Geodesic
Methods of shock wave calculations
Dalʹnevostočnyj matematičeskij žurnal, Tome 2 (2001) no. 2, pp. 45-59.

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

A comparative analysis of the existing methods of shock wave calculations is presented in the paper. A study is done into dissipative properties, distraction and monotony of the difference schemes proposed by the authors of the methods. The paper shows the role of these methods at the transition from Lagrangian to Eulerian coordinates. The paper discusses the approaches to oscillation suppression. 
@article{DVMG_2001_2_2_a3,
     author = {V. F. Kuropatenko},
     title = {Methods of shock wave calculations},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {45--59},
     publisher = {mathdoc},
     volume = {2},
     number = {2},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2001_2_2_a3/}
}
TY  - JOUR
AU  - V. F. Kuropatenko
TI  - Methods of shock wave calculations
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2001
SP  - 45
EP  - 59
VL  - 2
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2001_2_2_a3/
LA  - ru
ID  - DVMG_2001_2_2_a3
ER  - 
%0 Journal Article
%A V. F. Kuropatenko
%T Methods of shock wave calculations
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2001
%P 45-59
%V 2
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2001_2_2_a3/
%G ru
%F DVMG_2001_2_2_a3
V. F. Kuropatenko. Methods of shock wave calculations. Dalʹnevostočnyj matematičeskij žurnal, Tome 2 (2001) no. 2, pp. 45-59. http://geodesic.mathdoc.fr/item/DVMG_2001_2_2_a3/

[1] J. Neumann, R. Richtmayer, “A method for the numerical calculation of hydrodynamical shocks”, J. Appl. Phys., 21:3 (1950), 232–237 | DOI | MR | Zbl

[2] P. D. Lax, “Weak solution of nonlinear hyperbolic equations and their numerical computations”, Comn. Pure and Appl. Math., 7 (1954), 159–193 | DOI | MR | Zbl

[3] S. K. Godunov, “Raznostnyi metod scheta razryvnykh reshenii uravnenii gazodinamiki”, Matem. sb., 47(89):3 (1959), 271–306 | MR | Zbl

[4] V. F. Kuropatenko, “Metod rascheta udarnykh voln”, DAN SSSR, 3:4 (1960), 771 | MR

[5] B. L. Rozhdestvenskii, N. N. Yanenko, Sistemy kvazilineinykh uravnenii i ikh prilozheniya k gazovoi dinamike, Nauka, M., 1968, 592 pp. | MR

[6] R. Rikhtmaier, K. Morton, Raznostnye metody resheniya kraevykh zadach, Mir, 1972, 418 pp.

[7] A. A. Samarskii, V. Ya. Arsenin, “O chislennom reshenii uravnenii gazodinamiki s razlichnymi tipami vyazkostei”, Zh. vychisl. matem. i matem. fiz., 1:2 (1961), 357–380

[8] M. L. Uilkins, “Raschet uprugoplasticheskikh techenii”, Vychisl. metody v gidrodinamike, Mir, M., 1967, 212–263

[9] V. F. Kuropatenko, “Lokalnaya konservativnost raznostnykh skhem dlya uravnenii gazovoi dinamiki”, Zhurnal vych. matem. i matem. fiziki, 25:8 (1985), 1176–1188, M. | MR

[10] V. F. Kuropatenko, “Ob odnom raznostnom metode rascheta udarnykh voln”, Zhurnal vychisl. matematiki i matematicheskoi fiziki, 3:1 (1963), 201–204 | MR | Zbl

[11] V. F. Kuropatenko, “O raznostnykh metodakh dlya uravnenii gidrodinamiki”, Trudy matem. inst. im. V. A. Steklova, 74, 1966, 107–137 | MR | Zbl

[12] V. F. Kuropatenko, I. R. Makeeva, Raznostnyi metod rascheta udarnykh voln s povyshennymi svoistvami monotonnosti, Preprint VNIITF No 120, 1997

[13] V. F. Kuropatenko, “Metod postroeniya raznostnykh skhem dlya chislennogo integrirovaniya uravnenii gazodinamiki”, Izvestiya VUZov ser. Matematika, 28:3 (1962), 75–83 | MR

[14] V. F. Kuropatenko, “Ob odnoi forme psevdovyazkosti”, Izv. SO AN SSSR. Ser. tekhnich., 3:3 (1967), 81–82

[15] P. D. Lax, B. Wendroff, “System of Conservation Laws”, Comp. Pure Appl. Math., 13 (1960), 217 | DOI | MR | Zbl

[16] P. D. Lax, B. Wendroff, “Difference Schemes for Hyperbolic Equation with High Order of Accuracy”, Comp. Pure Appl. Math., 17 (1964), 381 | DOI | MR | Zbl

[17] O. M. Belotserkovskii, Yu. M. Davydov, “Nestatsionarnyi metod “krupnykh chastits” dlya gazdinamicheskikh raschetov”, Zhurnal vychisl. matematiki i matematicheskoi fiziki, 11:1 (1971), 182–207

[18] O. M. Belotserkovskii, Yu. M. Davydov, “Metod “krupnykh chastits” v gazovoi dinamike”, Vychislitelnyi eksperiment, Nauka, M., 1982, 392 pp.