Специальные адаптивные сетки и коррекция Рунге-Ричардсона в задачах со слоями

Translated title of the contribution: Special adaptive grids and Runge Richardson correction in problems with layers

D. Liseikin Vladimir, I. Paasonen Victor

Research output: Contribution to journalArticlepeer-review

Abstract

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 arc 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 arc investigated. They are compared with an analogue of the scheme with central difference that docs 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.

Translated title of the contributionSpecial adaptive grids and Runge Richardson correction in problems with layers
Original languageRussian
Article number3
Pages (from-to)27-38
Number of pages12
JournalJournal of Computational Technologies
Volume26
Issue number4
DOIs
Publication statusPublished - 2021

OECD FOS+WOS

  • 1.02 COMPUTER AND INFORMATION SCIENCES
  • 1.01 MATHEMATICS

State classification of scientific and technological information

  • 27 MATHEMATICS

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