The Rayleigh–Taylor instability (RTI) problem is one of the classic hydrodynamic instability cases in natural scenarios and industrial applications. For the numerical simulation of the RTI 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 (PPE) 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 RTI, 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.
Numerical simulation of single- and multi-mode Rayleigh–Taylor instability with surface tension in two dimensions
