A direct-forcing immersed boundary method for the thermal lattice Boltzmann method
A direct-forcing immersed boundary method for the thermal lattice Boltzmann method
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DOI：
10.1016/j.compfluid.2011.04.016
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发表时间：
2011-10
影响因子：
2.8
通讯作者：
Shin K. Kang;Y. Hassan
中科院分区：
文献类型：
--
作者：
Shin K. Kang;Y. Hassan
本文提出了一种直接强迫浸没边界方法（IBM）用于热格子Boltzmann方法（TLBM）模拟非等温流动。基于两个TLBM模型导出了热方程的直接强迫IBM公式：一个是简化的热格子Boltzmann方程的双粒子数模型（模型1），一个是温度对流扩散方程的混合模型（模型2）。作为界面格式，由于边界和计算网格之间的不匹配在IBM中，基于二阶双线性和线性插值的尖锐界面格式（而不是扩散界面格式，它使用离散δ函数）被采用，以获得更精确的结果。通过不仅具有固定边界而且具有移动边界的对流传热问题--具有偏心圆柱体的方形空腔中的自然对流和无限通道中的冷颗粒沉降--验证了所提出的方法。在精度方面，从IBM的两个模型的基础上的结果是可比的，并显示出良好的协议与其他数值方法。相比之下，基于Model 2的IBM比基于Model 1的IBM更有效。
In this study, a direct-forcing immersed boundary method (IBM) for thermal lattice Boltzmann method (TLBM) is proposed to simulate the non-isothermal flows. The direct-forcing IBM formulas for thermal equations are derived based on two TLBM models: a double-population model with a simplified thermal lattice Boltzmann equation (Model 1) and a hybrid model with an advection–diffusion equation of temperature (Model 2). As an interface scheme, which is required due to a mismatch between boundary and computational grids in the IBM, the sharp interface scheme based on second-order bilinear and linear interpolations (instead of the diffuse interface scheme, which uses discrete delta functions) is adopted to obtain the more accurate results. The proposed methods are validated through convective heat transfer problems with not only stationary but also moving boundaries – the natural convection in a square cavity with an eccentrically located cylinder and a cold particle sedimentation in an infinite channel. In terms of accuracy, the results from the IBM based on both models are comparable and show a good agreement with those from other numerical methods. In contrast, the IBM based on Model 2 is more numerically efficient than the IBM based on Model 1.