Volume 6, Issue 2
Multiscale Asymptotic Method for Heat Transfer Equations in Lattice-Type Structures

Int. J. Numer. Anal. Mod., 6 (2009), pp. 232-255.

Published online: 2009-06

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• Abstract

In this paper, we discuss the initial-boundary value problem for the heat transfer equation in lattice-type structures that arises from the aerospace industry and the structural engineering. The main results obtained in this paper are the convergence theorems by using the homogenization method and the multiscale asymptotic method (see Theorems 2.1 and 2.2). Some numerical examples are given for three types of lattice structures. These numerical results suggest that the first-order multiscale method should be a better choice compared with the homogenization method and the second-order multiscale method for solving the heat transfer equations in lattice-type structures.

• Keywords

Homogenization, multiscale asymptotic expansion, parabolic equation, lattice-type structure, multiscale finite element method.

65F10, 65W05

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@Article{IJNAM-6-232, author = {F.-M. and Zhai and and 21024 and and F.-M. Zhai and L.-Q. and Cao and and 21025 and and L.-Q. Cao}, title = {Multiscale Asymptotic Method for Heat Transfer Equations in Lattice-Type Structures}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2009}, volume = {6}, number = {2}, pages = {232--255}, abstract = {

In this paper, we discuss the initial-boundary value problem for the heat transfer equation in lattice-type structures that arises from the aerospace industry and the structural engineering. The main results obtained in this paper are the convergence theorems by using the homogenization method and the multiscale asymptotic method (see Theorems 2.1 and 2.2). Some numerical examples are given for three types of lattice structures. These numerical results suggest that the first-order multiscale method should be a better choice compared with the homogenization method and the second-order multiscale method for solving the heat transfer equations in lattice-type structures.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/765.html} }
TY - JOUR T1 - Multiscale Asymptotic Method for Heat Transfer Equations in Lattice-Type Structures AU - Zhai , F.-M. AU - Cao , L.-Q. JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 232 EP - 255 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/765.html KW - Homogenization, multiscale asymptotic expansion, parabolic equation, lattice-type structure, multiscale finite element method. AB -

In this paper, we discuss the initial-boundary value problem for the heat transfer equation in lattice-type structures that arises from the aerospace industry and the structural engineering. The main results obtained in this paper are the convergence theorems by using the homogenization method and the multiscale asymptotic method (see Theorems 2.1 and 2.2). Some numerical examples are given for three types of lattice structures. These numerical results suggest that the first-order multiscale method should be a better choice compared with the homogenization method and the second-order multiscale method for solving the heat transfer equations in lattice-type structures.

F.-M. Zhai & L.-Q. Cao. (1970). Multiscale Asymptotic Method for Heat Transfer Equations in Lattice-Type Structures. International Journal of Numerical Analysis and Modeling. 6 (2). 232-255. doi:
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