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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. ed. / Theodore E. Simos; Charalambos Tsitouras. American Institute of Physics Inc., 2020. 370002 (AIP Conference Proceedings; Vol. 2293).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Kovyrkina, O & Ostapenko, V 2020, On the accuracy of finite-difference schemes in smooth parts of calculated weak solutions. in TE Simos & C Tsitouras (eds), International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019., 370002, AIP Conference Proceedings, vol. 2293, American Institute of Physics Inc., International Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019, Rhodes, Greece, 23.09.2019. https://doi.org/10.1063/5.0026831

APA

Kovyrkina, O., & Ostapenko, V. (2020). On the accuracy of finite-difference schemes in smooth parts of calculated weak solutions. In T. E. Simos, & C. Tsitouras (Eds.), International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019 [370002] (AIP Conference Proceedings; Vol. 2293). American Institute of Physics Inc.. https://doi.org/10.1063/5.0026831

Vancouver

Kovyrkina O, Ostapenko V. On the accuracy of finite-difference schemes in smooth parts of calculated weak solutions. In Simos TE, Tsitouras C, editors, International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019. American Institute of Physics Inc. 2020. 370002. (AIP Conference Proceedings). doi: 10.1063/5.0026831

Author

Kovyrkina, Olyana ; Ostapenko, Vladimir. / On the accuracy of finite-difference schemes in smooth parts of calculated weak solutions. International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019. editor / Theodore E. Simos ; Charalambos Tsitouras. American Institute of Physics Inc., 2020. (AIP Conference Proceedings).

BibTeX

@inproceedings{281a20eec4f24d87bb6f43adf4528bf2,
title = "On the accuracy of finite-difference schemes in smooth parts of calculated weak solutions",
abstract = "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.",
author = "Olyana Kovyrkina and Vladimir Ostapenko",
note = "Funding Information: The work was carried out with support by the Russian Science Foundation (grant No. 16-11-10033). Publisher Copyright: {\textcopyright} 2020 American Institute of Physics Inc.. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.; International Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019 ; Conference date: 23-09-2019 Through 28-09-2019",
year = "2020",
month = nov,
day = "24",
doi = "10.1063/5.0026831",
language = "English",
series = "AIP Conference Proceedings",
publisher = "American Institute of Physics Inc.",
editor = "Simos, {Theodore E.} and Charalambos Tsitouras",
booktitle = "International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019",

}

RIS

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