Geodesic
Numerical analysis of a quasi-gasdynamic algorithm as applied to the Euler equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 11, pp. 1953-1969 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The computational properties of a quasi-gasdynamic algorithm are analyzed as applied to strong-shock Riemann problems and acoustic disturbance propagation. It is shown that a unified treatment can be given to these problems in the framework of the algorithm. Stability conditions are numerically obtained, and the error and computational complexity of the difference scheme are estimated. 
@article{ZVMMF_2009_49_11_a4,
     author = {T. G. Elizarova and E. V. Shilnikov},
     title = {Numerical analysis of a~quasi-gasdynamic algorithm as applied to the {Euler} equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1953--1969},
     year = {2009},
     volume = {49},
     number = {11},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_11_a4/}
}
TY  - JOUR
AU  - T. G. Elizarova
AU  - E. V. Shilnikov
TI  - Numerical analysis of a quasi-gasdynamic algorithm as applied to the Euler equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2009
SP  - 1953
EP  - 1969
VL  - 49
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_11_a4/
LA  - ru
ID  - ZVMMF_2009_49_11_a4
ER  - 
%0 Journal Article
%A T. G. Elizarova
%A E. V. Shilnikov
%T Numerical analysis of a quasi-gasdynamic algorithm as applied to the Euler equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2009
%P 1953-1969
%V 49
%N 11
%U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_11_a4/
%G ru
%F ZVMMF_2009_49_11_a4
T. G. Elizarova; E. V. Shilnikov. Numerical analysis of a quasi-gasdynamic algorithm as applied to the Euler equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 11, pp. 1953-1969. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_11_a4/

[1] Elizarova T. G., Shilnikov E. V., “Vozmozhnosti kvazigazodinamicheskogo algoritma dlya chislennogo modelirovaniya techenii nevyazkogo gaza”, Zh. vychisl. matem. i matem. fiz., 49:3 (2009), 549–566 | MR

[2] Sheretov Yu. V., Matematicheskoe modelirovanie techenii zhidkosti i gaza na osnove kvazigidrodinamicheskikh i kvazigazodinamicheskikh uravnenii, Tverskoi gos. un-t, Tver, 2000

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

[4] Chetverushkin B. N., Kineticheskie skhemy i kvazigazodinamicheskaya sistema uravnenii, Maks Press, M., 2004

[5] Elizarova T. G., Khokhlova A. A., “Kvazigazodinamicheskie uravneniya dlya techenii gaza s vneshnimi istochnikami tepla”, Vestn. MGU. Seriya 3. Fizika, astronomiya, 2007, no. 3, 10–13 | MR

[6] Sheretov Yu. V., “O raznostnykh approksimatsiyakh kvazigazodinamicheskikh uravnenii dlya osesimmetrichnykh techenii”, Primenenie funktsionalnogo analiza v teorii priblizhenii, Tverskoi gos. un-t, Tver, 2001, 191–207

[7] Sheretov Yu. V., “Analiz ustoichivosti modifitsirovannoi kineticheski-soglasovannoi raznostnoi skhemy v akusticheskom priblizhenii”, Primenenie funktsionalnogo analiza v teorii priblizhenii, Tverskoi gos. un-t, Tver, 2004, 147–160

[8] Rozhdestvenskii B. L., Yanenko H. H., Sistemy kvazilineinykh uravnenii, Nauka, M., 1978

[9] Kalitkin H. H., Chislennye metody, Nauka, M., 1978 | MR

[10] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1989 | MR

[11] Tang H., Liu T., “A note on the conservative schemes for Euler equations”, J. Comput. Phys., 218 (2006), 451–459 | DOI | Zbl

[12] Antonov A. H., Elizarova T. G., Pavlov A. N., Chetverushkin B. N., “Matematicheskoe modelirovanie kolebatelnykh rezhimov pri obtekanii tela s igloi”, Matem. modelirovanie, 1:1 (1989), 13–23

[13] Antonov A. N., Elizarova T. G., Chetverushkin B. N., Sheretov Yu. V., “Chislennoe modelirovanie pulsatsionnykh rezhimov pri sverkhzvukovom obtekanii pologo tsilindra”, Zh. vychisl. matem. i matem. fiz., 30:4 (1990), 548–556 | MR | Zbl

[14] Antonov M. A., Graur I. A., Kosarev L. V., Chetverushkin B. N., “Chislennoe modelirovanie pulsatsii davleniya v trekhmernykh vyemkakh”, Matem. modelirovanie, 8:5 (1996), 76–90 | MR | Zbl

[15] Elizarova T. G., Khokhlov A. A., Sheretov Yu. V., “Quasi-gasdynamic numerical algorithm for gas flow simulations”, Internat. J. for Numer. Meth. in Fluids, 56:8 (2008), 1209–1215 | DOI | MR | Zbl

[16] Elizarova T. G., Nikolskii P. H., “Chislennoe modelirovanie laminarno-turbulentnogo perekhoda v techenii za obratnym ustupom”, Vestn. MGU. Seriya 3. Fizika. Astronomiya, 2007, no. 4, 14–17

[17] Chetverushkin B. N., Shilnikov E. V., “Vychislitelnyi i programmnyi instrumentarii dlya modelirovaniya trekhmernykh techenii vyazkogo gaza na mnogoprotsessornykh sistemakh”, Zh. vychisl. matem. i matem. fiz., 48:2 (2008), 309–320 | MR

[18] Tarn C. K W., Webb J. C., “Dispersion-relation-preserving finite difference schemes for computational acoustics”, J. Comput. Phys., 107 (1993), 262–281 | DOI | MR

[19] Abalakin I. V., Kozubskaya T. K., “Mnogoparametricheskoe semeistvo skhem povyshennoi tochnosti dlya lineinogo uravneniya perenosa”, Matem. modelirovanie, 19:7 (2007), 56–66 | MR | Zbl

[20] Sheretov Yu. V., “Analiz zadachi o rasprostranenii zvuka dlya linearizovannykh KGD-sistem”, Primenenie funktsionalnogo analiza v teorii priblizhenii, Tverskoi gos. un-t, Tver, 2001, 178–191

[21] Landau L. D., Lifshits E. M., Gidrodinamika, Nauka, M., 1986 | MR

[22] Williams S., Shalf J., Oliker L. et al., “Scientific computing kernels on the Cell processor”, Internat. J. Parallel Program., 35:3 (2007), 263–298 | DOI