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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2011, Volume 51, Number 7, Pages 1308–1316 (Mi zvmmf9481)  
This article is cited in 1 scientific paper (total in 1 paper)

Basis difference method for orthogonal systems on a surface

V. A. Korobitsyn

Tomsk State University, pr. Lenina 36, Tomsk, 634050 Russia
Full-text PDF (589 kB) Citations (1)
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Abstract: The basis operator method intended for constructing systems of difference approximations to differential operators in vector and tensor analysis is extended to orthogonal systems on a surface. A class of completely conservative differential-difference schemes for continuum mechanics in Lagrangian variables is constructed. Basis operators are constructed using the finite volume equation, consistency conditions for discrete operators of the first derivative, and consistent projection operators for grid functions. A system of differential-difference continuum mechanics equations on a surface is obtained, which implies all conservation laws typical of the continuum case, including additional ones. A stability estimate is derived for discrete equations of an incompressible viscous fluid.
Key words: discrete curvilinear surfaces, orthogonal coordinates; consistent basis operators, conservative difference schemes, conservation laws.
Received: 18.12.2009
Revised: 22.11.2010
English version:
Computational Mathematics and Mathematical Physics, 2011, Volume 51, Issue 7, Pages 1222–1230
DOI: https://doi.org/10.1134/S0965542511070116
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: V. A. Korobitsyn, “Basis difference method for orthogonal systems on a surface”, Zh. Vychisl. Mat. Mat. Fiz., 51:7 (2011), 1308–1316; Comput. Math. Math. Phys., 51:7 (2011), 1222–1230
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/zvmmf9481
  • https://www.mathnet.ru/eng/zvmmf/v51/i7/p1308
    • This publication is cited in the following 1 articles:
    1. A. M. Bubenchikov, V. A. Korobitsyn, D. V. Korobitsyn, P. P. Kotov, Yu. I. Shokin, “Numerical simulation of multiply connected axisymmetric discontinuous incompressible potential flows”, Comput. Math. Math. Phys., 54:7 (2014), 1167–1175  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    Abstract page:272
    Full-text PDF :94
    References:59
    First page:264
     
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