Numerical simulation of Rayleigh-Taylor Instability with periodic boundary condition using MPS method

The Multiphase Moving Particle Semi-implicit(MMPS) method is adopted to simulate the Rayleigh-Taylor Instability (RTI) process in an incompressible viscous two-phase immiscible fluid. To eliminate influences of the initial disturbance arrangement and boundary conditions in RTI simulations, the initial velocity distribution is deduced and the periodic boundary condition is developed in this paper. The RTI cases in this paper include those with single-mode disturbance and multimode disturbance. For the single-mode RTI process, cases with different initial disturbance wavelengths, different Atwood numbers and different surface tension coefficients are simulated. Results are quantitatively compared with analytical solutions in a linear growth stage and the simulation results fit well with the theoretical results. The long-term development of simulations is presented for investigating changes in the topology of rising bubbles and falling spikes in RTI, and the steady velocity conforms well with that calculate by theoretical solution. What's more, the multimode RTI processes are also simulated in this paper, and bubbles' competition and mergence process can be observed.