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 Matem. Mod., 2018, Volume 30, Number 5, Pages 76–98 (Mi mm3969)

On the monotonicity of the CABARET scheme approximating a scalar conservation law with alternating characteristic field

N. A. Zyuzinaab, O. A. Kovyrkinaa, V. V. Ostapenkoab

a Lavrentyev Institute of Hydrodynamics SB RAS
b Novosibirsk State University

Abstract: The monotonicity of the CABARET scheme approximating quasi-linear scalar conservation law with a convex flux is analyzed. Monotonicity conditions for this scheme are obtained in the areas where propagation velocity of characteristics has constant sign as well as in the areas of sonic lines, sonic bands and shock waves on which propagation velocity of characteristics of approximated divergent equation changes sign. Test computations are presented that illustrate these properties of the CABARET scheme.

Keywords: CABARET finite difference scheme, scalar conservation law with convex flux, sonic lines, monotonicity.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00333_à

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Citation: N. A. Zyuzina, O. A. Kovyrkina, V. V. Ostapenko, “On the monotonicity of the CABARET scheme approximating a scalar conservation law with alternating characteristic field”, Matem. Mod., 30:5 (2018), 76–98

Citation in format AMSBIB
\Bibitem{ZyuKovOst18} \by N.~A.~Zyuzina, O.~A.~Kovyrkina, V.~V.~Ostapenko \paper On the monotonicity of the CABARET scheme approximating a scalar conservation law with alternating characteristic field \jour Matem. Mod. \yr 2018 \vol 30 \issue 5 \pages 76--98 \mathnet{http://mi.mathnet.ru/mm3969}