Geodesic
Theoretical study of stability of nodal completely conservative difference schemes with viscous filling for gas dynamics equations in Euler variables
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 24 (2022) no. 3, pp. 317-330.

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

For the equations of gas dynamics in Eulerian variables, a family of two-layer time-fully conservative difference schemes (FCDS) with space-profiled time weights is investigated. Nodal schemes and a class of divergent adaptive viscosities for FCDS with space-time profiled weights connected with variable masses of moving nodal particles of the medium are developed. Considerable attention is paid to the methods of constructing regularized flows of mass, momentum and internal energy that preserve the properties of fully conservative difference schemes of this class, to the analysis of their stability and to the possibility of their use on uneven grids. The effective preservation of the internal energy balance in this class of divergent difference schemes is ensured by the absence of constantly operating sources of difference origin that produce "computational’’ entropy (including entropy production on the singular features of the solution). Developed schemes may be used in modelling of high-temperature flows in temperature-disequilibrium media, for example, if it is necessary to take into account the electron-ion relaxation of temperature in a short-living plasma under conditions of intense energy input.
Keywords: gas dynamics, support operator method, fully conservative difference schemes, stability of the scheme. 
@article{SVMO_2022_24_3_a5,
     author = {M. E. Ladonkina and Yu. A. Poveschenko and O. R. Rahimly and H. Zhang},
     title = {Theoretical study of stability of nodal completely conservative difference schemes with viscous filling for gas dynamics equations in {Euler} variables},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {317--330},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2022_24_3_a5/}
}
TY  - JOUR
AU  - M. E. Ladonkina
AU  - Yu. A. Poveschenko
AU  - O. R. Rahimly
AU  - H. Zhang
TI  - Theoretical study of stability of nodal completely conservative difference schemes with viscous filling for gas dynamics equations in Euler variables
JO  - Žurnal Srednevolžskogo matematičeskogo obŝestva
PY  - 2022
SP  - 317
EP  - 330
VL  - 24
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SVMO_2022_24_3_a5/
LA  - ru
ID  - SVMO_2022_24_3_a5
ER  - 
%0 Journal Article
%A M. E. Ladonkina
%A Yu. A. Poveschenko
%A O. R. Rahimly
%A H. Zhang
%T Theoretical study of stability of nodal completely conservative difference schemes with viscous filling for gas dynamics equations in Euler variables
%J Žurnal Srednevolžskogo matematičeskogo obŝestva
%D 2022
%P 317-330
%V 24
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SVMO_2022_24_3_a5/
%G ru
%F SVMO_2022_24_3_a5
M. E. Ladonkina; Yu. A. Poveschenko; O. R. Rahimly; H. Zhang. Theoretical study of stability of nodal completely conservative difference schemes with viscous filling for gas dynamics equations in Euler variables. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 24 (2022) no. 3, pp. 317-330. http://geodesic.mathdoc.fr/item/SVMO_2022_24_3_a5/

[1] A. A. Samarskii, Yu. P. Popov, Raznostnye metody resheniya zadach gazovoi dinamiki, Nauka, Moskva, 1980, 352 pp.

[2] Yu. P. Popov, A. A. Samarskii, “Polnostyu konservativnye raznostnye skhemy”, Zh. vychisl. matem. i matem. fiz., 9:4 (1969), 953–958

[3] A.V. Kuzmin, V.L. Makarov, “Ob odnom algoritme postroeniya polnostyu konservativnykh raznostnykh skhem”, ZhVMiMF., 22:1 (1982), 123-132

[4] A.V. Kuzmin, V.L. Makarov, G.V. Meladze, “Ob odnoi polnostyu konservativnoi raznostnoi skheme dlya uravneniya gazovoi dinamiki v peremennykh eilera”, ZhVMiMF., 20:1 (1980), 171-181

[5] V.M. Goloviznin, I.V. Krayushkin, M.A. Ryazanov, A.A. Samarskii, “Dvumernye polnostyu konservativnye raznostnye skhemy gazovoi dinamiki s raznesennymi skorostyami”, Preprinty IPM im M.V. Keldysha, 1983, 105

[6] A. V. Koldoba, Yu. A. Poveschenko, Yu. P. Popov, “Dvukhsloinye polnostyu konservativnye raznostnye skhemy dlya uravnenii gazovoi dinamiki v peremennykh Eilera”, Zh. vychisl. matem. i matem. fiz., 27:5 (1987), 779–784

[7] A. V. Koldoba, O. A. Kuznetsov, Yu. A. Poveschenko, Yu. P. Popov, “Ob odnom podkhode k raschetu zadach gazovoi dinamiki s peremennoi massoi kvazichastitsy”, Preprinty IPM im M.V. Keldysha, 1985, 57

[8] A.V. Koldoba, Yu.A. Poveschenko, “Polnostyu konservativnye raznostnye skhemy dlya uravnenii gazovoi dinamiki pri nalichii istochnikov massy”, Preprinty IPM im M.V. Keldysha, 1982, 160

[9] A.A. Samarskii, A.V. Koldobav, Yu.A. Poveschenko, V.F. Tishkin, A.P. Favorskii, Raznostnye skhemy na neregulyarnykh setkakh, ZAO «Kriterii», Minsk, 1996, 275 pp.

[10] A. V. Koldoba, Yu. A. Poveschenko, I. V. Gasilova, E. Yu. Dorofeeva, “Raznostnye skhemy metoda opornykh operatorov dlya uravnenii teorii uprugosti”, Matem. modelirovanie, 24:12 (2012), 86–96 | MR

[11] Yu. A. Poveschenko, V. O. Podryga, Yu. S. Sharova, “Integralno-soglasovannye metody rascheta samogravitiruyuschikh i magnitogidrodinamicheskikh yavlenii”, Preprinty IPM im. M. V. Keldysha, 2018, 160, 21 pp. | DOI

[12] Yu.V. Popov, I.V. Fryazinov, Metoda adaptivnoi iskusstvennoi vyazkosti chislennogo resheniya uravnenii gazovoi dinamiki, «Krasand», M., 2014, 288 pp.

[13] Yu. A. Poveschenko, M. E. Ladonkina, V. O. Podryga, O. R. Ragimli, Yu. S. Sharova, “Ob odnoi dvukhsloinoi polnostyu konservativnoi raznostnoi skheme gazovoi dinamiki v eilerovykh peremennykh s adaptivnoi regulyarizatsiei resheniya”, Preprinty IPM im. M. V. Keldysha, 2019, 14, 23 pp.

[14] O. Rahimly, V. Podryga, Y. Poveshchenko, P. Rahimly, Y. Sharova, “Two-Layer Completely Conservative Difference Scheme of Gas Dynamics in Eulerian Variables with Adaptive Regularization of Solution.”, Lecture Notes in Computer Science, 11958, 2020, 618–625 | DOI | MR

[15] M. E. Ladonkina, Yu. A. Poveschenko, O. R. Ragimli, Kh. Chzhan, “Teoreticheskii analiz polnostyu konservativnykh raznostnykh skhem s adaptivnoi vyazkostyu”, Zhurnal SVMO, 23:4 (2021), 412–423 | DOI