A simplified thermal lattice Boltzmann method without evolution of distribution functions
A simplified thermal lattice Boltzmann method without evolution of distribution functions
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DOI：
10.1016/j.ijheatmasstransfer.2016.10.032
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发表时间：
2017-02
影响因子：
5.2
通讯作者：
Zhen Chen;C. Shu;D. Tan
中科院分区：
文献类型：
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作者：
Zhen Chen;C. Shu;D. Tan
本文提出了一种不考虑分布函数演化的简化热晶格玻尔兹曼方法（STLBM），用于模拟不可压缩热流。借助于分步技术，通过预测-校正方案求解了从Chapman-Enskog （C-E）展开分析中恢复的宏观控制方程。然后在预测和校正步骤中，利用晶格张量的等熵性质和C-E分析关系，从平衡和非平衡分布函数中显式计算宏观流动变量。在STLBM中，平衡分布函数由宏观变量计算，非平衡分布函数由两个平衡分布函数在不同位置和时间水平上的差值评估。因此，STLBM在计算过程中直接更新宏观变量，降低了虚拟内存成本，便于物理边界条件的实现。通过von Neumann稳定性分析，证明了该方法是无条件稳定的，并通过数值试验进一步验证了该方法的有效性。通过三个典型的实例验证了该算法在实际仿真中的鲁棒性以及在不同网格和边界上的灵活性。
In this paper, a simplified thermal lattice Boltzmann method (STLBM) without evolution of the distribution functions is developed for simulating incompressible thermal flows. With the assistance of the fractional step technique, the macroscopic governing equations recovered from Chapman–Enskog (C–E) expansion analysis are resolved through a predictor–corrector scheme. Then in both the predictor and corrector steps, using the isentropic properties of lattice tensors and relationships of C–E analysis, the macroscopic flow variables are explicitly calculated from the equilibrium and non-equilibrium distribution functions. In STLBM, the equilibrium distribution functions are calculated from the macroscopic variables, while the non-equilibrium distribution functions are evaluated from the differences between two equilibrium distribution functions at different locations and time levels. Therefore, STLBM directly updates the macroscopic variables during the computational process, which lowers the virtual memory cost and facilitates the implementation of physical boundary conditions. Through von Neumann stability analysis, the present method is proven to be unconditionally stable, which is further validated by numerical tests. Three representative examples are presented to demonstrate the robustness of STLBM in practical simulations and its flexibility on different types of meshes and boundaries.