On strong monotonicity of two-layer in time CABARET scheme
Matematičeskoe modelirovanie, Tome 30 (2018) no. 5, pp. 5-18.

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The notion of strong monotonicity of the two-layer in time CABARET scheme is introduced. This notion assumes that the difference scheme does not increase the number of generalized local extrema in the difference solution when passing from one time layer to another. It is proposed a special modification of the two-layer in time CABARET scheme possessing the property of a strong monotonicity. Test calculations illustrating this property of the modified CABARET scheme are given.
Keywords: two-layer in time CABARET scheme, strong monotonicity of difference solution
Mots-clés : correction of flux variables.
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V. V. Ostapenko. On strong monotonicity of two-layer in time CABARET scheme. Matematičeskoe modelirovanie, Tome 30 (2018) no. 5, pp. 5-18. http://geodesic.mathdoc.fr/item/MM_2018_30_5_a1/

[1] Iserles A., “Generalized leapfrog methods”, IMA J. of Num. Anal., 6:3 (1986), 381–392 | DOI | MR | Zbl

[2] Goloviznin V. M., Samarskii A. A., “Raznostnaia approksimatsiia konvektivnogo perenosa s prostranstvennym rasshchepleniem vremennoi proizvodnoi”, Mat. mod., 10:1 (1998), 86–100

[3] Goloviznin V. M., Samarskii A. A., “Nekotorye svoistva raznostnoi skhemy “Kabare””, Matem. modelirovanie, 10:1 (1998), 101–116 | Zbl

[4] Rozhdestvenskii B. L., Ianenko N. N., Sistemy kvazilineinykh uravnenii, Nauka, M., 1978

[5] Kulikovskii A. G., Pogorelov N. V., Semenov F. Iu., Matematicheskie voprosy chislennogo resheniia giperbolicheskikh sistem uravnenii, Fizmatlit, M., 2001

[6] Goloviznin V. M., “Balansno-kharakteristicheskii metod chislennogo resheniia uravnenii gazovoi dinamiki”, Dokl. AN, 72:1 (2005), 619–623

[7] Woodward P., Colella P., “The numerical simulation of two-dimensional fluid flow with strong shocks”, J. Comp. Phys., 54:1 (1984), 115–173 | DOI | MR | Zbl

[8] Ostapenko V. V., “O monotonnosti balansno-kharakteristicheskoi skhemy”, Matem. modelirovanie, 21:7 (2009), 29–42 | Zbl

[9] Karabasov S. A., Goloviznin V. M., “New efficient high-resolution method for nonlinear problems in aeroacoustics”, AIAA J., 45:12 (2007), 2861–2871 | DOI

[10] Karabasov S. A., Berloff P. S., Goloviznin V. M., “Cabaret in the ocean gyres”, Ocean Modelling, 30:2 (2009), 155–168 | DOI

[11] Goloviznin V. M., Zaitsev M. A., Karabasov S. A., Korotkin I. A., Novye algoritmy vychislitelnoi gidrodinamiki dlia mnogoprotsessornykh vychislitelnykh kompleksov, Izdatelstvo Moskovskogo universiteta, M., 2013

[12] Kovyrkina O. A., Ostapenko V. V., “O monotonnosti dvukhsloinoi po vremeni skhemy kabare”, Matem. modelirovanie, 24:9 (2012), 97–112

[13] Kovyrkina O. A., Ostapenko V. V., “On the Monotonicity of the CABARET Scheme in the Multidimensional Case”, Dokl. Math., 462:4 (2015), 385–390 | DOI | Zbl

[14] Kovyrkina O. A., Ostapenko V. V., “Monotonicity of the CABARET scheme approximating a hyperbolic equation with a sign-changing characteristic field”, Zh. Vychisl. Mat. Mat. Fiz., 56:5 (2016), 796–815 | DOI | Zbl

[15] Zyuzina N. A., Ostapenko V. V., “On the Monotonicity of the CABARET Scheme Approximating a Scalar Conservation Law with a Convex Flux”, Dokl. Math., 466:5 (2016), 513–517 | Zbl

[16] 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., 470:4 (2016), 375–379 | DOI | Zbl

[17] Godunov S. K., “A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics”, Mat. Sb. (N.S.), 47(89):3 (1959), 271–306 | Zbl

[18] Ostapenko V. V., “On the monotonicity of difference schemes”, Sibirsk. Mat. Zh., 39:5 (1998), 1111–1126 | Zbl

[19] Ostapenko V. V., “On the strong monotonicity of three-point difference schemes”, Sibirsk. Mat. Zh., 39:6 (1998), 1357–1367 | Zbl

[20] Ostapenko V. V., “On the strong monotonicity of nonlinear difference schemes”, Zh. Vychisl. Mat. Mat. Fiz., 38:7 (1998), 1170–1185 | Zbl

[21] Liu X., Tadmor E., “Third order nonoscillatory central scheme for hyperbolic conservation laws”, Numer. Math., 79 (1998), 397–425 | DOI | MR | Zbl

[22] Ostapenko V. V., “On the strong monotonicity of the CABARET scheme”, Zh. Vychisl. Mat. Mat. Fiz., 52:3 (2012), 447–460 | Zbl