Development of meshless phase field method for two-phase flow

Abstract

The purpose of the present paper is the development of meshless diffuse approximate method in connection with the phase field formulation for solution of two-phase flow problems. The numerical approach enables single-domain, fixed-node treatment of the involved moving boundaries. The problem is formulated for Newtonian fluids based on a physical model that involves a coupled set of Navier–Stokes and Cahn–Hilliard equations. Diffuse approximate method is structured with a second order polynomial basis, Gaussian weight function, adaptive upwind scheme and eleven-node local subdomain. The pressure-velocity coupling is performed by the incremental fractional step method and explicit time discretization is used to solve the governing equations. The method is demonstrated in axisymmetry for a problem of two co-flowing immiscible fluids with different material properties that yield dripping or jetting of the core fluid. An assessment of the novel method is carried out based on comparison of the present results with the finite volume method outcome. A sensitivity study of various process parameters is carried out and verified against the previously published results. The paper represents a pioneering development in simulation of two-phase flows by a meshless method.