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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2024, Volume 64, Number 8, Pages 1500–1516
DOI: https://doi.org/10.31857/S0044466924080148 (Mi zvmmf11817) 		 
Mathematical physics

Density gradient model in spherically symmetric formulation and its explicit-implicit dissipative discretization for the study of phase boundary dynamics

V. A. Balashova, E. A. Pavlishinab, E. B. Savenkova

a Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia
b Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudnyi, Moscow oblast, Russia
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DOI: https://doi.org/10.31857/S0044466924080148
Abstract: An unconditionally gradient-stable (dissipative) numerical method is developed for solving a conservative model of the density gradient in the spherically symmetric formulation. The algorithm is constructed using Eyre’s method based on a convex splitting of the free energy of the system. The gradient stability of the constructed algorithm in the semidiscrete and fully discrete cases is proved. The theoretical results are confirmed by test computations. The proposed numerical method is used to analyze the influence exerted by the way of specifying the diffusion mobility on the evolution of the phase boundary.
Key words: density gradient theory, dissipative method, explicit-implicit approximation, convex splitting, spherically symmetric formulation.
Funding agency Grant number
Russian Science Foundation 22-11-00203
This work was supported by the Russian Science Foundation, project no. 22-11-00203.
Received: 02.04.2024
Revised: 02.04.2024
Accepted: 02.05.2024
English version:
Computational Mathematics and Mathematical Physics, 2024, Volume 64, Issue 8, Pages 1823–1839
DOI: https://doi.org/10.1134/S0965542524700787
Bibliographic databases:
Document Type: Article
UDC: 519.635
Language: Russian
Citation: V. A. Balashov, E. A. Pavlishina, E. B. Savenkov, “Density gradient model in spherically symmetric formulation and its explicit-implicit dissipative discretization for the study of phase boundary dynamics”, Zh. Vychisl. Mat. Mat. Fiz., 64:8 (2024), 1500–1516; Comput. Math. Math. Phys., 64:8 (2024), 1823–1839
Citation in format AMSBIB
\Bibitem{BalPavSav24}
\by V.~A.~Balashov, E.~A.~Pavlishina, E.~B.~Savenkov
\paper Density gradient model in spherically symmetric formulation and its explicit-implicit dissipative discretization for the study of phase boundary dynamics
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2024
\vol 64
\issue 8
\pages 1500--1516
\mathnet{http://mi.mathnet.ru/zvmmf11817}
\crossref{https://doi.org/10.31857/S0044466924080148}
\elib{https://elibrary.ru/item.asp?id=75224112}
\transl
\jour Comput. Math. Math. Phys.
\yr 2024
\vol 64
\issue 8
\pages 1823--1839
\crossref{https://doi.org/10.1134/S0965542524700787}
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