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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2011, Volume 51, Number 7, Pages 1308–1316
(Mi zvmmf9481)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/zvmmf9481 https://www.mathnet.ru/eng/zvmmf/v51/i7/p1308
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Abstract page: | 237 | Full-text PDF : | 83 | References: | 47 | First page: | 264 |
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