Parallelized Simulations of Two-fluid Dispersions

Two-fluid dynamics is a challenging subject, rich both in physics and in practical applications, which range from manufacturing to lubricated transport. Mechanisms unique to a flow can be exploited to enhance functionality in applications. For example, density-matching can be used to depress the effect of gravity, or of centripetal acceleration in rotating systems, making it possible to manipulate the locations occupied by the fluid, as well as the shapes of the interfaces between the fluids. Viscosity segregation can be used to promote mixing and demixing, and thus the displacement of one fluid by another (as in the problem of oil recovery), or to segregate one molten plastic from another by encapsulation. The lubrication of one (highly viscous) fluid by another (less viscous) fluid is a particularly important branch of two-fluid dynamics. Many configurations are possible for the flow of two immiscible fluids: layers, fingers, encapsulated regimes, and drops. One of the difficulties in the study of flows of two immiscible fluids is that the domain contains an interface. The interface moves under the effects of the flow and can sometimes undergo severe deformations, including breakup. In the numerical treatment of these flows, we must answer three questions: (1) How do we represent the interface on a mesh? (2) How will the interface evolve in time? (3) How should we apply the boundary conditions on the interface? There are many interface-tracking methods, such as the moving-grid method, the front-tracking method, the level-set method, and the volume-of-fluid (VOF) method. The VOF method provides a simple way to treat the topological changes of the interface, as well as ease of generalization to the three-dimensional case. The interested reader is referred to a recent review article [4] and its references. Our two-fluid code is composed of three parts: a second-order VOF method for tracking the interface, a projection method for solving the Navier–Stokes equations on the MAC grid (to be defined later), and, finally, a continuum method for modeling the interfacial tension.