Hyperbolic quasi-gasdynamic system
Matematičeskoe modelirovanie, Tome 30 (2018) no. 2, pp. 81-98.

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

The hyperbolic modification of quasi-gas dynamic system is discussed in this paper. In this case the second derivatives on time with small parameter are exist. The application of this system for high computer modeling is also demonstrated. There were discussed some problems of theoretical verification the hyperbolic quasi gas dynamic system.
Keywords: high performance computing, kinetic models, quasi-gas dynamic system, conservation laws.
@article{MM_2018_30_2_a4,
     author = {B. N. Chetverushkin},
     title = {Hyperbolic quasi-gasdynamic system},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {81--98},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2018_30_2_a4/}
}
TY  - JOUR
AU  - B. N. Chetverushkin
TI  - Hyperbolic quasi-gasdynamic system
JO  - Matematičeskoe modelirovanie
PY  - 2018
SP  - 81
EP  - 98
VL  - 30
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2018_30_2_a4/
LA  - ru
ID  - MM_2018_30_2_a4
ER  - 
%0 Journal Article
%A B. N. Chetverushkin
%T Hyperbolic quasi-gasdynamic system
%J Matematičeskoe modelirovanie
%D 2018
%P 81-98
%V 30
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2018_30_2_a4/
%G ru
%F MM_2018_30_2_a4
B. N. Chetverushkin. Hyperbolic quasi-gasdynamic system. Matematičeskoe modelirovanie, Tome 30 (2018) no. 2, pp. 81-98. http://geodesic.mathdoc.fr/item/MM_2018_30_2_a4/

[1] Sydney Chapman, T. G. Cowling, The Mathematical Theory of Non-uniform Gases, Cambridge University Press, 1970, 423 pp. | MR

[2] Libov R., Vvedenie v teoriiu kineticheskikh uravnenii, Mir, M., 1974

[3] Vedeniapin V. V., Kineticheskie uravneniia Boltsmana i Vlasova, Fizmatlit, M., 2001, 112 pp.

[4] Volchinskaia M. I., Pavlov A. N., Chetverushkin B. N., “Ob odnoi skheme integrirovaniia uravnenii gazovoi dinamiki”, Keldysh Institute preprints, 1983, 113, 12 pp.

[5] Elizarova T. G., Chetverushkin B. N., “Ob odnom vychislitelnom algoritme dlia rascheta gazodinamicheskikh techenii”, DAN SSSR, 279:1 (1984), 80–83

[6] Elizarova T. G., Chetverushkin B. N., “Ispolzovanie kineticheskikh modelei dlia rascheta gazodinamicheskikh techenii”, Matematicheskoe modelirovanie. Protsessy v nelineinykh sredakh, Nauka, M., 1986, 261–278

[7] Chetverushkin B. N., Kinetic Schemes and Quasi-Gas Dynamic System of Equations, CIMNE, Barcelona, 2008

[8] Elizarova T. G., Quasi-Gas Dynamic Equations, Springer-Verlag, Berlin–Heidelberg–New York, 2009 | MR

[9] Hirschfelder Joseph O., Curtiss Charles Francis, Bird Robert Byron, Molecular theory of gases and liquids, University of Wisconsin, Theoretical Chemistry Laboratory, Wiley, 1954, 1249 pp.

[10] Andreev S. S., Davydov A. A., Dbar S. A., et al., “The experience of building a sample hybrid NUMA claster”, Proc. Inter. Conf. “Distributed computing and grid technologies in science and education” (Dubna, Russia, 2008)

[11] Samarskii A. A., The theory of difference schemes, Marcel Dekker Inc., New York, 2001, 788 pp. | MR

[12] Zlotnik A. A., Chetverushkin B. N., “Parabolicity of the quasi-gas-dynamic system of equations, its hyperbolic second-order modification, and the stability of small perturbations for them”, Computational Mathematics and Mathematical Physics, 48:3 (2008), 420–446 | DOI | MR

