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Volume 15, Issue 1
Multi-Modes Multiscale Approach of Heat Transfer Problems in Heterogeneous Solids with Uncertain Thermal Conductivity

Shan Zhang, Zihao Yang & Xiaofei Guan

Adv. Appl. Math. Mech., 15 (2023), pp. 69-93.

Published online: 2022-10

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  • Abstract

Stochastic temperature distribution should be carefully inspected in the thermal-failure design of heterogeneous solids with unexpected random energy excitations. Stochastic multiscale modeling for these problems involve multiscale and high-dimensional uncertain thermal parameters, which remains limitation of prohibitive computation. In this paper, we propose a multi-modes based constrained energy minimization generalized multiscale finite element method (MCEM-GMsFEM), which can transform the original stochastic multiscale model into a series of recursive multiscale models sharing the same deterministic material parameters by multiscale analysis. Thus, MCEM-GMsFEM reveals an inherent low-dimensional representation in random space, and is designed to effectively reduce the complexity of repeated computation of discretized multiscale systems. In addition, the convergence analysis is established, and the optimal error estimates are derived. Finally, several typical random fluctuations on multiscale thermal conductivity are considered to validate the theoretical results in the numerical examples. The numerical results indicate that the multi-modes multiscale approach is a robust integrated method with the excellent performance.

  • AMS Subject Headings

65N12, 65N15, 80M10, 80M22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-15-69, author = {Zhang , ShanYang , Zihao and Guan , Xiaofei}, title = {Multi-Modes Multiscale Approach of Heat Transfer Problems in Heterogeneous Solids with Uncertain Thermal Conductivity}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {15}, number = {1}, pages = {69--93}, abstract = {

Stochastic temperature distribution should be carefully inspected in the thermal-failure design of heterogeneous solids with unexpected random energy excitations. Stochastic multiscale modeling for these problems involve multiscale and high-dimensional uncertain thermal parameters, which remains limitation of prohibitive computation. In this paper, we propose a multi-modes based constrained energy minimization generalized multiscale finite element method (MCEM-GMsFEM), which can transform the original stochastic multiscale model into a series of recursive multiscale models sharing the same deterministic material parameters by multiscale analysis. Thus, MCEM-GMsFEM reveals an inherent low-dimensional representation in random space, and is designed to effectively reduce the complexity of repeated computation of discretized multiscale systems. In addition, the convergence analysis is established, and the optimal error estimates are derived. Finally, several typical random fluctuations on multiscale thermal conductivity are considered to validate the theoretical results in the numerical examples. The numerical results indicate that the multi-modes multiscale approach is a robust integrated method with the excellent performance.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0048}, url = {http://global-sci.org/intro/article_detail/aamm/21126.html} }
TY - JOUR T1 - Multi-Modes Multiscale Approach of Heat Transfer Problems in Heterogeneous Solids with Uncertain Thermal Conductivity AU - Zhang , Shan AU - Yang , Zihao AU - Guan , Xiaofei JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 69 EP - 93 PY - 2022 DA - 2022/10 SN - 15 DO - http://doi.org/10.4208/aamm.OA-2022-0048 UR - https://global-sci.org/intro/article_detail/aamm/21126.html KW - Stochastic multiscale heat transfer problems, uncertainty quantification, MCEM-GMsFEM, multimodes expansion. AB -

Stochastic temperature distribution should be carefully inspected in the thermal-failure design of heterogeneous solids with unexpected random energy excitations. Stochastic multiscale modeling for these problems involve multiscale and high-dimensional uncertain thermal parameters, which remains limitation of prohibitive computation. In this paper, we propose a multi-modes based constrained energy minimization generalized multiscale finite element method (MCEM-GMsFEM), which can transform the original stochastic multiscale model into a series of recursive multiscale models sharing the same deterministic material parameters by multiscale analysis. Thus, MCEM-GMsFEM reveals an inherent low-dimensional representation in random space, and is designed to effectively reduce the complexity of repeated computation of discretized multiscale systems. In addition, the convergence analysis is established, and the optimal error estimates are derived. Finally, several typical random fluctuations on multiscale thermal conductivity are considered to validate the theoretical results in the numerical examples. The numerical results indicate that the multi-modes multiscale approach is a robust integrated method with the excellent performance.

Shan Zhang, Zihao Yang & Xiaofei Guan. (2022). Multi-Modes Multiscale Approach of Heat Transfer Problems in Heterogeneous Solids with Uncertain Thermal Conductivity. Advances in Applied Mathematics and Mechanics. 15 (1). 69-93. doi:10.4208/aamm.OA-2022-0048
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