An axisymmetric incompressible lattice BGK model for simulation of the pulsatile flow in a circular pipe
An axisymmetric incompressible lattice BGK model for simulation of the pulsatile flow in a circular pipe
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DOI：
10.1002/fld.997
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发表时间：
2005-09-10
影响因子：
1.8
通讯作者：
Shu, C
中科院分区：
文献类型：
--
作者：
Lee, TS;Huang, H;Shu, C
应用Halliday等人的思想，通过在二维格子Boltzmann方程中引入“源”项，恢复圆柱坐标系下的不可压Navier-Stokes方程，建立了一个轴对称不可压格子BGK D2 Q9模型，用于模拟圆管中的脉动流.研究了I < Re < 2000（雷诺数与管径有关），Womersley数I < alpha < 25的圆管脉动流，并与精确解析解进行了比较。数值解和解析解之间的良好协议验证了我们的模型。讨论了压力梯度实施方案的影响以及模型的空间精度。为了验证该模型的有效性，本文还分别用由标准LBM导出的Halliday轴对称模型和三维不可压LBGK模型对同样的问题进行了数值模拟。据观察，本模型减少了Halliday模型中的可压缩性效应，并且对于轴对称脉动流问题比LBGK D3 Q19模型有效得多。版权所有（c）2005年约翰威利父子有限公司。
Applying the idea of Halliday et al., through inserting the 'source' term into the two-dimensional lattice Boltzmann equation to recover the incompressible Navier-Stokes equation in the cylindrical coordinates, an axisymmetric incompressible Lattice-BGK D2Q9 model was proposed here to simulate the pulsatile flows in a circular pipe. The pulsatile flows in a circular pipe with I < Re < 2000 (Reynolds number is based on pipe's diameter), Womersley number I < alpha < 25 were investigated and compared with the exact analytical solutions. The excellent agreements between numerical and the analytical solution validate our model. The effect of schemes to implement pressure gradient and the model's spatial accuracy were also discussed. To show the performance of the proposed model, the same problems were also simulated by Halliday's axisymmetric model which derived from standard LBM and the three-dimensional incompressible LBGK model. It is observed that the present model reduces the compressibility effect in Halliday's model and is much more efficient than the LBGK D3Q19 model for an axisymmetric pulsatile flow problem. Copyright (c) 2005 John Wiley & Sons, Ltd.