Lattice Boltzmann method for non-Newtonian (power-law) fluids
Lattice Boltzmann method for non-Newtonian (power-law) fluids
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DOI：
10.1103/physreve.72.046312
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发表时间：
2005-10-01
影响因子：
2.4
通讯作者：
Koplik, J
中科院分区：
文献类型：
--
作者：
Gabbanelli, S;Drazer, G;Koplik, J
我们研究了一个特设的扩展的格子玻尔兹曼方法，允许广义牛顿模型描述的非牛顿流体的模拟。我们广泛测试的剪切变稀和剪切增厚截断幂律流体的平行板几何形状的情况下，该方法的准确性，并表明，相对误差与解析解衰减近似线性的晶格分辨率。最后，我们还测试了该方法在再入流的几何形状，其中的剪切速率不再是一个标量和两个奇异点的存在下，需要高精度，以获得满意的分辨率在这些点附近的局部应力。在这种几何形状中，我们还发现了与标准有限元方法获得的解决方案非常一致，并且随着晶格分辨率的提高，这种一致性得到了提高。
We study an ad hoc extension of the lattice Boltzmann method that allows the simulation of non-Newtonian fluids described by generalized Newtonian models. We extensively test the accuracy of the method for the case of shear-thinning and shear-thickening truncated power-law fluids in the parallel plate geometry, and show that the relative error compared to analytical solutions decays approximately linear with the lattice resolution. Finally, we also tested the method in the reentrant-flow geometry, in which the shear rate is no longer a scalar and the presence of two singular points requires high accuracy in order to obtain satisfactory resolution in the local stress near these points. In this geometry, we also found excellent agreement with the solutions obtained by standard finite-element methods, and the agreement improves with higher lattice resolution.