An Exact Numerical Method for Tracking Bubble Coalescence

In this article, a numerical method based on a combination of the level-set approach and the SIMPLE procedure in the finite-volume framework has been developed to simulate two-dimensional laminar incompressible two-phase flows. A level-set function is used for tracking the gas-liquid interface, and a TVD scheme of second-order upwind coupled with flux limiter is proposed for solving the level-set equation to control the instability caused by nonlinear convection. A modification of Godunov's method of a third-order total variation diminishing (TVD)-Runge-Kutta explicit time-stepping procedure and a fifth-order essentially nonoscillatory (ENO) approximation are presented to re-initialize the level-set function to an exact signed distance function all the time. The governing equations are discretized on the collocated grids in a body-fitted coordinate, and the QUICK scheme with third-order accuracy is used for discretizing the convection terms. A dynamic behavior of a single rising bubble and two bubbles' coalescence in a vertical container is simulated by using this developed code.