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Mathematical Models and Computer Simulations

Erschienen in:

01.06.2023

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

verfasst von: O. A. Kovyrkina, A. A. Kurganov, V. V. Ostapenko

Erschienen in: Mathematical Models and Computer Simulations | Ausgabe 3/2023

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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.

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Titel: Comparative Analysis of the Accuracy of Three Different Schemes in the Calculation of Shock Waves
verfasst von: O. A. Kovyrkina
A. A. Kurganov
V. V. Ostapenko
Publikationsdatum: 01.06.2023
Verlag: Pleiades Publishing
Erschienen in: Mathematical Models and Computer Simulations / Ausgabe 3/2023
Print ISSN: 2070-0482
Elektronische ISSN: 2070-0490
DOI: https://doi.org/10.1134/S2070048223030092

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