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

• Published in: Mathematical models and computer simulations Vol. 16; no. Suppl 1; pp. S105 - S118
• Main Authors: Ponomarev, A. S., Zipunova, E. V.
• Format: Journal Article
• Language: English
• 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

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...