Geodesic
On the monotonicity of the CABARET scheme approximating a scalar conservation law with alternating characteristic field
Matematičeskoe modelirovanie, Tome 30 (2018) no. 5, pp. 76-98.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MM_2018_30_5_a5,
     author = {N. A. Zyuzina and O. A. Kovyrkina and V. V. Ostapenko},
     title = {On the monotonicity of the {CABARET} scheme approximating a scalar conservation law with alternating characteristic field},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {76--98},
     publisher = {mathdoc},
     volume = {30},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2018_30_5_a5/}
}
TY  - JOUR
AU  - N. A. Zyuzina
AU  - O. A. Kovyrkina
AU  - V. V. Ostapenko
TI  - On the monotonicity of the CABARET scheme approximating a scalar conservation law with alternating characteristic field
JO  - Matematičeskoe modelirovanie
PY  - 2018
SP  - 76
EP  - 98
VL  - 30
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2018_30_5_a5/
LA  - ru
ID  - MM_2018_30_5_a5
ER  - 
%0 Journal Article
%A N. A. Zyuzina
%A O. A. Kovyrkina
%A V. V. Ostapenko
%T On the monotonicity of the CABARET scheme approximating a scalar conservation law with alternating characteristic field
%J Matematičeskoe modelirovanie
%D 2018
%P 76-98
%V 30
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2018_30_5_a5/
%G ru
%F MM_2018_30_5_a5
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. Matematičeskoe modelirovanie, Tome 30 (2018) no. 5, pp. 76-98. http://geodesic.mathdoc.fr/item/MM_2018_30_5_a5/

[1] V.M. Goloviznin, A.A Samarskii, “Raznostnaia approksimatsiia konvektivnogo perenosa s prostranstvennym rasshchepleniem vremennoj proizvodnoj”, Matem. modelirovanie, 10:1 (1998), 86–100

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

[3] B.L. Rozhdestvenskii, N.N. Yanenko, Sistemy kvasilineinykh uravnenij, Nauka, M., 1978, 687 pp.

[4] A.G. Kulikovskii, N.V. Pogorelov, A.Yu. Semenov, Matematicheskie voprosy chislennogo resheniia giperbolicheskikh sistem yravnenij, Fizmatlit, M., 2001, 607 pp.

[5] V.M. Goloviznin, “Balanced characteristic method for systems of hyperbolic conservation laws”, Dokl. Math., 72:1 (2005), 619–623

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

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

[8] V.V. Ostapenko, “On the strong monotonicity of the CABARET scheme”, Comp. Math. and Math. Phys., 52:3 (2012), 387–399 | DOI | MR | Zbl

[9] V.M. Goloviznin, A.A. Kanaev, “The principle of minimum of partial local variations for determining convective flows in the numerical solution of one-dimensional nonlinear scalar hyperbolic equations”, Comp. Math. and Math. Phys., 51:5 (2011), 824–839 | DOI | MR | Zbl

[10] V.M. Goloviznin, M.A. Zaitsev, S.A. Karabasov, I.A. Korotkin, Novye algoritmy vychislitelnoj gidrodinamiki dlia mnogoprotsessornykh vychislitelnykh kompleksov, Izdatelstvo Moskovskogo universiteta, M., 2013, 480 pp.

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

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

[13] V.M. Goloviznin, V.A. Isakov, “Balance-characteristic scheme as applied to the shallow water equations over a rough bottom”, Comp. Math. and Math. Phys., 57:7 (2017), 1140–1157 | DOI | MR | Zbl

[14] O.A. Kovyrkina, V.V. Ostapenko, “On monotonicity of two-layer in time CABARET scheme”, Math. Model. Comp. Simul., 5:2 (2013), 180–189 | DOI | MR

[15] O.A. Kovyrkina, V.V. Ostapenko, “Monotonicity of the CABARET scheme approximating a hyperbolic equation with a sign-changing characteristic field”, Com. Math. and Math. Phys., 56:5 (2016), 783–801 | DOI | DOI | MR | Zbl

[16] O.A. Kovyrkina, V.V. Ostapenko, “On the monotonicity of the CABARET scheme in the multidimensional case”, Dokl. Math., 91:3 (2015), 323–328 | DOI | DOI | MR | Zbl

[17] N.A. Zuzina, V.V. Ostapenko, “On the monotonicity of the CABARET scheme approximating a scalar conservation law with a convex flux”, Dokl. Math., 93:1 (2016), 69–73 | DOI | DOI | MR | Zbl

[18] N.A. Zuzina, V.V. Ostapenko, “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 | DOI | MR | Zbl

[19] S.K. Godunov, “Raznostnyj metod chislennogo rascheta razryvnych reshenij uravnenij gidrodinamiki”, Matem. Sbornik, 47:3 (1959), 271–306 | Zbl