A Simplified Lattice Boltzmann Method without Evolution of Distribution Function
A Simplified Lattice Boltzmann Method without Evolution of Distribution Function
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DOI：
10.4208/aamm.oa-2016-0029
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发表时间：
2017-02-01
影响因子：
1.4
通讯作者：
Tan, D.
中科院分区：
文献类型：
--
作者：
Chen, Z.;Shu, C.;Tan, D.
本文开发了一种无需分布函数演化的简化格子玻尔兹曼方法（SLBM），用于模拟不可压缩粘性流。该方法是通过将分数阶技术应用到利用 Chapman-Enskog 展开分析从格子 Boltzmann 方程恢复的宏观 Navier-Stokes (N-S) 方程中发展而来的。在SLBM中，平衡分布函数是根据宏观变量计算的，而非平衡分布函数是简单地根据两个平衡分布函数的差来评估的。因此，SLBM 跟踪宏观变量的演化而不是分布函数。因此，需要较低的虚拟内存，并且可以直接实现物理边界条件。通过高雷诺数下的数值试验，该方法表现出了很好的数值稳定性。对二维泰勒-格林流的精度测试表明，潜射弹道导弹在空间上具有二阶精度。进行了更多基准测试，包括库埃特流、泊肃叶流以及二维盖驱动腔流，以进一步验证本方法；仿真结果与文献中的数据吻合良好。
In this paper, a simplified lattice Boltzmann method (SLBM) without evolution of the distribution function is developed for simulating incompressible viscous flows. This method is developed from the application of fractional step technique to the macroscopic Navier-Stokes (N-S) equations recovered from lattice Boltzmann equation by using Chapman-Enskog expansion analysis. In SLBM, the equilibrium distribution function is calculated from the macroscopic variables, while the non-equilibrium distribution function is simply evaluated from the difference of two equilibrium distribution functions. Therefore, SLBM tracks the evolution of the macroscopic variables rather than the distribution function. As a result, lower virtual memories are required and physical boundary conditions could be directly implemented. Through numerical test at high Reynolds number, the method shows very nice performance in numerical stability. An accuracy test for the 2D Taylor-Green flow shows that SLBM has the second-order of accuracy in space. More benchmark tests, including the Couette flow, the Poiseuille flow as well as the 2D lid-driven cavity flow, are conducted to further validate the present method; and the simulation results are in good agreement with available data in literatures.