{"title":"Numerical Studies of the Phase Field Model Describing Electric\nBreakdown in a Heterogeneous Medium","authors":"E. V. Zipunova, A. A. Kuleshov, E. B. Savenkov","doi":"10.1134/S1990478924030207","DOIUrl":null,"url":null,"abstract":"<p> This paper presents the results of numerical studies of the phase field model for the\ndevelopment of an electrical breakdown path. The model consists of Maxwell’s equations in the\nquasi(electro)stationary approximation, the electric charge balance equation, and the Allen–Cahn\nequation describing the phase field evolution. Several problem settings concerning the\ndevelopment of a breakdown path in homogeneous as well as macro- and microheterogeneous\nmedia are considered.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 3","pages":"612 - 630"},"PeriodicalIF":0.5800,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478924030207","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
This paper presents the results of numerical studies of the phase field model for the
development of an electrical breakdown path. The model consists of Maxwell’s equations in the
quasi(electro)stationary approximation, the electric charge balance equation, and the Allen–Cahn
equation describing the phase field evolution. Several problem settings concerning the
development of a breakdown path in homogeneous as well as macro- and microheterogeneous
media are considered.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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