Shear stress in lattice Boltzmann simulations
Shear stress in lattice Boltzmann simulations
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DOI：
10.1103/physreve.79.046704
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发表时间：
2009-04-01
影响因子：
2.4
通讯作者：
Raabe, Dierk
中科院分区：
文献类型：
--
作者：
Krueger, Timm;Varnik, Fathollah;Raabe, Dierk
一个彻底的研究内的格子玻尔兹曼方法的剪切应力。通过标准的多尺度Chapman-Enskog展开，我们调查的剪切应力的误差对网格分辨率的依赖性，表明由格子Boltzmann方法得到的剪切应力是二阶精度。然而，这种收敛通常被边界条件破坏。还研究了松弛参数的哪个值可以使误差最小化。此外，对于使用速度边界条件的模拟，经常观察到人为的质量增加。这是晶格玻尔兹曼流体的可压缩性的结果。我们调查这个问题，并推导出一个解析表达式的时间依赖性的流体密度的雷诺数，马赫数，和一个几何因子的情况下，Poiquillille流通过一个矩形通道在三维空间。与晶格玻尔兹曼模拟结果的解析表达式的比较显示出良好的协议。
A thorough study of shear stress within the lattice Boltzmann method is provided. Via standard multiscale Chapman-Enskog expansion we investigate the dependence of the error in shear stress on grid resolution showing that the shear stress obtained by the lattice Boltzmann method is second-order accurate. This convergence, however, is usually spoiled by the boundary conditions. It is also investigated which value of the relaxation parameter minimizes the error. Furthermore, for simulations using velocity boundary conditions, an artificial mass increase is often observed. This is a consequence of the compressibility of the lattice Boltzmann fluid. We investigate this issue and derive an analytic expression for the time dependence of the fluid density in terms of the Reynolds number, Mach number, and a geometric factor for the case of a Poiseuille flow through a rectangular channel in three dimensions. Comparison of the analytic expression with results of lattice Boltzmann simulations shows excellent agreement.