A weighted essentially nonoscillatory‐based phase field lattice Boltzmann method for incompressible two‐phase flows with high density contrast

Abstract

AbstractIn this article, a high order weighted essentially nonoscillatory finite difference‐based phase field lattice Boltzmann method (WENO‐PFLBM) is proposed for simulations of incompressible two‐phase flows with high density contrast. The weighted essentially nonoscillatory finite difference scheme is applied to discretize the convection term of the discrete Boltzmann equation for flow field. Moreover, the WENO scheme is also adopted to discretize the convection term of the modified Cahn–Hilliard equation for interface tracking. Numerical validations of the proposed WENO‐PFLBM are implemented by simulating stationary droplet, layered Poiseuille flow, Rayleigh–Taylor instability, bubble rising, and droplet impact on a thin film. Various numerical challenges like high density ratios (up to 1000), complex interfaces, and high Reynolds numbers are included in these examples, which demonstrate the robustness of the present method. In addition, the current method can achieve relatively small spurious velocity compared with the LB‐based model owing to the high order accuracy.