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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2009, Volume 49, Number 5, Pages 826–839
(Mi zvmmf4688)
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This article is cited in 19 scientific papers (total in 20 papers)
Generation of structured difference grids in two-dimensional nonconvex domains using mappings
B. N. Azarenok Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
Abstract:
Generation of structured difference grids in two-dimensional nonconvex domains is considered using a mapping of a parametric domain with a given nondegenerate grid onto a physical domain. For that purpose, a harmonic mapping is first used, which is a diffeomorphism under certain conditions due to Rado's theorem. Although the harmonic mapping is a diffeomorphism, its discrete implementation can produce degenerate grids in nonconvex domains with highly curved boundaries. It is shown that the degeneration occurs due to approximation errors. To control the coordinate lines of the grid, an additional mapping is used and universal elliptic differential equations are solved. This makes it possible to generate a nondegenerate grid with cells of a prescribed shape.
Key words:
structured grids, harmonic mapping, control metric, universal differential equations.
Received: 02.07.2008
Citation:
B. N. Azarenok, “Generation of structured difference grids in two-dimensional nonconvex domains using mappings”, Zh. Vychisl. Mat. Mat. Fiz., 49:5 (2009), 826–839; Comput. Math. Math. Phys., 49:5 (2009), 797–809
Linking options:
https://www.mathnet.ru/eng/zvmmf4688 https://www.mathnet.ru/eng/zvmmf/v49/i5/p826
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Abstract page: | 432 | Full-text PDF : | 237 | References: | 47 | First page: | 10 |
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