A particle method for two-phase flows with large density difference

Abstract

A new numerical approach for solving incompressible two-phase flows is presented in the framework of the recently developed Consistent Particle Method (CPM). In the context of the Lagrangian particle formulation, the CPM computes spatial derivatives based on the generalized finite difference scheme and produces good results for single-phase flow problems. Nevertheless, for two-phase flows, the method cannot be directly applied near the fluid interface because of the abrupt discontinuity of fluid density resulting in large change in pressure gradient. This problem is resolved by dealing with the pressure gradient normalized by density, leading to a two-phase CPM of which the original singlephase CPM is a special case. In addition, a new adaptive particle selection scheme is proposed to overcome the problem of ill-conditioned coefficient matrix of pressure Poisson equation when particles are sparse and non-uniformly spaced. Numerical examples of Rayleigh-Taylor instability, gravity current flow, water-air sloshing and dam break are presented to demonstrate the accuracy of the proposed method in wave profile and pressure solution.