The direct numerical simulation of two-phase flows with interface capturing methods

Multiphase flows play a central role in problems related to the environment and industry. Common, but significant, features of such problems are complex geometries and topography, transport processes across phase boundaries, and internal interfaces that merge, break, and deform. Requirements to predict fluid motion under such conditions provide significant challenges for computational fluid dynamics, particularly for direct simulation of flows involving internal interfaces. In this paper, we will focus on two models that capture the motion of internal interfaces implicitly and can resolve complex flows down to computational grid sizes. The methods are based on the phase-field approach, which are also applied in its general form to viscoelastic and phase separating polymeric systems - in the latter case using a self-consistent field theoretic approach. For processes occurring over very small length scales, e.g. nucleation and growth, such computations result in finite thickness interfaces and capture the necessary physics. For larger length-scale multiphase structures, the interface becomes a contact discontinuity, and the method smoothly transitions into a level-set-like formulation. However, in this second form the sharp interface is computationally difficult to handle. A variation of the ghost-fluid method in which sharp interfaces can be captured will be presented. Applications will be shown at the two extremes of scales, including early stages of nucleation, growth and coarsening of multiphase structures, as well as macroscopic flows in which length-scales and velocities are large.