On the accuracy of WENO schemes in the calculation of shock waves

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Abstract

We have studied the integral and local accuracy of the WENO schemes in calculations with shocks propagating with a variable velocity. The integral accuracy is defined as the convergence order of spatial integrals of the difference solution calculated by the trapezoid or parabolic formulas. The local accuracy is associated with the determination of the errors in the calculation of invariants of exact solution. It is shown that when using the trapezoid formula, both the WENO3 and WENO5 schemes have only the first order of integral convergence in the intervals with one of their boundaries is in the shock influence region. If the parabolic formula is used, then the order of integral convergence for the WENO schemes decreases sharply in the intervals containing whole area of the shock wave influence. As a result, in these schemes, the local accuracy of the invariant calculations sharply decreases in the shock influence area. Moreover, in this area the local accuracy of the WENO3 and WENO5 schemes is approximately the same and much lower than the accuracy of the combined scheme, in which the Rusanov scheme is basic and the CABARET scheme is internal.

Original languageEnglish
Title of host publicationInternational Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019
EditorsTheodore E. Simos, Charalambos Tsitouras
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735440258
DOIs
Publication statusPublished - 24 Nov 2020
EventInternational Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019 - Rhodes, Greece
Duration: 23 Sep 201928 Sep 2019

Publication series

NameAIP Conference Proceedings
Volume2293
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceInternational Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019
CountryGreece
CityRhodes
Period23.09.201928.09.2019

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