Meshless numerical model based on radial basis function (RBF) method to simulate the Rayleigh–Taylor instability (RTI)

Abstract

The Rayleigh-Taylor instability (RTI) is the instability at the interface between two fluids when a heavier fluid is placed on top of lighter fluid in a gravitational field. In the present work, the RTI was studied numerically by using a meshless radial basis function (RBF) method. The present manuscript describes the development of the meshless RBF method to solve the RTI problem in an incompressible viscous two-phase immiscible fluid. This method can address the difficulty of the classical base method which often requires much computing time for the generation of the computational mesh. Moreover, the meshless RBF method does not require connectivity information among the nodes. Consequently, the present manuscript provides a new numerical procedure in the solution of the RTI problem by the combination of meshless RBF and Cahn-Hilliard equations. In the present numerical study, the RBF method was combined with the domain decomposition method (DDM) to solve the large scale problem. The problem was governed by the Navier-Stokes and Cahn-Hilliard equations in a primitive variable formulation. The Cahn-Hilliard equations were used to capture the interface between two fluids systems. The RBF method was used for spatial discretization and the Euler implicit method was implemented for time discretization. The fractional step scheme was used to solve the pressure velocity coupling. Here, the effects of Atwood numbers as representing the density ratio on the RTI were investigated. As a result, it was found that the position of the rising bubble and falling spike during RTI conforms well to the results from the previous works.