A Finite-Difference Scheme for the Generalized Diffuse Interface Model of the Electrical Breakdown Process

The subject of the present work is numerical studies of a generalization of a diffuse interface model describing the development of the electrical breakdown channel. The Allen–Cahn type equation governing the phase field evolution is a nonlinear partial differential equation including 4th order term...

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Published inMathematical models and computer simulations Vol. 16; no. Suppl 1; pp. S105 - S118
Main Authors Ponomarev, A. S., Zipunova, E. V.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.12.2024
Springer Nature B.V
Subjects
Boundary conditions
Electrical faults
Finite difference method
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Nonlinear differential equations
Partial differential equations
Simulation and Modeling
electrical breakdown
diffuse interface model
phase field
stability
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Summary:The subject of the present work is numerical studies of a generalization of a diffuse interface model describing the development of the electrical breakdown channel. The Allen–Cahn type equation governing the phase field evolution is a nonlinear partial differential equation including 4th order terms. The solutions of this equation may have singular behavior in some cases. In the paper, we propose a new finite-difference scheme allowing an exact accounting of the singularities of the solution and its accurate computation, even in the case when the boundary conditions are defined on objects of higher codimension.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2070-0482
2070-0490
DOI:10.1134/S2070048224700844