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Volume 41, Issue 3
A Finite Volume Method Preserving Maximum Principle for the Conjugate Heat Transfer Problems with General Interface Conditions

Huifang Zhou, Zhiqiang Sheng & Guangwei Yuan

DOI: 10.4208/jcm.2107-m2020-0266

J. Comp. Math., 41 (2023), pp. 345-369.

Published online: 2023-02

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  • Abstract

In this paper, we present a unified finite volume method preserving discrete maximum principle (DMP) for the conjugate heat transfer problems with general interface conditions. We prove the existence of the numerical solution and the DMP-preserving property. Numerical experiments show that the nonlinear iteration numbers of the scheme in [24] increase rapidly when the interfacial coefficients decrease to zero. In contrast, the nonlinear iteration numbers of the unified scheme do not increase when the interfacial coefficients decrease to zero, which reveals that the unified scheme is more robust than the scheme in [24]. The accuracy and DMP-preserving property of the scheme are also veri ed in the numerical experiments.

  • Keywords

Conjugate heat transfer problems, General interface conditions, Finite volume scheme, Discrete maximum principle.

  • AMS Subject Headings

65M08, 35K59

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

13614405274@163.com (Huifang Zhou)

sheng zhiqiang@iapcm.ac.cn (Zhiqiang Sheng)

yuan_guangwei@iapcm.ac.cn (Guangwei Yuan)

  • BibTex
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  • TXT
@Article{JCM-41-345, author = {Zhou , HuifangSheng , Zhiqiang and Yuan , Guangwei}, title = {A Finite Volume Method Preserving Maximum Principle for the Conjugate Heat Transfer Problems with General Interface Conditions}, journal = {Journal of Computational Mathematics}, year = {2023}, volume = {41}, number = {3}, pages = {345--369}, abstract = {

In this paper, we present a unified finite volume method preserving discrete maximum principle (DMP) for the conjugate heat transfer problems with general interface conditions. We prove the existence of the numerical solution and the DMP-preserving property. Numerical experiments show that the nonlinear iteration numbers of the scheme in [24] increase rapidly when the interfacial coefficients decrease to zero. In contrast, the nonlinear iteration numbers of the unified scheme do not increase when the interfacial coefficients decrease to zero, which reveals that the unified scheme is more robust than the scheme in [24]. The accuracy and DMP-preserving property of the scheme are also veri ed in the numerical experiments.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2107-m2020-0266}, url = {http://global-sci.org/intro/article_detail/jcm/21388.html} }
TY - JOUR T1 - A Finite Volume Method Preserving Maximum Principle for the Conjugate Heat Transfer Problems with General Interface Conditions AU - Zhou , Huifang AU - Sheng , Zhiqiang AU - Yuan , Guangwei JO - Journal of Computational Mathematics VL - 3 SP - 345 EP - 369 PY - 2023 DA - 2023/02 SN - 41 DO - http://doi.org/10.4208/jcm.2107-m2020-0266 UR - https://global-sci.org/intro/article_detail/jcm/21388.html KW - Conjugate heat transfer problems, General interface conditions, Finite volume scheme, Discrete maximum principle. AB -

In this paper, we present a unified finite volume method preserving discrete maximum principle (DMP) for the conjugate heat transfer problems with general interface conditions. We prove the existence of the numerical solution and the DMP-preserving property. Numerical experiments show that the nonlinear iteration numbers of the scheme in [24] increase rapidly when the interfacial coefficients decrease to zero. In contrast, the nonlinear iteration numbers of the unified scheme do not increase when the interfacial coefficients decrease to zero, which reveals that the unified scheme is more robust than the scheme in [24]. The accuracy and DMP-preserving property of the scheme are also veri ed in the numerical experiments.

Huifang Zhou, Zhiqiang Sheng & Guangwei Yuan. (2023). A Finite Volume Method Preserving Maximum Principle for the Conjugate Heat Transfer Problems with General Interface Conditions. Journal of Computational Mathematics. 41 (3). 345-369. doi:10.4208/jcm.2107-m2020-0266
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