Geodesic
Implicit finite difference scheme for barotropic gas equations
Čebyševskij sbornik, Tome 18 (2017) no. 3, pp. 306-317.

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

An implicit finite difference scheme approximated barotropic gas equations is proposed. This scheme ensures positivity of density compared to previous methods. Existence of a solution to this scheme is proved for any time and space mesh-steps, an iterative method for solving the system of nonlinear equations on each time step is proposed.
Keywords: difference scheme, iterative process, flow of an ideal (viscous) barotropic gas. 
@article{CHEB_2017_18_3_a17,
     author = {G. M. Kobel'kov and A. G. Sokolov},
     title = {Implicit finite difference scheme  for barotropic gas equations},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {306--317},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2017_18_3_a17/}
}
TY  - JOUR
AU  - G. M. Kobel'kov
AU  - A. G. Sokolov
TI  - Implicit finite difference scheme  for barotropic gas equations
JO  - Čebyševskij sbornik
PY  - 2017
SP  - 306
EP  - 317
VL  - 18
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2017_18_3_a17/
LA  - ru
ID  - CHEB_2017_18_3_a17
ER  - 
%0 Journal Article
%A G. M. Kobel'kov
%A A. G. Sokolov
%T Implicit finite difference scheme  for barotropic gas equations
%J Čebyševskij sbornik
%D 2017
%P 306-317
%V 18
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2017_18_3_a17/
%G ru
%F CHEB_2017_18_3_a17
G. M. Kobel'kov; A. G. Sokolov. Implicit finite difference scheme  for barotropic gas equations. Čebyševskij sbornik, Tome 18 (2017) no. 3, pp. 306-317. http://geodesic.mathdoc.fr/item/CHEB_2017_18_3_a17/

[1] Belotserkovskii O. M., Vasil'ev M. O., Vedernikov A. B., Dymnikov V. P., Zamyshlyaev B. V., Krysanov B. Yu., Kovshov N. V., Kunitsyn V. E., Molokov E. A., Repin A. Yu., Sidorenkova N. A., Stupitskii E. L., Kholodov Ya. A., Kholodov A. S., “Numerical simulation of some problems of interaction of Earth's lithosphere, hydrosphere and atmosphere”, Hystory fragments and achievements of the Design Automatization Institute of Russian Academy of Sciences. 1986–2011, Publishing House “Johnatan flight”, 2011, 14–71

[2] Popov I. V., Fryazinov I. V., Adaptive artificial viscosity method, Krasand, M., 2014

[3] Antontsev S. N., Kazhikhov A. V., Monakhov V. N., Boundary value problems of inhomogenious flows, Наука, Новосибирск, 1983 | MR

[4] Amosov A. A., Zlotnik A. A., “Second order accuracy finite difference schemes for 1D viscous gas flow”, Zh. Vychisl. Mat. Mat. Fiz., 27:7 (1987), 1032–1049 | Zbl

[5] Kulikovskii A. G., Pogorelov N. V., Semenov A. Yu., Mathematical problems of numerical solution of systems of hyperbolic equations, Nauka, M., 2001

[6] Lions P.-L., Mathematical Topics in Fluid Mechanics, v. 2, Oxford Lecture Series in Mathematics and its Applications, 10, Compressible Models, Clarendon Press, Oxford, 1998 | MR | Zbl

[7] Ladyzhenskaya O. A., The Mathematical Theory of Viscous Incompressible Flow, Nauka, M., 1970