Geodesic
TVD scheme for stiff problems of wave dynamics of heterogeneous media of nonhyperbolic nonconservative type
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 12, pp. 2098-2109 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A finite-difference TVD scheme is presented for problems in nonequilibrium wave dynamics of heterogeneous media with different velocities and temperatures but with identical pressures of the phases. A nonlinear form of artificial viscosity depending on the phase relaxation time is proposed. The computed solutions are compared with exact self-similar ones for an equilibrium heterogeneous medium. The performance of the scheme is demonstrated by numerical simulation with varying particle diameters, grid sizes, and particle concentrations. It is shown that the scheme is efficient in terms of Fletcher's criterion as applied to stiff problems. 
@article{ZVMMF_2016_56_12_a10,
     author = {D. V. Sadin},
     title = {TVD scheme for stiff problems of wave dynamics of heterogeneous media of nonhyperbolic nonconservative type},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2098--2109},
     year = {2016},
     volume = {56},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a10/}
}
TY  - JOUR
AU  - D. V. Sadin
TI  - TVD scheme for stiff problems of wave dynamics of heterogeneous media of nonhyperbolic nonconservative type
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2016
SP  - 2098
EP  - 2109
VL  - 56
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a10/
LA  - ru
ID  - ZVMMF_2016_56_12_a10
ER  - 
%0 Journal Article
%A D. V. Sadin
%T TVD scheme for stiff problems of wave dynamics of heterogeneous media of nonhyperbolic nonconservative type
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2016
%P 2098-2109
%V 56
%N 12
%U http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a10/
%G ru
%F ZVMMF_2016_56_12_a10
D. V. Sadin. TVD scheme for stiff problems of wave dynamics of heterogeneous media of nonhyperbolic nonconservative type. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 12, pp. 2098-2109. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a10/

[1] Nigmatulin R. I., Osnovy mekhaniki geterogennykh sred, Nauka, M., 1987

[2] Baer M., Nunziato J., “A two-phase mixture theory for the deflagration-to detonation transition (DDT) in reactive granular materials”, Int. J. Multiphase Flows, 12 (1986), 861–889 | DOI | Zbl

[3] Saurel R., Abgrall R., “A multiphase Godunov method for compressbile multifluid and multiphase flows”, J. Comput. Phys., 150:2 (1999), 425–467 | DOI | MR | Zbl

[4] Zhilin A. A., Fedorov A. V., “Primenenie skhemy TVD dlya rascheta dvukhfaznykh techenii s razlichnymi skorostyami i davleniyami komponentov”, Matem. modelirovanie, 20:1 (2008), 29–47

[5] Sadin D. V., Guzenkov V. O., Lyubarskii S. D., “Chislennoe issledovanie struktury nestatsionarnoi dvukhfaznoi tonkodispersnoi strui”, Prikl. mekhan. i tekhn. fiz., 46:2 (2005), 91–97 | Zbl

[6] Petitpas F., Franquet E., Saurel R., Le Metayer O., “A relaxation-projection method for compressible flows. Part II: Artificial heat exchanges for multiphase shocks”, J. Comput. Phys., 225:2 (2007), 2214–2248 | DOI | MR | Zbl

[7] Saurel R., Petitpas F., Berry R. A., “Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures”, J. Comput. Phys., 228:5 (2009), 1678–1712 | DOI | MR | Zbl

[8] Fringer O. B., Armfield S. W., Street R. L., “Reducing numerical diffusion in interfacial gravity wave simulations”, Int. J. Numer. Meth. Fluids, 49 (2005), 301–329 | DOI | MR | Zbl

[9] Hirsch C., Numerical computation of internal and external flows, v. 2, Computational Methods for Inviscid and Viscous Flows, Wiley, New York, 1990 | Zbl

[10] Tropin D. A., Fedorov A. V., “Chislennaya skhema vysokogo poryadka dlya modelirovaniya dinamiki v smesi reagiruyuschikh gazov i inertnykh chastits”, Vychislitelnye tekhnologii, 18:4 (2013), 64–76

[11] Chen G., Levermore C., Liu T., “Hyperbolic conservation laws with stiff relaxation terms and entropy”, Comm. Pure. Appl. Math., 47 (1994), 787–830 | DOI | MR | Zbl

[12] Sadin D. V., “Modifitsirovannyi metod krupnykh chastits dlya rascheta nestatsionarnykh techenii gaza v poristoi srede”, Zh. vychisl. matem. i matem. fiz., 36:10 (1996), 158–164 | Zbl

[13] Sadin D. V., “Problema zhestkosti pri modelirovanii volnovykh techenii geterogennykh sred s trekhtemperaturnoi skhemoi mezhfaznogo teplo- i massoobmena”, Prikl. mekhan. i tekhn. fiz., 43:2 (2002), 136–141 | Zbl

[14] Sadin D. V., “O zhestkosti sistem differentsialnykh uravnenii v chastnykh proizvodnykh, opisyvayuschikh dvizheniya geterogennykh sred”, Matem. modelirovanie, 14:11 (2002), 43–53 | Zbl

[15] Gubaidullin A. A., Ivandaev A. I., Nigmatulin R. I., “Modifitsirovannyi metod krupnykh chastits dlya rascheta nestatsionarnykh volnovykh protsessov v mnogofaznykh sredakh”, Zh. vychisl. matem. i matem. fiz., 17:6 (1977), 1531–1544 | Zbl

[16] Sadin D. V., “Metod rascheta volnovykh geterogennykh techenii s intensivnym mezhfaznym vzaimodeistviem”, Zh. vychisl. matem. i matem. fiz., 38:6 (1998), 1033–1039 | Zbl

[17] Sadin D. V., “Reshenie zhestkikh zadach techenii dvukhfaznykh sred so slozhnoi volnovoi strukturoi”, Fiziko-khimicheskaya kinetika v gazovoi dinamike, 15:4 (2014), 1–17

[18] Sternin L. E., Maslov B. P., Shraiber A. A., Podvysotskii A. M., Dvukhfaznye mono- i polidispersnye techeniya gaza s chastitsami, Mashinostr., M., 1980

[19] Chudnovskii A. F., Teploobmen v dispersnykh sredakh, Gostekhteorizdat, M., 1954

[20] Harten A., “High resolution schemes for hyperbolic conservation laws”, J. Comput. Phys., 49 (1983), 357–393 | DOI | MR | Zbl

[21] Sadin D. V., “O skhodimosti odnogo klassa raznostnykh skhem dlya uravnenii nestatsionarnogo dvizheniya gaza v dispersnoi srede”, Zh. vychisl. matem. i matem. fiz., 38:9 (1998), 1572–1577 | Zbl

[22] Ivanov A. S., Kozlov V. V., Sadin D. V., “Nestatsionarnoe istechenie dvukhfaznoi dispersnoi sredy iz tsilindricheskogo kanala konechnykh razmerov v atmosferu”, Izv. RAN. Mekhan. zhidkosti i gaza, 1996, no. 3, 60–66

[23] Sadin D. V., Osnovy teorii modelirovaniya volnovykh geterogennykh protsessov, Voennyi inzhenerno-kosmicheskii un-t, SPb., 2000

[24] Fletcher K., Vychislitelnye metody v dinamike zhidkostei, V 2-kh tomakh, v. 1, Mir, M., 1991