MULTI-PHASE FLOW MODELS AND METHODS FOR LAVA LAMPS AND LIFE SCIENCES

摘要

Multi-phase flows, that involve immiscible fluids, arise in many natural and industrial processes and their accurate and efficient simulation will play an increasingly vital role in the life sciences. Surface tension, characteristic of these flows, creates a discontinuous pressure drop across each surface separating two liquid phases that is proportional to the surface's mean curvature. The primary computational challenge is to solve for the pressure whose laplacian has a singular term consisting of a distribution supported on the separating surfaces. In this paper we discuss models and methods for multiphase flows that include simplifying assumptions, boundary integral representations, and wavelet-based discretization and multilevel preconditioning. We also discuss the validation of these models and methods through the simulation of lava lamps, whose simple two-phase flows and convenient availability provide an ideal laboratory testbed.