Asymptotic analysis of the lattice Boltzmann method for generalized Newtonian fluidflows

Yang Zaibao; Yong Wenan

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Asymptotic analysis of the lattice Boltzmann method for generalized Newtonian fluidflows

Yang Zaibao 1,Yong Wenan 2 *

1.Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084

2.Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084

*Correspondence author

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Funding: Tsinghua University Initiative Scientific Research Program （No.20121087902）, Specialized Research Fund for the Doctoral Program of Higher Education（No.Grant No. 20100002110085）

Opened online: 3 September 2013

Accepted by: none

Citation: Yang Zaibao ,Yong Wenan .Asymptotic analysis of the lattice Boltzmann method for generalized Newtonian fluidflows[OL]. [ 3 September 2013] http://en.paper.edu.cn/en_releasepaper/content/4557185

In this article, we present a detailed asymptotic analysis of the lattice Boltzmann methodwith two different collision mechanisms of BGK-type on the D2Q9-lattice forgeneralized Newtonian fluids. Unlike that based on the Chapman-Enskog expansion leadingto the compressible Navier-Stokes equations, our analysis gives theincompressible ones directly and exposes certain important features of the lattice Boltzmann solutions.Moreover, our analysis provides a theoretical basisfor using the iteration to compute the rate-of-strain tensor, which makes sensespecially for generalized Newtonian fluids.As a by-product, a seemingly new structural condition on the generalized Newtonian fluidsis singled out. This condition reads as ``the magnitude of the stress tensor increaseswith increasing the shear rate". We verify this conditionfor all the existing constitutive relations which are known to us.In addition, it it straightforward to extend our analysis to MRT modelsor to three-dimensional lattices.

Keywords:Computational Mathematics; Lattice Boltzmann method; generalizedNewtonian fluid; asymptotic analysis; constitutive relation; construction criterion

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