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Sibirskii Zhurnal Industrial'noi Matematiki, 2022, Volume 25, Number 1, Pages 39–53
DOI: https://doi.org/10.33048/SIBJIM.2022.25.103
(Mi sjim1160)
 

This article is cited in 1 scientific paper (total in 1 paper)

Nonisothermal diffuse interface model for electrical breakdown channel propagation

E. V. Zipunova, A. A. Kuleshov, E. B. Savenkov

Keldysh Institute of Applied Mathematics RAS, Miusskaya sq. 4, Moscow 125047, Russia
Full-text PDF (590 kB) Citations (1)
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Abstract: The paper is devoted to the derivation of the gradient (weakly nonlocal) diffuse interface model, which describes an electrical breakdown channel propagation under the application of an electric field. In contrast to earlier presented models, the derived one is nonisothermal and consists of Maxwell's equations in quasi(electro)stationary approximation, Allen—Cahn type equation which governs phase field evolution, and energy balance equation. The derivation of the model is provided based on the rational thermomechanics framework using M.Gurtin microstress and microforce theory and Coleman-Noll procedure to derive constitutive relations of the model. The derived model is thermodynamically consistent and satisfies entropy inequality in the respective form. The closed-form formulation of the model and complete set of constitutive relations are presented.
Keywords: diffuse interface model, phase field, order parameter, electrical breakdown. .
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1623
Received: 11.08.2021
Revised: 01.10.2021
Accepted: 21.10.2021
Bibliographic databases:
Document Type: Article
UDC: 51--72:517.9:538.91
Language: Russian
Citation: E. V. Zipunova, A. A. Kuleshov, E. B. Savenkov, “Nonisothermal diffuse interface model for electrical breakdown channel propagation”, Sib. Zh. Ind. Mat., 25:1 (2022), 39–53
Citation in format AMSBIB
\Bibitem{ZipKulSav22}
\by E.~V.~Zipunova, A.~A.~Kuleshov, E.~B.~Savenkov
\paper Nonisothermal diffuse interface model for electrical breakdown channel
propagation
\jour Sib. Zh. Ind. Mat.
\yr 2022
\vol 25
\issue 1
\pages 39--53
\mathnet{http://mi.mathnet.ru/sjim1160}
\crossref{https://doi.org/10.33048/SIBJIM.2022.25.103}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4461394}
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  • https://www.mathnet.ru/eng/sjim/v25/i1/p39
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский журнал индустриальной математики
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    References:52
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