A dynamic mesh adaptation method for magnetohydrodynamics problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 11, pp. 1898-1912 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A dynamic adaptation method is used to numerically solve the MHD equations. The basic idea behind the method is to use an arbitrary nonstationary coordinate system for which the numerical procedure and the mesh refinement mechanism are formulated as a unified differential model. Numerical examples of multidimensional MHD flows on dynamic adaptive meshes are given to illustrate the method.
@article{ZVMMF_2007_47_11_a7,
     author = {A. G. Zhilkin},
     title = {A~dynamic mesh adaptation method for magnetohydrodynamics problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1898--1912},
     year = {2007},
     volume = {47},
     number = {11},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_11_a7/}
}
TY  - JOUR
AU  - A. G. Zhilkin
TI  - A dynamic mesh adaptation method for magnetohydrodynamics problems
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2007
SP  - 1898
EP  - 1912
VL  - 47
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_11_a7/
LA  - ru
ID  - ZVMMF_2007_47_11_a7
ER  - 
%0 Journal Article
%A A. G. Zhilkin
%T A dynamic mesh adaptation method for magnetohydrodynamics problems
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2007
%P 1898-1912
%V 47
%N 11
%U http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_11_a7/
%G ru
%F ZVMMF_2007_47_11_a7
A. G. Zhilkin. A dynamic mesh adaptation method for magnetohydrodynamics problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 11, pp. 1898-1912. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_11_a7/

[1] Godunov S. K., Zabrodin A. B., Ivanov M. Ya. i dr., Chislennoe reshenie mnogomernykh zadach gazovoi dinamiki, Nauka, M., 1976 | MR | Zbl

[2] Dwyer H. A., “Grid adaptation lor problems in fluid dynamics”, AIAA Journal, 22:12 (1984), 1705–1712 | DOI | Zbl

[3] Oran E., Boris Dzh., Chislennoe modelirovanie reagiruyuschikh potokov, Mir, M., 1990 | MR

[4] Kruglyakova L. V., Neledova A. B., Tishkin V. F., Filatov A. Yu., “Nestrukturirovannye adaptivnye setki dlya zadach matematicheskoi fiziki (obzor)”, Matem. modelirovanie, 10:3 (1998), 93–116 | MR

[5] Gilmanov A. N., Metody adaptivnykh setok v zadachakh gazovoi dinamiki, Fizmatlit, M., 2000 | MR

[6] Kulikovskii A. G., Pogorelov N. V., Semenov A. Yu., Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii, Fizmatlit, M., 2001 | MR

[7] Berger M. J., Oliger J., “Adaptive mesh refinement for hyperbolic partial differential equations”, J. Comput. Phys., 53 (1984), 484–512 | DOI | MR | Zbl

[8] Berger M. J., Colella P., “Local adaptive mesh refinement for shock hydrodynamics”, J. Comput. Phys., 82 (1989), 64–84 | DOI | Zbl

[9] Liseikin V. D., “Obzor metodov postroeniya strukturnykh adaptivnykh setok”, Zh. vychisl. matem. i matem. fiz., 36:1 (1996), 3–41 | MR

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

[11] Sidorov A. F., Ushakov O. B., “Ob odnom algoritme postroeniya optimalnykh raznostnykh setok i ego prilozheniyakh”, Chisl. metody mekhan. sploshnoi sredy, 18, no. 5, ITPM SO AN SSSR, Novosibirsk, 1985, 101–115 | MR

[12] Rudenko D. V., Utyuzhnikova C. B., “Primenenie dinamicheski adaptivnykh k resheniyu setok dlya modelirovaniya prostranstvennykh nestatsionarnykh techenii gaza s bolshimi gradientami”, Zh. vychisl. matem. i matem. fiz., 42:3 (2002), 395–409 | MR | Zbl

[13] Gilmanov H. A., “Primenenie dinamicheski adaptivnykh setok k issledovaniyu techenii s mnogomasshtabnoi strukturoi potoka”, Zh. vychisl. matem. i matem. fiz., 41:2 (2001), 311–326 | MR

