O. A. Kovyrkina, V. V. Ostapenko, “On monotony of two layer in time cabaret scheme”, Mat. Model., 24:9 (2012), 97–112; Math. Models Comput. Simul., 5:2 (2013), 180

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Matematicheskoe modelirovanie, 2012, Volume 24, Number 9, Pages 97–112 (Mi mm3313)

This article is cited in 19 scientific papers (total in 19 papers)

On monotony of two layer in time cabaret scheme

O. A. Kovyrkina^ab, V. V. Ostapenko^ab

^a Lavrentyev Institute of Hydrodynamics SD RAS, Novosibirsk
^b Novosibirsk State University

Full-text PDF (322 kB) Citations (19)

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Abstract: The monotony analysis of two-layer in time cabaret scheme is carried out. It is shown that there is no local unitary correction of flux variables which would provide monotony of this scheme at any monotonous initial data. It is offered a modification of two-layer in time cabaret scheme, connected with double correction of flux variables, which in case of a variable time step guarantees monotony of the scheme at any Currant numbers at which it is stable. The results of the test calculations illustrating advantages of the modified scheme are listed.

Keywords: two-layer in time cabaret scheme, monotony, correction of flux variables.

Received: 23.01.2012

English version:
Mathematical Models and Computer Simulations, 2013, Volume 5, Issue 2, Pages 180–189
DOI: https://doi.org/10.1134/S2070048213020051

Bibliographic databases:

Document Type: Article

UDC: 519.63

Language: Russian

Citation: O. A. Kovyrkina, V. V. Ostapenko, “On monotony of two layer in time cabaret scheme”, Mat. Model., 24:9 (2012), 97–112; Math. Models Comput. Simul., 5:2 (2013), 180–189

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mm3313

https://www.mathnet.ru/eng/mm/v24/i9/p97

This publication is cited in the following 19 articles:

Olyana A. Kovyrkina, Vladimir V. Ostapenko, “On the accuracy of shock-capturing schemes when calculating Cauchy problems with periodic discontinuous initial data”, Russian Journal of Numerical Analysis and Mathematical Modelling, 39:2 (2024), 97
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
Kulikov Yu.M. Son E.E., “Double Shear Layer Evolution on the Non-Uniform Computational Mesh”, Phys. Scr., 96:12 (2021), 125262
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
Yu. M. Kulikov, E. E. Son, “Taylor-green vortex simulation using cabaret scheme in a weakly compressible formulation”, Eur. Phys. J. E, 41:3 (2018), 41
N. A. Zyuzina, V. V. Ostapenko, E. I. Polunina, “Splitting method for CABARET scheme approximating the non-uniform scalar conservation law”, Num. Anal. Appl., 11:2 (2018), 146–157
V. V. Ostapenko, “On strong monotonicity of two-layer in time CABARET scheme”, Math. Models Comput. Simul., 11:1 (2019), 1–8
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
V. M. Goloviznin, V. A. Isakov, “Balance-characteristic scheme as applied to the shallow water equations over a rough bottom”, Comput. Math. Math. Phys., 57:7 (2017), 1140–1157
V. V. Ostapenko, A. A. Cherevko, “Application of the cabaret scheme for calculation of discontinuous solutions of the scalar conservation law with nonconvex flux”, Dokl. Phys., 62:10 (2017), 470–474
O. A. Kovyrkina, V. V. Ostapenko, “Monotonicity of the CABARET scheme approximating a hyperbolic equation with a sign-changing characteristic field”, Comput. Math. Math. Phys., 56:5 (2016), 783–801
Zyuzina N.A. Ostapenko V.V., “Monotone approximation of a scalar conservation law based on the CABARET scheme in the case of a sign-changing characteristic field”, Dokl. Math., 94:2 (2016), 538–542
Zyuzina N.A. Ostapenko V.V., “On the monotonicity of the CABARET scheme approximating a scalar conservation law with a convex flux”, Dokl. Math., 93:1 (2016), 69–73
Kovyrkina O. Ostapenko V., “On the Onotonicity of Multidimensional Finite Difference Schemes”, Application of mathematics in technical and natural sciences (amitans'16), AIP Conf. Proc., 1773, ed. Todorov M., Amer. Inst. Phys., 2016, 100007
M F Ivanov, A D Kiverin, S G Pinevich, I S Yakovenko, “Application of dissipation-free numerical method CABARET for solving gasdynamics of combustion and detonation”, J. Phys.: Conf. Ser., 754:10 (2016), 102003
N. A. Zyuzina, V. V. Ostapenko, “Modification of the Cabaret scheme ensuring its high accuracy on local extrema”, Math. Models Comput. Simul., 8:3 (2016), 231–237
Kovyrkina O.A., Ostapenko V.V., “On the Monotonicity of the Cabaret Scheme in the Multidimensional Case”, Dokl. Math., 91:3 (2015), 323–328

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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