Rayleigh-Taylor Instability Studied With Multi-Relaxation Lattice Boltzmann Method

Multi relaxation lattice Boltzmann method is implemented to study Rayleigh-Taylor instabilities. Two immiscible fluids (oil and water) are arrayed into three layers. D2Q9 lattice arrangement for two dimensional computational domains is employed. Density distribution functions for each fluid and distribution functions for the coloring step are determined. The evolution of the interface is identified with the coloring step. Buoyancy and other interaction forces, created by buoyancy, between phases are modeled. Two cases are studied one with periodic boundary condition instead of a side wall, and one bounded on all sides. The study is done with an aspect ratio of two and a density ratio of 1.2. The early and late stages of the instability are characterized. The early stage of both cases shows the initial periodic disturbance being amplified rapidly on the lower interface. The late stages show mushroom-like structures, with significant distortions occurring on the bounded case.