[14] Mazhukin V. I., Takoeva L. Yu., “Printsipy postroeniya dinamicheski adaptiruyuschikhsya k resheniyu setok v odnomernykh kraevykh zadachakh”, Matem. modelirovanie, 2:3 (1990), 101–118 | MR | Zbl

[15] Darin H. A., Mazhukin V. I., Samarskii A. A., “Konechno-raznostnyi metod resheniya uravnenii gazovoi dinamiki s ispolzovaniem adaptivnykh setok, dinamicheski svyazannykh s resheniem”, Zh. vychisl. matem. i matem. fiz., 28:8 (1988), 1210–1225 | MR

[16] Darin H. A., Mazhukin V. I., “Matematicheskoe modelirovanie nestatsionarnykh dvumernykh kraevykh zadach na setkakh s dinamicheskoi adaptatsiei”, Matem. modelirovanie, 1:3 (1989), 29–43 | MR

[17] Mazhukin V. I., Samarskii A. A., Shapranov A. B., “Metod dinamicheskoi adaptatsii v probleme Byurgersa”, Dokl. RAN, 333:2 (1993), 165–169 | MR | Zbl

[18] Breslavskii P. V., Mazhukin V. I., “Metod dinamicheskoi adaptatsii v zadachakh gazovoi dinamiki”, Matem. modelirovanie, 7:12 (1995), 48–78 | MR

[19] Mazhukin V. I., Samarskii A. A., Chuiko M. M., “Metod dinamicheskoi adaptatsii dlya chislennogo resheniya nestatsionarnykh mnogomernykh zadach Stefana”, Dokl. RAN, 368:3 (1999), 307–310 | MR | Zbl

[20] Demin M. M., Mazhukin V. I., Shapranov A. A., “Metod dinamicheskoi adaptatsii v probleme laminarnogo goreniya”, Zh. vychisl. matem. i matem. fiz., 41:4 (2001), 648–661 | MR | Zbl

[21] Rozhdestvenskii B. L., Yanenko H. H., Sistemy kvazilineinykh uravnenii i ikh prilozheniya k gazovoi dinamike, Nauka, M., 1968

[22] Hui W. H., Li P. Y., Li Z. W., “A unified coordinate system for solving the two-dimensional Euler equations”, J. Comput. Phys., 153 (1999), 596–637 | DOI | MR | Zbl

[23] Hui W. H., Kudriakov S., “A unified coordinate system for solving the three-dimensional Euler equations”, J. Comput. Phys., 172 (2001), 235–260 | DOI | MR | Zbl

[24] Wu Z. N., “A note on the unified coordinate system for computing shock waves”, J. Comput. Phys., 180 (2002), 110–119 | DOI | MR | Zbl

[25] Mazeran C., Despres B., “Lagrangian gas dynamics in dimension two and Lagrangian systems”, Arch. Ration. Mech. and Analys., 178:3 (2005), 327–372 | DOI | MR | Zbl

[26] Dudorov A. E., Zhilkin A. G., Kuznetsov O. A., “Kvazimonotonnaya raznostnaya skhema povyshennogo poryadka tochnosti dlya uravnenii magnitnoi gidrodinamiki”, Matem. modelirovanie, 11:1 (1999), 101–116 | MR

[27] Lax P. D., “Weak solutions of nonlinear hyperbolic equations and their numerical computation”, Communs Pure and Appl. Math., 7:1 (1954), 159–193 | DOI | MR | Zbl

[28] Chakravarthy S. R., Osher S., A new class of high accuracy TVD schemes for hyperbolic conservation laws, AIAA Papers No 85-0363, 1985

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

[30] Vyaznikov K. V., Tishkin V. F., Favorskii A. P., “Postroenie monotonnykh raznostnykh skhem povyshennogo poryadka approksimatsii dlya sistem uravnenii giperbolicheskogo tipa”, Matem. modelirovanie, 1:5 (1989), 95–120 | MR | Zbl