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.
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”, Mat. Model., 30:5 (2018), 76–98; Math. Models Comput. Simul., 11:1 (2019), 46–60
\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 Mat. Model.
\yr 2018
\vol 30
\issue 5
\pages 76--98
\mathnet{http://mi.mathnet.ru/mm3969}
\transl
\jour Math. Models Comput. Simul.
\yr 2019
\vol 11
\issue 1
\pages 46--60
\crossref{https://doi.org/10.1134/S2070048219010186}
Linking options:
https://www.mathnet.ru/eng/mm3969
https://www.mathnet.ru/eng/mm/v30/i5/p76
This publication is cited in the following 3 articles:
P. A. Mishchenko, T. A. Gimon, V. A. Kolotilov, “Application of the CABARET and WENO Schemes for Solving the Nonlinear Transport Equation in the Problem of Simulating the Propagation of a Sonic Boom Wave in the Atmosphere”, Comput. Math. and Math. Phys., 64:5 (2024), 1076
O. A. Kovyrkina, A. A. Kurganov, V. V. Ostapenko, “Comparative analysis of the accuracy of three different schemes in the calculation of shock waves”, Matem. Mod., 34:10 (2022), 43–64
O. A. Kovyrkina, V. V. Ostapenko, “On accuracy of MUSCL type scheme when calculating discontinuous solutions”, Math. Models Comput. Simul., 13:5 (2021), 810–819
Citation in format AMSBIB
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