Based on phase‐field theory, we develop a simple and robust single relaxation time (SRT) lattice Boltzmann (LB) model for simulating complex multiphase flows with large density ratios (up to 2000). The approach utilizes two LB equations (LBE), one is used to describe the interface behavior and the other is used to calculate the hydrodynamic properties. To improve the accuracy and stability in capturing interface, the high‐order LB model derived through the fourth‐order Chapman‐Enskog expansion analysis is applied to Cahn‐Hilliard equation. For solution of the flow field, a modified particle distribution function in the pressure‐velocity formulation is constructed to correctly consider the effect of local density variation and continuous pressure field. With such improvement, the proposed multiphase LB model is able to maintain numerical stability for the problem with very large density ratio, lower relaxation parameter and complex interface. For validation, a series of benchmark cases are carried out. Specially, the full potential of the proposed model is validated by bubble bursting at a free surface, bubble rising and droplet splashing with a density ratio of 2000. In all test cases, the obtained numerical results agree well with the reference data or the analytical solutions.

中文翻译：

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基于高阶相场的格子Boltzmann模型，用于模拟大密度比的复杂多相流

基于相场理论，我们开发了一种简单且健壮的单弛豫时间（SRT）格子Boltzmann（LB）模型，用于模拟具有大密度比（高达2000）的复杂多相流。该方法利用两个LB方程（LBE），一个用于描述界面行为，另一个用于计算流体力学特性。为了提高捕获接口的准确性和稳定性，将通过四阶Chapman-Enskog展开分析得出的高阶LB模型应用于Cahn-Hilliard方程。为了解决流场问题，在压力-速度公式中构造了修改后的粒子分布函数，以正确考虑局部密度变化和连续压力场的影响。有了这样的改进，提出的多相LB模型能够解决密度比非常大，松弛参数较低，界面复杂的问题的数值稳定性。为了进行验证，执行了一系列基准案例。特别地，通过在自由表面上的气泡破裂，气泡上升和液滴飞溅（密度比为2000）验证了所提出模型的全部潜力。在所有测试案例中，所得数值结果均与参考数据或解析解吻合良好。