Geodesic
Resolution limits of continuous media models and their mathematical formulations
Matematičeskoe modelirovanie, Tome 24 (2012) no. 11, pp. 33-52.

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

In this work we present new mathematical formulations for a number of continuous media models. the developed formulations account for physical constraints on resolution level of media description. Compared to classical formulations the presented ones introduce additional terms which allow for construction of numerical schemes well suited for their efficient implementation for high-performance computer systems.
Keywords: high-performance computing, resolution limits, kinetic scheme. 
@article{MM_2012_24_11_a2,
     author = {Boris N. Chetverushkin},
     title = {Resolution limits of continuous media models and their mathematical formulations},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {33--52},
     publisher = {mathdoc},
     volume = {24},
     number = {11},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2012_24_11_a2/}
}
TY  - JOUR
AU  - Boris N. Chetverushkin
TI  - Resolution limits of continuous media models and their mathematical formulations
JO  - Matematičeskoe modelirovanie
PY  - 2012
SP  - 33
EP  - 52
VL  - 24
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2012_24_11_a2/
LA  - ru
ID  - MM_2012_24_11_a2
ER  - 
%0 Journal Article
%A Boris N. Chetverushkin
%T Resolution limits of continuous media models and their mathematical formulations
%J Matematičeskoe modelirovanie
%D 2012
%P 33-52
%V 24
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2012_24_11_a2/
%G ru
%F MM_2012_24_11_a2
Boris N. Chetverushkin. Resolution limits of continuous media models and their mathematical formulations. Matematičeskoe modelirovanie, Tome 24 (2012) no. 11, pp. 33-52. http://geodesic.mathdoc.fr/item/MM_2012_24_11_a2/

[1] Chetverushkin B. N., “High-performance computing: Fundamental problems in industrial applications”, Parallel, distributed and grid computing for engeneering, Saxe-Coburg Publications, eds. B. H. Topping, P. Ivanyi, 2009, 369–385

[2] Chetverushkin B. N., “Prikladnaya matematika i problemy ispolzovaniya vysokoproizvoditelnykh vychislitelnykh sistem”, Trudy MFTI, 3:4 (2011), 96–108

[3] Ladyzhenskaya O. A., Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, Nauka, M., 1970, 288 pp. | MR

[4] Koshelev A. I., Chelnak S. I., Regulyarnost resheniya nekotorykh kraevykh zadach dlya kvazilineinykh ellipticheskikh i parabolicheskikh sistem, Izd. S.-P. universiteta, SPb., 2000, 355 pp.

[5] Kobelkov G. M., “Suschestvovanie resheniya «v tselom» dlya uravnenii dinamiki okeana”, DAN, 107:1 (2006), 457–459 | MR

[6] Loitsyanskii L. G., Mekhanika zhidkosti i gaza, Nauka, M., 1987, 840 pp. | MR

[7] Vlasov A. A., Statisticheskie funktsii raspredeleniya, Nauka, M., 1966, 440 pp. | MR | Zbl

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

[9] Girshfelder Dzh., Kertis U., Berd R., Molekulyarnaya teoriya gazov i zhidkostei, IL, M., 1961, 916 pp.

[10] Chepmen S., Kauling T., Matematicheskaya teoriya neodnorodnykh gazov, IL, M., 1960, 510 pp. | MR

[11] Libov R., Vvedenie v teoriyu kineticheskikh uravnenii, Mir, M., 1974, 371 pp.

[12] Vedenyapin V. V., Kineticheskie uravneniya Boltsmana i Vlasova, Fizmatlit, M., 2001, 112 pp.

[13] Volchinskaya M. I., Pavlov A. N., Chetverushkin B. N., Ob odnoi skheme integrirovaniya uravnenii gazovoi dinamiki, Preprint No 113, IPM im. M. V. Keldysha AN SSSR, 1983, 12 pp. | MR

[14] Chetverushkin B. N., Kineticheskie skhemy i kvazigazodinamicheskaya sistema uravnenii, Maks-Press, M., 2004, 328 pp. ; Chetverushkin B. N., Kinetic Shemes and Quasi-Gas Dynamics system of Equations, CIMNE, Barcelona, 2008, 298 pp. | Zbl

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

[16] Elizarova T. G., Kvazigazodinamicheskie uravneniya i metody rascheta vyazkikh techenii, Nauchnyi mir, M., 2007

[17] Zlotnik A. A., Chetverushkin B. N., “Parabolichnost kvazigazodinamicheskoi sistemy uravnenii, giperbolichnost odnoi ee modifikatsii i ustoichivost malykh vozmuschenii dlya nikh”, Zhurnal vych. mat. i mat. fiziki, 49:3 (2008), 445–472 | MR

[18] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1989, 616 pp. | MR

[19] Davydov A. A., Chetverushkin B. N., Shilnikov E. V., “Modelirovanie techenii neszhimaemoi zhidkosti i slaboszhimaemogo gaza na mnogoyadernykh gibridnykh vychislitelnykh sistemakh”, Zhurnal vych. mat. i mat. fiz., 2010, no. 12, 2275–2284 | MR | Zbl

[20] McNamara G. R., Zanetti G., “Use of the Boltzmann equation for simulate lattice gas automata”, Phys. Rev. Lett., 61:20 (1988), 2332–2335 | DOI

[21] Tsutahara M., Takada N., Kataoka N., Lattice gas and Lattice Boltzmann methods. New methods of computational fluid dynamics, Corona Publishing, Tokyo, 1999, 162 pp. (in Japan)

[22] Succi S., The Lattice Boltzmann equation in fluid dynamics and beyond, Clarendon Press, Oxford, 2001, 304 pp. | MR | Zbl

[23] Oñate E., “Derivation of stabilized equations for numerical solution of advective — diffusive transport and fluid flow problems”, Comput. Math. Appl. Mech. Eng., 151 (1998), 233–265 | DOI | MR | Zbl

[24] Oñate E., Manzan M., Stabilization techniques for finite element analysis and convection diffusion problems, Publication CIMNE No 183, Barcelona, 2000, 43 pp.

[25] Basniev L. S., Kochina I. N., Maksimov V. M., Podzemnaya gidromekhanika, Nauka, M., 1993, 416 pp.

[26] Bakhvalov N. S., Panasenko G. P., Osrednenie protsessov v periodicheskikh sredakh, Nauka, M., 1984, 352 pp. | MR | Zbl

[27] Trapeznikova M. A., Belotserkovskaya M. S., Chetverushkin B. N., “Analog kineticheski-soglasovannykh skhem dlya modelirovaniya zadachi filtratsii”, Matematicheskoe modelirovanie, 14:10 (2002), 69–76 | MR | Zbl

[28] Morozov D. N., Trapeznikova M. A., Chetverushkin B. N., Churbanova N. G., “Ispolzovanie yavnykh skhem dlya modelirovaniya protsessa dvukhfaznoi filtratsii”, Mat. modelirovanie, 23:7 (2011), 52–60 | Zbl

[29] Wieser W., “L'équation de Boltzmann avec terme de viscosité. Solution globales sous des hypotheses faibles sur la condition initial”, C.R. Acad. Sc., Paris, serie I.N.S., 298 (1989)

[30] Sheretov Yu. V., Matematicheskoe modelirovanie techenii zhidkosti i gaza na osnove kvazigdrodinamicheskikh i kvazigazodinamicheskikh uravnenii, Tverskoi gos. universitet, Tver, 2000