Numerical Simulation of Rayleigh-Taylor Instability by Multiphase MPS Method

The Rayleigh-Taylor instability problem is one of the classic hydrodynamic instability cases in natural scenarios and industrial applications. For the numerical simulation of the Rayleigh-Taylor instability problem, this paper presents a multiphase method based on the moving particle semi-implicit (MPS) method. Herein, the incompressibility of the fluids is satisfied by solving a Poisson Pressure Equation and the pressure fluctuation is suppressed. A single set of equations is utilized for fluids with different densities, making the method relatively simple. To deal with the mathematical discontinuity of density in the two-phase interface, a transitional region is introduced into this method. For particles in the transitional region, a density smoothing scheme is applied to improve the numerical stability. The simulation results show that the present MPS multiphase method is capable of capturing the evolutionary features of the Rayleigh-Taylor instability, even in the later stage when the two-phase interface is quite distorted. The unphysical penetration in the interface is limited, proving the stability and accuracy of the proposed method.