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.

中文翻译：

---

一种用于具有高密度对比度的不可压缩两相流的基于加权基本非振荡的相场格子 Boltzmann 方法

在本文中，提出了一种基于高阶加权基本非振荡有限差分的相场格子玻尔兹曼方法 (WENO-PFLBM)，用于模拟具有高密度对比度的不可压缩两相流。加权基本非振荡有限差分格式用于离散流场离散 Boltzmann 方程的对流项。此外，还采用 WENO 方案对改进的 Cahn-Hilliard 方程的对流项进行离散化以进行界面跟踪。通过模拟静止液滴、分层泊肃叶流、瑞利-泰勒不稳定性、气泡上升和液滴对薄膜的影响，对所提出的 WENO-PFLBM 进行了数值验证。各种数值挑战，如高密度比（高达 1000）、复杂的界面、这些示例中包括高雷诺数，这证明了本方法的稳健性。此外，与基于 LB 的模型相比，当前方法可以实现相对较小的伪速度，因为它具有高阶精度。