Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
On the accuracy of finite-difference schemes in smooth parts of calculated weak solutions. / Kovyrkina, Olyana; Ostapenko, Vladimir.
International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019. ред. / Theodore E. Simos; Charalambos Tsitouras. American Institute of Physics Inc., 2020. 370002 (AIP Conference Proceedings; Том 2293).Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
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TY - GEN
T1 - On the accuracy of finite-difference schemes in smooth parts of calculated weak solutions
AU - Kovyrkina, Olyana
AU - Ostapenko, Vladimir
N1 - Funding Information: The work was carried out with support by the Russian Science Foundation (grant No. 16-11-10033). Publisher Copyright: © 2020 American Institute of Physics Inc.. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/11/24
Y1 - 2020/11/24
N2 - We consider explicit two-layer in time finite-difference schemes intended for the shock capturing calculation of weak solutions of quasilinear hyperbolic systems of conservation laws. The accuracy of these schemes in the areas of smoothness of the calculated weak solution is studied. It is shown that in these regions the errors of the difference solution approximately satisfy the hyperbolic system of differential equations, which have characteristics fields that are the same as the approximated system of conservation laws. This implies that in the shock influence region the convergence rate of the difference solution essentially depends on the accuracy with which the scheme approximates the Hugoniot conditions at the shock front. This explains the decrease in the convergence order of NFC (Nonlinear Flux Correction) schemes in the shock influence regions.
AB - We consider explicit two-layer in time finite-difference schemes intended for the shock capturing calculation of weak solutions of quasilinear hyperbolic systems of conservation laws. The accuracy of these schemes in the areas of smoothness of the calculated weak solution is studied. It is shown that in these regions the errors of the difference solution approximately satisfy the hyperbolic system of differential equations, which have characteristics fields that are the same as the approximated system of conservation laws. This implies that in the shock influence region the convergence rate of the difference solution essentially depends on the accuracy with which the scheme approximates the Hugoniot conditions at the shock front. This explains the decrease in the convergence order of NFC (Nonlinear Flux Correction) schemes in the shock influence regions.
UR - http://www.scopus.com/inward/record.url?scp=85098004267&partnerID=8YFLogxK
U2 - 10.1063/5.0026831
DO - 10.1063/5.0026831
M3 - Conference contribution
AN - SCOPUS:85098004267
T3 - AIP Conference Proceedings
BT - International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019
A2 - Simos, Theodore E.
A2 - Tsitouras, Charalambos
PB - American Institute of Physics Inc.
T2 - International Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019
Y2 - 23 September 2019 through 28 September 2019
ER -
ID: 27326649