Comparative Analysis of the Accuracy of Three Different Schemes in the Calculation of Shock Waves Full article
| Journal |
Mathematical Models and Computer Simulations
ISSN: 2070-0482 |
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| Output data | Year: 2023, Volume: 15, Number: 3, Pages: 401-414 Pages count : 14 DOI: 10.1134/s2070048223030092 | ||||||
| Tags | weak solutions with shocks, numerical schemes, increased order of convergence | ||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Российский фонд фундаментальных исследований | 21-51-53012 ГФЕН_а |
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.
Cite:
Kovyrkina O.A.
, Kurganov A.A.
, Ostapenko V.V.
Comparative Analysis of the Accuracy of Three Different Schemes in the Calculation of Shock Waves
Mathematical Models and Computer Simulations. 2023. V.15. N3. P.401-414. DOI: 10.1134/s2070048223030092 Scopus РИНЦ OpenAlex
Comparative Analysis of the Accuracy of Three Different Schemes in the Calculation of Shock Waves
Mathematical Models and Computer Simulations. 2023. V.15. N3. P.401-414. DOI: 10.1134/s2070048223030092 Scopus РИНЦ OpenAlex
Original:
Ковыркина О.А.
, Курганов А.А.
, Остапенко В.В.
Сравнительный анализ точности трех различных схем при сквозном расчете ударных волн
Математическое моделирование. 2022. Т.34. №10. С.43-64. DOI: 10.20948/mm-2022-10-03 РИНЦ OpenAlex
Сравнительный анализ точности трех различных схем при сквозном расчете ударных волн
Математическое моделирование. 2022. Т.34. №10. С.43-64. DOI: 10.20948/mm-2022-10-03 РИНЦ OpenAlex
Identifiers:
| Scopus: | 2-s2.0-85159654943 |
| Elibrary: | 60038746 |
| OpenAlex: | W4376878165 |