An Interface-Corrected Diffuse Interface Model for Incompressible Multiphase Flows with Large Density Ratios

Abstract

An interface-corrected diffuse interface method is presented in this work for the simulation of incompressible multiphase flows with large density ratios. In this method, an interface correction term together with a mass correction term is introduced into the diffuse-interface Cahn–Hilliard model to maintain both mass conservation and interface shapes between binary fluids simultaneously. The interface correction term is obtained by connecting the signed distance functions in the Hamilton–Jacobian equation with the order parameter of the Cahn–Hilliard model. In addition, an improved multiphase lattice Boltzmann flux solver is introduced, in which the fluxes are obtained by considering the contributions of the particle distribution functions before and after the streaming process through a local switch function. The proposed method is validated by simulating multiphase flows, such as the Laplace law, the evolution of a square bubble, the merging of two bubbles, Rayleigh–Taylor instability, and a droplet impacting on a film with a density ratio of 1000. Numerical results show that the presented method can not only reduce the interface diffusion but also has good control over the interface thickness and mass conservation. The improved numerical method has great potential for use in practical applications involving multiphase flows.