A numerical study of Rayleigh-Taylor instability for various atwood numbers using ISPH method

In this paper, the wall bounded single-mode Rayleigh Taylor Instability (RTI) for a two-phase immiscible fluid system in a confined domain is investigated numerically for various Atwood numbers ranging from $A_t = 0.2$ to $A_t = 0.8$. Governing equations are discretized using the Smoothed Particle Hydrodynamics (SPH) method. A robust numerical scheme is used to simulate the RTI phenomenon and in order to model the fluid-flow in the vicinity of the interface, transport parameters such as density and viscosity are smoothed using color function. The surface tension force is coupled to the momentum equation using Continuum Surface Force (CSF) model. It is shown that in general the RTI evolves in three distinct stages, namely linear stability, mushroom-head formation and long-term evolution. The growth rate in the first stage, i.e. the linear instability, shows good agreement with the analytical solution in the literature. The qualitative and quantitative results of second and third stages are introduced and relevant discussions are made.