We develop a multicomponent lattice Boltzmann (LB) model for the two-dimensional Rayleigh–Taylor turbulence with a Shan–Chen pseudopotential implemented on GPUs. In the immiscible case, this method is able to accurately overcome the inherent numerical complexity caused by the complicated structure of the interface that appears in the fully developed turbulent regime. The accuracy of the LB model is tested both for early and late stages of instability. For the developed turbulent motion, we analyse the balance between different terms describing variations of the kinetic and potential energies. Then we analyse the role of the interface in the energy balance and also the effects of the vorticity induced by the interface in the energy dissipation. Statistical properties are compared for miscible and immiscible flows. Our results can also be considered as a first validation step to extend the application of LB model to three-dimensional immiscible Rayleigh-Taylor turbulence.

This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.

我们为二维 Rayleigh-Taylor 湍流开发了多分量格子 Boltzmann (LB) 模型，并在 GPU 上实现了 Shan-Chen 赝势。在不相容的情况下，该方法能够准确地克服在完全发展的湍流状态下出现的界面复杂结构所带来的固有数值复杂性。LB 模型的准确性在不稳定的早期和晚期都进行了测试。对于发展的湍流运动，我们分析了描述动能和势能变化的不同术语之间的平衡。然后我们分析了界面在能量平衡中的作用以及界面引起的涡度对能量耗散的影响。比较混溶和不混溶流的统计特性。

本文是主题问题“流体动力学模拟中尺度方法的进展”的一部分。