Abstract:
The CABARET scheme is compared with some schemes from the family of MUSCL-type schemes. Description and analysis of these schemes are presented as applied to the linear constant-coefficient advection equation. A new representation, which can be treated as a modification of the MUSCL scheme, is proposed for the CABARET scheme. Three types of limiters are considered in the MUSCL-type schemes: TVD, TVB and a new NOLD limiter. The schemes are evaluated on a number of linear problems (discontinuous and continuous profiles, uniform and non-uniform mesh) as well as on the nonlinear blast wave problem.
Citation:
A. V. Rodionov, “A comparison between the CABARET scheme and the MUSCL-type schemes”, Mat. Model., 25:9 (2013), 109–136; Math. Models Comput. Simul., 6:2 (2014), 203–225
\Bibitem{Rod13}
\by A.~V.~Rodionov
\paper A comparison between the CABARET scheme and the MUSCL-type schemes
\jour Mat. Model.
\yr 2013
\vol 25
\issue 9
\pages 109--136
\mathnet{http://mi.mathnet.ru/mm3405}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3203283}
\transl
\jour Math. Models Comput. Simul.
\yr 2014
\vol 6
\issue 2
\pages 203--225
\crossref{https://doi.org/10.1134/S2070048214020094}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84925940193}
Linking options:
https://www.mathnet.ru/eng/mm3405
https://www.mathnet.ru/eng/mm/v25/i9/p109
This publication is cited in the following 6 articles:
Alexander V. Rodionov, “On the Solution Accuracy Downstream of Shocks When Using Shock-Capturing Methods. I. Sources of Errors in One-Dimensional Problems”, SSRN Journal, 2022
Yeganeh S.M., Farzi J., “A Class of Non-Oscillatory Direct-Space-Time Schemes For Hyperbolic Conservation Laws”, Appl. Math. Comput., 399 (2021), 126013
M. D. Bragin, Yu. A. Kriksin, V. F. Tishkin, “Discontinuous Galerkin method with entropic slope limiter for Euler equations”, Math. Models Comput. Simul., 12:5 (2020), 824–833
Y. A. Kriksin, V. F. Tishkin, “Entropy stable discontinuous Galerkin method for Euler equations using non-conservative variables”, Math. Models Comput. Simul., 13:3 (2021), 416–425
M. D. Bragin, Yu. A. Kriksin, V. F. Tishkin, “Obespechenie entropiinoi ustoichivosti razryvnogo metoda Galerkina v gazodinamicheskikh zadachakh”, Preprinty IPM im. M. V. Keldysha, 2019, 051, 22 pp.
A. V. Rodionov, “On correlation between the discontinuous Galerkin method and MUSCL-type schemes”, Math. Models Comput. Simul., 8:3 (2016), 285–300
Citation in format AMSBIB
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