Geodesic
A comparison between the CABARET scheme and the MUSCL-type schemes
Matematičeskoe modelirovanie, Tome 25 (2013) no. 9, pp. 109-136

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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.
Mots-clés : CABARET scheme
Keywords: MUSCL-type schemes, TVD- and TVB-limiters, blast wave problem. 
@article{MM_2013_25_9_a9,
     author = {A. V. Rodionov},
     title = {A comparison between the {CABARET} scheme and the {MUSCL-type} schemes},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {109--136},
     publisher = {mathdoc},
     volume = {25},
     number = {9},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2013_25_9_a9/}
}
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A. V. Rodionov. A comparison between the CABARET scheme and the MUSCL-type schemes. Matematičeskoe modelirovanie, Tome 25 (2013) no. 9, pp. 109-136. http://geodesic.mathdoc.fr/item/MM_2013_25_9_a9/