Side wall boundary effect on the Rayleigh–Taylor instability

Abstract

Rayleigh–Taylor instability (RTI) is a common phenomenon in daily life and in industrial application. Despite the long history of investigating the RTI with periodic boundary condition, there are only few studies for the RTI with no-slip side wall boundary condition. In fact, the RTI with the side wall boundary condition is more realistic physics. In this work, we investigate the side wall boundary effect on the RTI using a phase-field model. No-slip conditions are employed on all boundaries. The governing equations are the coupled Navier–Stokes (NS) and Cahn–Hilliard (CH) system. We temporally solve the NS equation using Chorin’s projection method and the CH equation using Eyre’s nonlinear splitting scheme. A multigrid method is employed to solve the discrete system of CH equation. By various numerical experiments, we find that the side wall will delays the evolution of bubble and spike, causes a longer interface length and complex interface shape. Besides that, some other parameters, such as Reynolds number and aspect ratio of domain etc., can also cause significantly different phase evolutions.