A sharp-interface treatment technique for two-phase flows in meshless methods

Abstract

In this paper, a new interface treatment technique for multi-phase meshless methods is proposed for two-dimensional simulations. It enables the interface conditions to be applied effectively on the interface points involving interface tension and high viscosity. This technique is incorporated in the Meshless Local Petrov–Galerkin method with the Rankine source solution (MLPG_R) and the model predictions are validated through a number of standard test cases. Convergent results that agreed well with both available analytical and numerical solutions from other methods are obtained in simulations of square-droplet deformation, capillary wave, bubble rising and Rayleigh–Taylor instability. In these cases, sharp pressure discontinuity at the interface is well predicted with depressed parasitic current and the capability of the technique in dealing with high viscosity is comprehensively demonstrated.