Finite Element Convergence Analysis of Two-Scale Non-Newtonian Flow Problems

Hou, Liang; Zhao, Jun; Li, Han Ling

doi:10.4028/www.scientific.net/amr.718-720.1723

Cited by 4 publications

(3 citation statements)

References 9 publications

(10 reference statements)

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“…In fact, (10) Here the stress  is regarded as a given value which is a In the numerical experiments, we adopt Lagrange interpolation function with 16-point bicubic elements on the space; two-step Adams explicit and Crank-Nicolson scheme on the time. Consider the 2×2 grid.…”

Section: IIImentioning

confidence: 99%

Finite Element Method on Contact Problem of Non-newtonian Fluid Material

Ma¹,

Hou²

2017

Proceedings of the 3rd International Conference on Wireless Communication and Sensor Networks (WCSN 2016)

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Abstract-In this paper, we use finite element method to study contact problem of non-Newtonian fluid material. We focus on Cauchy equation which describes the velocity changes in the flow field. The space domain is discrete by Lagrange interpolation function with 16-point bicubic elements. The time domain is discrete by two schemes: two-step Adams explicit scheme and Crank-Nicolson scheme. We study the convergence. In numerical experiments, the error of the equation is shown by comparing the numerical solutions with the exact solutions.Keywords-non-Newtonian fluid; finite element method; contact problem; two-step Adams explicit scheme I.INTRODUCTION With the continuous development of network and modern communication technology, the concept of the networked intelligent sensor based on the technology of wireless produced. In some special goods transport, environmental parameters have higher requirements for container. Wireless sensor network (WSN) is a good way to monitoring parameters. We apply WSN to warehouse management. Three dimensional space deployment of the wireless sensor network nodes is one of the big problems in the research. One of the effective node deployment plan, is to perform finite element meshes based on cube or sphere on the certain storage space.Under the condition of high speed collision, the solid material can cause enormous deformation in such a short time. Thus, we can agree that it also has fluid property. Socalled non-Newtonian fluid is a fluid whose shear stress and shear rate cannot always keep a linear relationship, such as blood, toothpaste, oil paint and slurry. Different rheological properties of different type of non-Newtonian fluid will appear under the changes of shear rate. For example, Bingham plastic body exists yield stress. Besides, dilatants fluid has shear thickening properties. With the continuous development of materials science and related research technology, the applications of non-Newtonian fluid material field are deepening.In the research of non-Newtonian fluid material, we always use coupled PDE equations. The standard P-T/T equation is the best estimates for the stress over-shoot. Cauchy conservation equation may be used to calculate the large deformation resulting from stress (shear thinning). It can be used to describe the velocity and the stress distribution in the contract problem.In this paper, we focus on the Cauchy equation which describes the velocity changes in the flow field.

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Section: IIImentioning

confidence: 99%

Finite Element Method on Contact Problem of Non-newtonian Fluid Material

Ma¹,

Hou²

2017

Proceedings of the 3rd International Conference on Wireless Communication and Sensor Networks (WCSN 2016)

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“…When the cars are crashing, automobile material will become deformed largely [3] in the short process of collision. Contact surface will appear the property similar to the boundary-layer fluid.…”

Section: The Variation Of the Coupled Equationmentioning

confidence: 99%

The Convergence of Coupled Boundary-Layer Equation in the Contact Interface

Hou

Faraz

Sun

et al. 2014

AMM

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This paper introduces two equations of non-Newtonian boundary-layer fluid: Cauchy equation of flow field and P-T/T equation of stress field. Secondly, we analyze the convergence of this system of fluid-solid coupled equation with semi-discrete finite element method. We use Galerkin finite element method on the space and semi-implicit C-N difference scheme on the time. Thus, the convergent order of the coupled equations is O（h2+k2） .

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“…The Cauchy equation has the nonlinear nature [1,2], what the general linear methods can't solve. But in order to study the convergence [3] of the Cauchy equation, we slove the Cauchy problem with the finite element [4] and finite difference.…”

Section: Introductionmentioning

confidence: 99%

The Semi-Discrete Finite Element Method for the Cauchy Equation

Hou

Sun

Qiu

2014

AMM

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In this paper, we employ semi-discrete finite element method to study the convergence of the Cauchy equation. The convergent order can reach. In numerical results, the space domain is discrete by Lagrange interpolation function with 9-point biquadrate element. The time domain is discrete by two difference schemes: Euler and Crank-Nicolson scheme. Numerical results show that the convergence of Crank-Nicolson scheme is better than that of Euler scheme.

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Finite Element Convergence Analysis of Two-Scale Non-Newtonian Flow Problems

Cited by 4 publications

References 9 publications

Finite Element Method on Contact Problem of Non-newtonian Fluid Material

Finite Element Method on Contact Problem of Non-newtonian Fluid Material

The Convergence of Coupled Boundary-Layer Equation in the Contact Interface

The Semi-Discrete Finite Element Method for the Cauchy Equation

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