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

Результат исследования: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучнаярецензирование

Аннотация

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.

Язык оригиналаанглийский
Название основной публикацииInternational Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019
РедакторыTheodore E. Simos, Charalambos Tsitouras
ИздательAmerican Institute of Physics Inc.
ISBN (электронное издание)9780735440258
DOI
СостояниеОпубликовано - 24 ноя 2020
СобытиеInternational Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019 - Rhodes, Греция
Продолжительность: 23 сен 201928 сен 2019

Серия публикаций

НазваниеAIP Conference Proceedings
Том2293
ISSN (печатное издание)0094-243X
ISSN (электронное издание)1551-7616

Конференция

КонференцияInternational Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019
СтранаГреция
ГородRhodes
Период23.09.201928.09.2019

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