ADI scheme for partially dimension reduced heat conduction models

The ADI type finite volume scheme is constructed to solve the non-classical heat conduction equation. The original 3D model in a tube is reduced to a hybrid dimension model in a large part of the domain. Special interface conditions are defined between 3D and 1D parts. It is assumed that the solutio...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2020-09, Vol.80 (5), p.1275-1286
Main Authors: Čiegis, R., Panasenko, G., Pileckas, K., Šumskas, V.
Format: Article
Language:English
Subjects:
ADI
Algorithms
Approximation
Conduction heating
Conduction model
Conductive heat transfer
Differential equations
Error analysis
Finite volume method
Heat conduction
Hybrid dimension
Mathematics
Operators (mathematics)
Three dimensional models
Time integration
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Summary:The ADI type finite volume scheme is constructed to solve the non-classical heat conduction equation. The original 3D model in a tube is reduced to a hybrid dimension model in a large part of the domain. Special interface conditions are defined between 3D and 1D parts. It is assumed that the solution satisfies radial symmetry conditions in 3D parts. The finite volume method is applied to approximate spatial differential operators and ADI splitting is used for time integration. It is proved that the ADI scheme is unconditionally stable. Efficient factorization algorithm is presented to solve the obtained systems of equations. Results of computational experiments confirm the theoretical error analysis.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2020.06.012