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Article information
2021 , Volume 26, ¹ 4, p.27-38
Liseikin V.D., Paasonen V.I.
Special adaptive grids and Runge-Richardson correction in problems with layers
It is highly desirable using difference schemes with high accuracy and uniform convergence in a small parameter as the grid steps tend to zero for solving the problems with both boundary and interior layers. However, these requirements turn out to be contradictory: highly-accurate schemes may not converge uniformly, and uniformly converging schemes usually have only the first order of accuracy. Nevertheless, there is a unique opportunity to resolve this contradiction by increasing the order of accuracy by applying the Richardson – Runge extrapolation corrections, which are linear combinations of difference solutions on nested grids. In this paper, using the example of several common difference schemes, we study the efficiency of such approach for calculations obtained on adaptive grids that are explicitly specified by special coordinate transformations. Two diagonal-dominated upstream-type uniformly converging schemes are investigated. They are compared with an analogue of the scheme with central difference that does not have a diagonal dominance and does not converge uniformly. In addition to simple corrections,double corrections are also used, which further increase the order of accuracy of the resulting solutions.
[full text]
Keywords: uniform convergence, adaptive grids, boundary layer, diagonal dominance, Runge-Richardson correction
doi: 10.25743/ICT.2021.26.4.004
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. Special adaptive grids and Runge-Richardson correction in problems with layers // Computational technologies. 2021. V. 26. ¹ 4. P. 27-38
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