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Article information
2020 , Volume 25, ¹ 5, p.66-79
Liseikin V.D., Paasonen V.I.
Convergence behavior of popular schemes in case of calculating on adaptive grids problems with layers
The paper compares solution quality to some model second- order equation with a small parameter obtained through three different schemes both on special adaptive grids specified explicitly by coordinate transformations eliminating layers and on uniform grids in a new coordinate related to the transformations. The schemes up to second order in physical and transformation variables both with a diagonal and not diagonal dominance and the simplest counter-flow scheme are analyzed. Predictions of a solution behavior based on estimates of solution errors are described, which are confirmed by numerical experiments and proofs. It is established, in particular, that the scheme of the second order with a diagonal dominance converges uniformly if the coefficient before the second derivative is small at the points of the boundary layer only. It was also demonstrated for the schemes without a diagonal dominance, mach better solutions without oscillations are obtained on uniform grids in new variables than on corresponding adaptive grids in the original physical coordinates.
[full text]
Keywords: uniform convergence, adaptive grid, boundary layer, diagonal dominance, small parameter
doi: 10.25743/ICT.2020.25.5.006
Author(s):
Liseikin Vladimir Dmitrievich
Dr. , Professor
Position: Leading research officer
Office: Federal Research Center for Information and Computational Technologies
Address: 630090, Russia, Novosibirsk, pr. Lavrentjeva, 6
Phone Office: (383) 330 73 73
E-mail: lvd@ict.nsc.ru
SPIN-code: 5198Paasonen Viktor Ivanovich
PhD. , Associate Professor
Position: Senior Research Scientist
Office: Federal Research Center for Information and Computational Technologies
Address: 630090, Russia, Novosibirsk, Ac. Lavrentiev ave. 6
Phone Office: (383) 330 86 56
E-mail: paas@ict.nsc.ru
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Bibliography link:
Liseikin V.D., Paasonen V.I. Convergence behavior of popular schemes in case of calculating on adaptive grids problems with layers // Computational technologies. 2020. V. 25. ¹ 5. P. 66-79
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