A weighted essentially nonoscillatory‐based phase field lattice Boltzmann method for incompressible two‐phase flows with high density contrast. (8th March 2021)

• Record Type: Journal Article
• Authors: Ma, Chao; Wu, Jie; Jiang, Lan
• Is Part Of: International journal for numerical methods in fluids. Volume 93:Number 7(2021)
• Page Start: 2272
• Page End: 2290
• Publication Date: 2021-03-08
• Subjects: high order accuracy -- lattice Boltzmann method -- phase field -- weighted essentially nonoscillatory; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4973
• Languages: English
• ISSNs: 0271-2091

Abstract

Abstract: In 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. Abstract : A WENO‐based phase field lattice Boltzmann method for incompressible two‐phase flows with high density contrast is proposed. The proposed WENO‐PFLBM could eliminate drawbacks of the LB‐based models such as the limitation of the uniform mesh and tie‐up between the time step and the mesh spacing. The current method can generate relatively small spurious velocity compared with the LB‐based model owing to the high order method employed.