Volume 26, Issue 5
Finite Element Analysis for Nonstationary Magneto-Heat Coupling Problem

Commun. Comput. Phys., 26 (2019), pp. 1471-1489.

Published online: 2019-08

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• Abstract

This paper is devoted to finite element analysis for the magneto-heat coupling model which governs the electromagnetic fields in large power transformers. The model, which couples Maxwell's equations and Heat equation through Ohmic heat source, is nonlinear. First we derive an equivalent weak formulation for the nonlinear magneto-heat model. We propose a linearized and temporally discrete scheme to approximate the continuous problem. The well-posedness and error estimates are proven for the semi-discrete scheme. Based on the results, we propose a fully discrete finite element problem and prove the error estimates for the approximate solutions. To validate the magneto-heat model and verify the efficiency of the finite element method, we compute an engineering benchmark problem of the International Compumag Society, P21b-MN. The numerical results agree well with experimental data.

• Keywords

Magneto-heat coupling model, eddy current problem, Maxwell equations, finite element method.

65N15, 65N30, 78A25

jxue@lsec.cc.ac.cn (Xue Jiang)

zdh@lsec.cc.ac.cn (Donghang Zhang)

zlb@lsec.cc.ac.cn (Linbo Zhang)

zwy@lsec.cc.ac.cn (Weiying Zheng)

• BibTex
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• TXT
@Article{CiCP-26-1471, author = {Jiang , Xue and Zhang , Donghang and Zhang , Linbo and Zheng , Weiying}, title = {Finite Element Analysis for Nonstationary Magneto-Heat Coupling Problem}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {5}, pages = {1471--1489}, abstract = {

This paper is devoted to finite element analysis for the magneto-heat coupling model which governs the electromagnetic fields in large power transformers. The model, which couples Maxwell's equations and Heat equation through Ohmic heat source, is nonlinear. First we derive an equivalent weak formulation for the nonlinear magneto-heat model. We propose a linearized and temporally discrete scheme to approximate the continuous problem. The well-posedness and error estimates are proven for the semi-discrete scheme. Based on the results, we propose a fully discrete finite element problem and prove the error estimates for the approximate solutions. To validate the magneto-heat model and verify the efficiency of the finite element method, we compute an engineering benchmark problem of the International Compumag Society, P21b-MN. The numerical results agree well with experimental data.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2019.js60.08}, url = {http://global-sci.org/intro/article_detail/cicp/13272.html} }
TY - JOUR T1 - Finite Element Analysis for Nonstationary Magneto-Heat Coupling Problem AU - Jiang , Xue AU - Zhang , Donghang AU - Zhang , Linbo AU - Zheng , Weiying JO - Communications in Computational Physics VL - 5 SP - 1471 EP - 1489 PY - 2019 DA - 2019/08 SN - 26 DO - http://doi.org/10.4208/cicp.2019.js60.08 UR - https://global-sci.org/intro/article_detail/cicp/13272.html KW - Magneto-heat coupling model, eddy current problem, Maxwell equations, finite element method. AB -

This paper is devoted to finite element analysis for the magneto-heat coupling model which governs the electromagnetic fields in large power transformers. The model, which couples Maxwell's equations and Heat equation through Ohmic heat source, is nonlinear. First we derive an equivalent weak formulation for the nonlinear magneto-heat model. We propose a linearized and temporally discrete scheme to approximate the continuous problem. The well-posedness and error estimates are proven for the semi-discrete scheme. Based on the results, we propose a fully discrete finite element problem and prove the error estimates for the approximate solutions. To validate the magneto-heat model and verify the efficiency of the finite element method, we compute an engineering benchmark problem of the International Compumag Society, P21b-MN. The numerical results agree well with experimental data.

Xue Jiang, Donghang Zhang, Linbo Zhang & Weiying Zheng. (2019). Finite Element Analysis for Nonstationary Magneto-Heat Coupling Problem. Communications in Computational Physics. 26 (5). 1471-1489. doi:10.4208/cicp.2019.js60.08
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