Numerical Simulation of Interfacial and Multiphase Flows Using the Front Tracking Method

Abstract

The rise of bubbles in viscous liquids is a very common process in many industrial applications and an important fundamental problem in fluid physics. A robust three-dimensional method for the direct numerical simulation of such flows is therefore developed by combining several powerful features. The interface is handled by a front tracking approach with transient mesh adaptation. One single set of the incompressible Navier-Stokes equations for the entire domain is solved by a modified SIMPLE algorithm on a Cartesian grid generated by PARAMESH: an adaptive mesh refinement tool for parallel computing. A moving reference frame is incorporated, making the simulation end time independent of the domain size. The method is shown to be robust for a wide range of Reynolds numbers and large density and viscosity ratios and is validated against experiments such as air bubbles rising in water. Successful simulations of path instability of rising bubbles and bubble-bubble interaction illustrate the capabilities of the method. A reformulation of the governing equations through sequential regularization is also investigated.