Comparison of the WENO and cabaret schemes at calculation of the scalar conservation law with a nonconvex flux

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Abstract

It is studied the accuracy of the WENO and CABARET finite-difference schemes when calculating Cauchy problem with piecewise constant initial data for the scalar conservation law with a nonconvex flux. As a specific conservation law, we consider the Buckley-Leverett equation, which is widely used in the numerical simulation of various physical processes. Test calculations have shown that a second-order CABARET-scheme with higher accuracy than the WENO3 and WENO5 schemes localizes the shocks and adjacent rarefaction waves.

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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