Geodesic
Application of the variational barrier method to hyperbolic gas dynamic problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 7, pp. 1072-1095 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{ZVMMF_2003_43_7_a11,
     author = {B. N. Azarenok},
     title = {Application of the variational barrier method to hyperbolic gas dynamic problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1072--1095},
     year = {2003},
     volume = {43},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_7_a11/}
}
TY  - JOUR
AU  - B. N. Azarenok
TI  - Application of the variational barrier method to hyperbolic gas dynamic problems
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2003
SP  - 1072
EP  - 1095
VL  - 43
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_7_a11/
LA  - ru
ID  - ZVMMF_2003_43_7_a11
ER  - 
%0 Journal Article
%A B. N. Azarenok
%T Application of the variational barrier method to hyperbolic gas dynamic problems
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2003
%P 1072-1095
%V 43
%N 7
%U http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_7_a11/
%G ru
%F ZVMMF_2003_43_7_a11
B. N. Azarenok. Application of the variational barrier method to hyperbolic gas dynamic problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 7, pp. 1072-1095. http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_7_a11/

[1] Thompson J. F., “A survey of dynamically-adaptive grids in the numerical solution of partial differential equations”, Appl. Numer. Math., 1 (1985), 3–27 | DOI | MR | Zbl

[2] Hawken D. F., Gottlieb J. J., Hansen J. S., “Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations”, J. Comput. Phys., 95 (1991), 254–302 | DOI | MR | Zbl

[3] Jacquotte O.-P., “Grid optimization methods for quality improvement and adaptation”, Handbook of Grid Generation, Ch. 33, CRC Press, Boca Raton, Fl., 1998

[4] Zegeling P. A., “Moving grid techniques”, Ibid., Ch. 37

[5] Carey G., Computational grids: Generation, adaptation, and solution strategies, Taylor Francis, Florida, 1997 | MR | Zbl

[6] Huang W., Sloan D. M., “A simple adaptive method in two dimensions”, SIAM J. Sci. Comput., 15 (1994), 776–797 | DOI | MR | Zbl

[7] Liu F., Ji S., Liao G., “An adaptive grid method and its application to steady Euler flow calculations”, SIAM J. Sci. Comput., 20 (1998), 811–825 | DOI | MR

[8] Cao W. M., Huang W. Z., Russel R. D., “A study of monitor functions for two dimensional adaptive mesh generation”, SIAM J. Sci. Comput., 20 (1999), 1978–1994 | DOI | MR | Zbl

[9] Liseikin V. D., “Application of notions and realizations of differential geometry to grid generation”, Russ. J. Numer. Analys. Math. Modelling, 16:1 (2001), 25–43 | MR

[10] Ivanenko S. A., “O suschestvovanii uravnenii dlya opisaniya klassov nevyrozhdennykh krivolineinykh koordinat v proizvolnoi oblasti”, Zh. vychisl. matem. i matem. fiz., 42:1 (2002), 47–52 | MR | Zbl

[11] Winslow A. M., “Numerical solution of the quasilinear Poisson equation in a nonuniform triangle mesh”, J. Comput. Phys., 1:2 (1966), 149–172 | DOI | MR | Zbl

[12] Brackbill J. U., Saltzman J. S., “Adaptive zoning for singular problems in two dimensions”, J. Comput. Phys., 46 (1982), 342–368 | DOI | MR | Zbl

[13] Liseikin V. D., “Postroenie strukturirovannykh setok na $n$-mernykh poverkhnostyakh”, Zh. vychisl. matem. i matem. fiz., 31:11 (1991), 1670–1683 | MR

[14] Liseikin V. D., Grid generation methods, Springer, New York, 1999 | MR | Zbl

[15] Eisman P. S., “Adaptive grid generation”, Comput. Meth. in Appl. Mech. and Engng., 64 (1987), 321–376 | DOI | MR

[16] Spekreijse S. P., Hagmeijer R., Boerstoel J. M., “Adaptive grid generation by using Laplace–Beltrami operator on a monitoring surface”, Numer. Grid Generation in Comput. Field Simulations, Proc. 5th Internat. Conf. (Missisipi State, MS, U.S., April 1996), 137–146

[17] Knupp P., Steinberg S., Fundamentals of grid generation, CRC Press, Boca Raton, Fl., 1994 | MR | Zbl

[18] Ivanenko S. A., Adaptivno-garmonicheskie setki, VTs RAN, M., 1997 | MR

[19] Sampson J. S., “Some properties and applications of harmonic mappings”, Ann. École Normal., 11 (1978), 211–228 | MR | Zbl

[20] Schoen R., Yau S. T., “On univalent harmonic maps between surfaces”, Invent. Math., 44 (1978), 265–278 | DOI | MR | Zbl

[21] Prokopov G. P., Universalnye variatsionnye funktsionaly dlya postroeniya dvumernykh setok, Preprint No 1, IPMatem. RAN, M., 2001, 36 pp.

[22] Ivanenko S. A., Charakhchyan A. A., “Krivolineinye setki iz vypuklykh chetyrekhugolnikov”, Zh. vychisl. matem. i matem. fiz., 28:4 (1988), 503–514 | MR

[23] Ivanenko S. A., “Adaptivnye setki i setki na poverkhnostyakh”, Zh. vychisl. matem. i matem. fiz., 33:9 (1993), 1333–1351 | MR | Zbl

[24] Azarenok B. N., Ivanenko S. A., “O primenenii adaptivnykh setok dlya chislennogo resheniya nestatsionarnykh zadach gazovoi dinamiki”, Zh. vychisl. matem. i matem. fiz., 40:9 (2000), 1386–1407 | MR | Zbl

[25] Ivanenko S. A., Azarenok B. N., “Application of moving adaptive grids for numerical solution of nonstationary problems in gas dynamics”, Internat. J. Numer. Meth. in Fluids, 39:1 (2002), 1–22 | DOI | MR | Zbl

[26] Eells J. E., Lemaire L., “Another report on harmonic mapps”, Bull. London Math. Soc., 20:387 (1988), 387 | MR

[27] Farrell F. T., Jones L. E., “Some non-homeomorphic harmonic homotopy equivalences”, Bull. of London Math. Soc., 28:131 (1996), 177–182 | DOI | MR | Zbl

[28] Godunov C. K., Ryabenkii B. C., Raznostnye skhemy, Nauka, M., 1977

[29] Godunov S. K., Zabrodin A. V., Prokopov G. P. i dr., Chislennoe reshenie mnogomernykh zadach gazovoi dinamiki, Nauka, M., 1976 | MR | Zbl

[30] Azarenok B. N., “Realization of a second-order Godunov's scheme”, Comput. Meth. in Appl. Mech. and Engng., 189:3 (2000), 1031–1052 | DOI | MR | Zbl

[31] Ivanov M. Ya., Koretskii B. B., Kurochkina N. Ya., “Issledovanie svoistv raznostnykh skhem skvoznogo scheta vtorogo poryadka approksimatsii”, Chisl. metody mekhan. sploshnoi sredy, 11, no. 2, ITPM SO AN SSSR, Novosibirsk, 1980, 41–63 | MR

[32] Mackenzie J. A., Russell R. D., Stockie J. M., “A moving mesh method for one dimensional hyperbolic conservation law”, SIAM J. Sci. Comput., 22 (2000), 1791–1813 | MR