Comparative Analysis of the Accuracy of Three Different Schemes in the Calculation of Shock Waves

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Comparative Analysis of the Accuracy of Three Different Schemes in the Calculation of Shock Waves. / Kovyrkina, O. A.; Kurganov, A. A.; Ostapenko, V. V.

In: Mathematical Models and Computer Simulations, Vol. 15, No. 3, 06.2023, p. 401-414.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{f1d65e78f05f40ea93ce1e49ff0294c1,

title = "Comparative Analysis of the Accuracy of Three Different Schemes in the Calculation of Shock Waves",

abstract = "We perform a comparative analysis of the accuracy of the weighted essentially nonoscillatory (WENO), compact high-order weak approximation (CWA), and central-upwind (CU) schemes used to compute discontinuous solutions containing shocks propagating with variable velocity. We demonstrate that the the accuracy of the formally high-order WENO and CU schemes, which are constructed using nonlinear flux correction mechanisms, reduces to approximately first order integral convergence on intervals in which one of the endpoints is in the region of influence of a shock wave. At the same time, the CWA scheme, which is designed to be high-order in the weak sense and does not rely on any nonlinear flux corrections, retains approximately the second order of integral convergence even in the regions of influence of shock waves. As a result, in these areas, the accuracy of the WENO and CU schemes is significantly lower than the accuracy of the CWA scheme. We provide a theoretical justification of these numerical results.",

keywords = "increased order of convergence, numerical schemes, weak solutions with shocks",

author = "Kovyrkina, {O. A.} and Kurganov, {A. A.} and Ostapenko, {V. V.}",

note = "This study was financially supported by the Russian Foundation for Basic Research and the National Natural Science Foundation of China (NSFC) as part of scientific project no. 21-51-53012 and was partially supported by NSFC grants nos. 11771201 and 1201101343, as well as by the Guangdong Provincial Foundation, Laboratory of Computing and Materials Science (no. 2019B030301001). Публикация для корректировки.",

year = "2023",

month = jun,

doi = "10.1134/S2070048223030092",

language = "English",

volume = "15",

pages = "401--414",

journal = "Mathematical Models and Computer Simulations",

issn = "2070-0482",

publisher = "Springer Science + Business Media",

number = "3",

}

RIS

TY - JOUR

T1 - Comparative Analysis of the Accuracy of Three Different Schemes in the Calculation of Shock Waves

AU - Kovyrkina, O. A.

AU - Kurganov, A. A.

AU - Ostapenko, V. V.

N1 - This study was financially supported by the Russian Foundation for Basic Research and the National Natural Science Foundation of China (NSFC) as part of scientific project no. 21-51-53012 and was partially supported by NSFC grants nos. 11771201 and 1201101343, as well as by the Guangdong Provincial Foundation, Laboratory of Computing and Materials Science (no. 2019B030301001). Публикация для корректировки.

PY - 2023/6

Y1 - 2023/6

N2 - We perform a comparative analysis of the accuracy of the weighted essentially nonoscillatory (WENO), compact high-order weak approximation (CWA), and central-upwind (CU) schemes used to compute discontinuous solutions containing shocks propagating with variable velocity. We demonstrate that the the accuracy of the formally high-order WENO and CU schemes, which are constructed using nonlinear flux correction mechanisms, reduces to approximately first order integral convergence on intervals in which one of the endpoints is in the region of influence of a shock wave. At the same time, the CWA scheme, which is designed to be high-order in the weak sense and does not rely on any nonlinear flux corrections, retains approximately the second order of integral convergence even in the regions of influence of shock waves. As a result, in these areas, the accuracy of the WENO and CU schemes is significantly lower than the accuracy of the CWA scheme. We provide a theoretical justification of these numerical results.

AB - We perform a comparative analysis of the accuracy of the weighted essentially nonoscillatory (WENO), compact high-order weak approximation (CWA), and central-upwind (CU) schemes used to compute discontinuous solutions containing shocks propagating with variable velocity. We demonstrate that the the accuracy of the formally high-order WENO and CU schemes, which are constructed using nonlinear flux correction mechanisms, reduces to approximately first order integral convergence on intervals in which one of the endpoints is in the region of influence of a shock wave. At the same time, the CWA scheme, which is designed to be high-order in the weak sense and does not rely on any nonlinear flux corrections, retains approximately the second order of integral convergence even in the regions of influence of shock waves. As a result, in these areas, the accuracy of the WENO and CU schemes is significantly lower than the accuracy of the CWA scheme. We provide a theoretical justification of these numerical results.

KW - increased order of convergence

KW - numerical schemes

KW - weak solutions with shocks

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85159654943&origin=inward&txGid=3fd6829603ba00d38a6512d40fd07ea0

UR - https://www.mendeley.com/catalogue/0329fd5a-c5aa-390f-a347-0f4c70c7a4a5/

U2 - 10.1134/S2070048223030092

DO - 10.1134/S2070048223030092

M3 - Article

VL - 15

SP - 401

EP - 414

JO - Mathematical Models and Computer Simulations

JF - Mathematical Models and Computer Simulations

SN - 2070-0482

IS - 3

ER -

ID: 59278351