechanisms: non-cyclic advection, solenoidal advection, and gravity segregation. Each term has specific mathematical properties that can be exploited by specialized numerical methods. We argue that to develop effective operator splitting methods, one needs to understand the interplay between these three mechanisms for the problem at hand.