Multiscale computation for transient heat conduction problem with radiation boundary condition in porous materials

Yang, Zhiqiang; Cui, Junzhi; Sun, Yi; Ge, Jingran

doi:10.1016/j.finel.2015.04.005

Cited by 35 publications

(14 citation statements)

References 27 publications

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“…(44), it is easy to deduce the corresponding SOTS asymptotic model. It follows that g 11 D 1 C r 2 , g 12 D r, g 21 D r, g 22…”

Section: Shear Transformationmentioning

confidence: 99%

“…In practical computation, it has been validated that the SOTS solutions are much better than the first-order solutions and homogenization solutions. After that, the SOTS analysis method has been developed and extended to study the linear elasticity and thermoelastic problems for quasi-periodic structures [18][19][20], the integrated heat transfer problems with conduction, convection and radiation in periodic or porous materials [21][22][23][24], and the dynamic thermoelastic problems of periodic composite or random particulate composites [25][26][27][28][29][30].As is known that in practical applications, various structures made of porous materials are designed and created to satisfy the industrial demand in many particular situations, such as the curved thermal protection layer in the thermal protection system of the spacecraft, hollow cylinder, ball, and the honeycomb structure, most of which are not periodically arranged along the Cartesian axis. However, the SOTS asymptotic expansion is based on the periodicity of the composite structures.…”

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confidence: 99%

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Asymptotic computation for transient heat conduction performance of periodic porous materials in curvilinear coordinates by the second‐order two‐scale method

Yang

et al. 2017

Math Methods in App Sciences

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A novel second‐order two‐scale (SOTS) analysis method is developed for predicting the transient heat conduction performance of porous materials with periodic configurations in curvilinear coordinates. Under proper coordinate transformations, some non‐periodic porous structures in Cartesian coordinates can be transformed into periodic structures in general curvilinear coordinates, which is our particular interest in this study. The SOTS asymptotic expansion formulas for computing the temperature field of transient heat conduction problem in curvilinear coordinates are constructed, some coordinate transformations are discussed, and the related SOTS formulas are given. The feature of this asymptotic model is that each of the cell functions defined in the periodic cell domain is associated with the macroscopic coordinates and the homogenized material coefficients varies continuously in the macroscopic domain behaving like the functional gradient material. Finally, the corresponding SOTS finite element algorithms are brought forward, and some numerical examples are given in detail. The numerical results demonstrate that the SOTS method proposed in this paper is valid to predict transient heat conduction performance of porous materials with periodicity in curvilinear coordinates. By proper coordinate transformations, the SOTS asymptotic analysis method can be extended to more general non‐periodic porous structures in Cartesian coordinates. Copyright © 2017 John Wiley & Sons, Ltd.

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“…(44), it is easy to deduce the corresponding SOTS asymptotic model. It follows that g 11 D 1 C r 2 , g 12 D r, g 21 D r, g 22…”

Section: Shear Transformationmentioning

confidence: 99%

mentioning

confidence: 99%

Asymptotic computation for transient heat conduction performance of periodic porous materials in curvilinear coordinates by the second‐order two‐scale method

Yang

et al. 2017

Math Methods in App Sciences

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“…where T ε 1 (x,t) and T ε 2 (x,t) are called the first-order and the second-order multiscale approximate solutions, respectively. It is worth noting that the expansions (3.35) are different from the traditional forms given by [14,17], the differences are that the correction terms N α 1 (x,y), N α 1 α 2 (x,y), B α 1 (x,y) and C α 1 (x,y) are constructed into the asymptotic expansions depending on the macroscopic variable x due to quasi-periodic effect of the materials.…”

Section: )mentioning

confidence: 99%

“…Meanwhile, Ma and Cui [14] proposed a second-order two-scale method to solve the coupled problems, and obtained the convergence order with O(ε 1/2 ). Cui et al [15][16][17] discussed the heat conduction and radiation problems in periodic or random porous materials, and developed a newly higher-order multiscale method for the problems. Later, Yang, Sun and Cui [18,19] obtained the second-order multiscale solutions for the dynamic thermo-elastic problems of porous materials with interior surface radiation.…”

Section: Introductionmentioning

confidence: 99%

“…Particularly, the nonlinear heat radiation account for the scale effect and sophisticated microstructures of the porous materials are considered in this study. The radiation boundary condition was investigated by Liu and Zhang [11], Bakhvalov [12] and Yang et al [15][16][17][18][19], and it is a classical physical model in practical applications. This paper is to establish a novel high-order multiscale method with less effort and computational cost to give a better approximation.…”

Section: Introductionmentioning

confidence: 99%

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A Multiscale Algorithm for Heat Conduction-Radiation Problems in Porous Materials with Quasi-Periodic Structures

Yang¹,

Sun²,

Cui³

et al. 2018

CICP

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This paper develops a second-order multiscale asymptotic analysis and numerical algorithms for predicting heat transfer performance of porous materials with quasi-periodic structures. In these porous materials, they have periodic configurations and associated coefficients are dependent on the macro-location. Also, radiation effect at microscale has an important influence on the macroscopic temperature fields, which is our particular interest in this study. The characteristic of the coupled multiscale model between macroscopic scale and microscopic scale owing to quasi-periodic structures is given at first. Then, the second-order multiscale formulas for solving temperature fields of the nonlinear problems are constructed, and associated explicit convergence rates are obtained on some regularity hypothesis. Finally, the corresponding finite element algorithms based on multiscale methods are brought forward and some numerical results are given in detail. Numerical examples including different coefficients are given to illustrate the efficiency and stability of the computational strategy. They show that the expansions to the second terms are necessary to obtain the thermal behavior precisely, and the local and global oscillations of the temperature fields are dependent on the microscopic and macroscopic part of the coefficients respectively.

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A second‐order reduced asymptotic homogenization approach for nonlinear periodic heterogeneous materials

Fish

Yang

Yuan

2019

Numerical Meth Engineering

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Summary An efficient second‐order reduced asymptotic homogenization approach is developed for nonlinear heterogeneous media with large periodic microstructure. The two salient features of the proposed approach are (i) an asymptotic higher‐order nonlinear homogenization that does not require higher‐order continuity of the coarse‐scale solution and (ii) an efficient model reduction scheme for solving higher‐order nonlinear unit cell problems at a fraction of computational cost in comparison to the direct computational homogenization. The former is a consequence of a sequential solution of increasing order solutions, which permits evaluation of higher‐order coarse‐scale derivatives by postprocessing from the zeroth‐order solution. The efficiency and accuracy of the formulation in comparison to the classical zeroth‐order homogenization and direct numerical simulations are assessed on hyperelastic and elastoplastic periodic structures.

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Multiscale computation for transient heat conduction problem with radiation boundary condition in porous materials

Cited by 35 publications

References 27 publications

Asymptotic computation for transient heat conduction performance of periodic porous materials in curvilinear coordinates by the second‐order two‐scale method

Asymptotic computation for transient heat conduction performance of periodic porous materials in curvilinear coordinates by the second‐order two‐scale method

A Multiscale Algorithm for Heat Conduction-Radiation Problems in Porous Materials with Quasi-Periodic Structures

A second‐order reduced asymptotic homogenization approach for nonlinear periodic heterogeneous materials

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