Implementation of merging of two fluid bubbles using the level set method

Abstract

Propagating interfaces occur in a wide variety of settings including ocean waves, combustion and flame propagation, crystal growth etc. We are interested in understanding, analyzing and computing such evolving interfaces. The equation of capturing interfaces in this thesis is called the level set equation. In this thesis, we implement merging of two fluid bubbles with the same density under the influence of gravity. In this work, the equations of motion are given by the Boussinesq approximation to the incompressible Stokes equations. We use the projection method and staggered grids to solve the Stokes equation. We also utilize the second order ENO scheme to approximation the convection terms. In addition, because the level set function does not remain as a distance function at later time, we re-initialize the level set function by using Godunov scheme. As a numerical simulation, we show that a bottom bubble with a lighter density rises. After all the two bubbles merge into a single bubble.