The lattice Boltzmann (LB) method has gained much success in a variety of fields involving fluid flow and/or heat transfer. In this method, the bounce-back scheme is a popular boundary scheme for treating nonslip boundaries. However, this scheme leads to staircase-shaped boundaries for curved walls. Therefore many curved boundary schemes have been proposed, but mostly suffer from mass leakage at the curved boundaries. Several correction schemes have been suggested for simulating single-phase flows, but very few discussions or studies have been made for two-phase LB simulations with curved boundaries. In this paper, the performance of three well-known types of curved boundary schemes in two-phase LB simulations is investigated through modeling a droplet resting on a circular cylinder. For all of the investigated schemes, the results show that the simulated droplet rapidly "evaporates" under the nonslip and isothermal conditions, owing to the imbalance between the mass streamed out of the system by the outgoing distribution functions and the mass streamed into the system by the incoming distribution functions at each boundary node. Based on the numerical investigation, we formulate two modified mass-conservative curved boundary schemes for two-phase LB simulations. The accuracy of the modified curved boundary schemes and their capability of conserving mass in two-phase LB simulations are numerically demonstrated.

中文翻译：

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两相晶格 Boltzmann 模拟的修正曲线边界方案

格子玻尔兹曼 (LB) 方法在涉及流体流动和/或传热的各种领域取得了很大成功。在这种方法中，反弹方案是处理防滑边界的流行边界方案。然而，这种方案导致弯曲墙的楼梯形边界。因此，已经提出了许多弯曲边界方案，但大多受到弯曲边界处质量泄漏的影响。已经提出了几种用于模拟单相流的校正方案，但对于具有弯曲边界的两相 LB 模拟进行的讨论或研究很少。在本文中，通过对停留在圆柱体上的液滴进行建模，研究了三种众所周知的弯曲边界方案在两相 LB 模拟中的性能。对于所有调查的方案，结果表明，模拟液滴在防滑和等温条件下迅速“蒸发”，这是由于输出分布函数流出系统的质量与每个边界处输入分布函数流入系统的质量之间的不平衡节点。基于数值研究，我们为两相 LB 模拟制定了两个改进的质量守恒曲线边界方案。数值证明了修改后的弯曲边界方案的准确性及其在两相 LB 模拟中的质量守恒能力。由于输出分布函数流出系统的质量与每个边界节点处输入分布函数流入系统的质量之间存在不平衡。基于数值研究，我们为两相 LB 模拟制定了两个改进的质量守恒曲线边界方案。数值证明了修改后的弯曲边界方案的准确性及其在两相 LB 模拟中的质量守恒能力。由于输出分布函数流出系统的质量与每个边界节点处输入分布函数流入系统的质量之间存在不平衡。基于数值研究，我们为两相 LB 模拟制定了两个改进的质量守恒曲线边界方案。数值证明了修改后的弯曲边界方案的准确性及其在两相 LB 模拟中的质量守恒能力。