Abstract:
The CABARET scheme is used for the numerical solution of the one-dimensional shallow water equations over a rough bottom. The scheme involves conservative and flux variables, whose values at a new time level are calculated by applying the characteristic properties of the shallow water equations. The scheme is verified using a series of test and model problems.
Key words:
system of hyperbolic equations, shallow water equations over a rough bottom, numerical methods, balance-characteristic scheme, CABARET scheme.
Citation:
V. M. Goloviznin, V. A. Isakov, “Balance-characteristic scheme as applied to the shallow water equations over a rough bottom”, Zh. Vychisl. Mat. Mat. Fiz., 57:7 (2017), 1142–1160; Comput. Math. Math. Phys., 57:7 (2017), 1140–1157
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\by V.~M.~Goloviznin, V.~A.~Isakov
\paper Balance-characteristic scheme as applied to the shallow water equations over a rough bottom
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2017
\vol 57
\issue 7
\pages 1142--1160
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\jour Comput. Math. Math. Phys.
\yr 2017
\vol 57
\issue 7
\pages 1140--1157
\crossref{https://doi.org/10.1134/S0965542517070089}
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Linking options:
https://www.mathnet.ru/eng/zvmmf10587
https://www.mathnet.ru/eng/zvmmf/v57/i7/p1142
This publication is cited in the following 11 articles:
V.M. Goloviznin, Pavel A. Maiorov, Petr A. Maiorov, A.V. Solovjev, “Validation of the low dissipation computational algorithm CABARET-MFSH for multilayer hydrostatic flows with a free surface on the lock-release experiments”, Journal of Computational Physics, 463 (2022), 111239
M. D. Bragin, O. A. Kovyrkina, M. E. Ladonkina, V. V. Ostapenko, V. F. Tishkin, N. A. Khandeeva, “Combined numerical schemes”, Comput. Math. Math. Phys., 62:11 (2022), 1743–1781
N. A. Afanasiev, N. È. Shagirov, V. M. Goloviznin, “Interpolatory conservative-characteristic scheme with improved dispersion properties for computational fluid dynamics”, Comput. Math. Math. Phys., 62:11 (2022), 1885–1899
N. Afanasiev, V. Goloviznin, “A locally implicit time-reversible sonic point processing algorithm for one-dimensional shallow-water equations”, J. Comput. Phys., 434 (2021), 110220
V. V. Ostapenko, T. V. Protopopova, “On monotonicity of CABARET scheme approximating the multidimensional scalar conservation law”, Num. Anal. Appl., 13:4 (2020), 360–367
V. M. Goloviznin, P. A. Maiorov, P. A. Maiorov, V A. Solovjev, “New numerical algorithm for the multi-layer shallow water equations based on the hyperbolic decomposition and the cabaret scheme”, Phys. Oceanogr., 26:6 (2019), 528–546
D Y Gorbachev, V M Goloviznin, “The Balance-Characteristic Numerical Method on Triangle Grids”, J. Phys.: Conf. Ser., 1392:1 (2019), 012036
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”, Math. Models Comput. Simul., 11:1 (2019), 46–60
N. A. Zyuzina, V. V. Ostapenko, “Decay of unstable strong discontinuities in the case of a convex-flux scalar conservation law approximated by the CABARET scheme”, Comput. Math. Math. Phys., 58:6 (2018), 950–966
O. A. Kovyrkina, V. V. Ostapenko, “Monotonicity of the CABARET scheme approximating a hyperbolic system of conservation laws”, Comput. Math. Math. Phys., 58:9 (2018), 1435–1450
Sergey I. Markov, Natalya B. Itkina, 2018 XIV International Scientific-Technical Conference on Actual Problems of Electronics Instrument Engineering (APEIE), 2018, 177
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