[13] Golant V. E., Zhilinskii A. P., Sakharov I. E., Osnovy fiziki plazmy, Atomizdat, M., 1977

[14] Chetverushkin B. N., Gulin A. V., “Explicit Schemes and Numerical Simulation Using Ultrahigh-Performance Computer Systems”, Doklady Mathematics, 86:2 (2012), 677–680 | DOI | MR

[15] Ascenzo N. D., Saveliev V. I., Chetverushkin B. N., “On an algorithm for solving parabolic and elliptic equations”, Computational Mathematics and Mathematical Physics, 55:8 (2015), 1290–1297 | DOI | MR

[16] Chetverushkin B. N., Achenzo N. D., Ishanov S., Saveliev V. I., “Hyperbolic type explicit kinetic scheme of magnetogasdynamics for high performance computing systems”, Russian Journ. Numer. Analys Math. Modeling, 30:1 (2015), 27–36 | MR

[17] A.A. Davydov, B.N. Chetverushkin, E.V. Shilnikov, “Simulating Flows of Incompressible and Weakly Compressible Fluids on Multicore Hybrid Computer Systems”, Comp. Mathematics and Mathematical Physics, 50:12 (2010), 2157–2165 | DOI | MR

[18] Chia U., Chia K. V., Shin C. T., “High Resolutions for incompressible flow using the Navier-Stokes equations and a multigrid method”, J. Comput. Physics, 48:3 (1982), 387–411 | DOI | MR

[19] Ladyzhenskaia O. A., Matematicheskie voprosy dinamiki neszhimaemoi viazkoi zhidkosti, Nauka, M., 1970, 288 pp.

[20] Sheretov Iu. V., Dinamika sploshchnykh sred pri prostranstvenno-vremennom soedinenii, NITs RKhD, Izhevsk, 2009

[21] Succi S., The Lattice-Boltzmann equation in fluid dynamics and beyond, Claredon Press, Oxford, 2001, 304 pp. | MR

[22] Repin S. I., Chetverushkin B. N., “Estimates of the Difference between Approximate Solutions of the Cauchy Problems for the Parabolic Diffusion Equation and a Hyperbolic Equation with a Small Parameter”, Doklady Mathematics, 88:1 (2013), 413–417 | DOI | MR

[23] Myshetskaya E. E., Tishkin V. F., “Estimates of the Hyperbolization Effect on the Heat Equation”, Comput. Math. and Math. Phys., 55:8 (2015), 1270–1275 | DOI | MR

[24] Surnachev M. D., Tishkin V. F., Chetverushkin B. N., “On Conservation Laws for Hyperbolized Equations”, Diff. Equat., 52:7 (2016), 817–823 | DOI | DOI | MR

[25] Sheretov Iu. V., “Kvazigidrodinamicheskie uravneniia kak model techenii viazkoi teploprovodnoi sredy”, Primenenie funktsionalnogo analiza v teorii priblizhenii, Izd. TGU, Tver, 1997, 127–155

[26] Zlotnik A. A., Chetverushkin B. N., “Entropy Balance for the One-Dimensional Hyperbolic Quasi-Gasdynamic System of Equations”, Doklady Mathematics, 95:3 (2017), 276–281 | DOI | MR

[27] Chetverushkin B. N., Aschenzo N. D., Savelev A. V., Savelev V. I., “Modelirovanie astrofizicheskikh iavlenii na osnove vysokoproizvoditelnykh vychislenii”, DAN, 472:5 (2017), 512–515

[28] Chetverushkin B. N., Kuleshov A. A., Savenkov E. B., “Supercomputing challenges in mathematical modeling for petroleum industry”, Oil Gas Field Engineering, 2014, no. 9, 26–35

[29] Chetverushkin B. N., Yakobovskiy M. V., “Numerical Algorithms and Fault Tolerance of Hyperexascale Computer Systems”, Dokl. Math., 95:1 (2017), 7–11 | DOI | MR