On the accuracy of finite-difference schemes in smooth parts of calculated weak solutions

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

Аннотация

We consider explicit two-layer in time finite-difference schemes intended for the shock capturing calculation of weak solutions of quasilinear hyperbolic systems of conservation laws. The accuracy of these schemes in the areas of smoothness of the calculated weak solution is studied. It is shown that in these regions the errors of the difference solution approximately satisfy the hyperbolic system of differential equations, which have characteristics fields that are the same as the approximated system of conservation laws. This implies that in the shock influence region the convergence rate of the difference solution essentially depends on the accuracy with which the scheme approximates the Hugoniot conditions at the shock front. This explains the decrease in the convergence order of NFC (Nonlinear Flux Correction) schemes in the shock influence regions.

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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