The numerical method of Lagrange particles on the basis of two dimentional gas dynamics wave equations

V. E. Troshchiev ; N. S. Bochkarev

Matematičeskoe modelirovanie, Tome 24 (2012) no. 11, pp. 53-64.

Résumé

In the paper we formulate the numerical method of particles based on the approximation of the system of gas dynamics equations in the form of second order nonlinear wave equations (NWE) in time and space variables. On the basis of "NWE" it allows one to construct finite difference and finite elements schemes with cells of balance both in the "finite volume" and lagrange "particles" framework. The investigation of the method of particles and numerical tests are performed for two dimensional gas dynamics problems in the Lagrange form on triangular grids.

Détail

Keywords: gas dynamics equations, nonlinear wave equations, finite difference schemes, finite elements schemes, particles and points methods.
Mots-clés : Lagrange variables

Bibliographie

[1] Babenko K. I. (red.), Teoreticheskie osnovy i konstruirovanie chislennykh algoritmov zadach matematicheskoi fiziki, Nauka, M., 1979, 295 pp. | MR

[2] Troschiev V. E., Nelineinye volnovye uravneniya gazovoi dinamiki i voprosy postroeniya chislennykh modelei na ikh osnove, Preprint 151-A, TRINITI, Troitsk, 2012, 20 pp.

[3] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1989, 616 pp. | MR

[4] Samarskii A. A., Popov Yu. P., Raznostnye metody resheniya zadach gazovoi dinamiki, Nauka, M., 2004, 423 pp. | MR

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

[6] Older B., Fernbakh S., Rotenberg M. (red.), Vychislitelnye metody v gidrodinamike, Mir, M., 1967, 384 pp.

[7] Godunov S. K., Zabrodin A. V., Ivanov M. Ya., Kraiko A. N., Prokopov G. P., Chislennoe reshenie mnogomernykh zadach gazovoi dinamiki, Nauka, M., 1976 | MR | Zbl

[8] Mikhailova N. V., Tishkin V. F., Tyurina N. N., Favorskii A. P., Shashkov M. Yu., “Chislennoe modelirovanie dvumernykh gazodinamicheskikh techenii na setke peremennoi struktury”, ZhVMiMF, 26:9 (1986), 1392–1406 | MR

[9] Fedorenko R. P., Vvedenie v vychislitelnuyu fiziku, Izdatelskii Dom «Intellekt», M., 2008, 503 pp.

[10] Dyachenko V. F., “Ob odnom novom metode chislennogo resheniya nestatsionarnykh zadach gazovoi dinamiki s dvumya prostranstvennymi peremennymi”, ZhVMiMF, 5:4 (1965), 680–688 | MR

[11] Diyankov O. V., “Metod nechetkikh setok dlya uravnenii v chastnykh proizvodnykh”, Matem. modelirovanie, 19:7 (2007), 101–111 | MR

[12] Godunov S. K., “Raznostnyi metod chislennogo rascheta razryvnykh reshenii uravnenii gidrodinamiki”, Matem. sb., 47 (1959), 271–306 | MR | Zbl

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

[14] Troschiev V. E., Apollonova O. V., Postroenie i issledovanie konechno-raznostnykh i konechno-elementnykh skhem dlya odnomernykh uravnenii gazovoi dinamiki, Preprint TRINITI 0059, TsNIIATOMINFORM, TRINITI, Troitsk, 1999, 22 pp.

[15] Troschiev V. E., Bochkarev N. S., Nelineinye volnovye uravneniya gazovoi dinamiki i chislennye metody na ikh osnove dlya odnomernykh techenii, Preprint 147-A, TRINITI, Troitsk, 2011, 23 pp.

[16] Troschiev V. E., Bochkarev N. S., “Chislennye metody lagranzhevykh chastits-tochek dlya odnomernykh volnovykh uravnenii gazovoi dinamiki”, Matem. modelirovanie, 24:6 (2012), 91–108

[17] Troschiev V. E., Shagaliev R. M., “Konservativnye uzlovye skhemy metodov konechnykh raznostei i konechnykh elementov dlya dvumernogo uravneniya teploprovodnosti”, Chislennye metody mekhaniki sploshnoi sredy, 15:4 (1984), 131–157

[18] Goloviznin V. M., Samarskii A. A., Favorskii A. P., “Variatsionnyi podkhod k postroeniyu konechno-raznostnykh matematicheskikh modelei”, Dokl. AN SSSR, 235:6 (1977), 1285–1288 | MR | Zbl

[19] Delone B. N., Peterburgskaya shkola teorii chisel, Izd-vo AN SSSR, M.–L., 1947

[20] Sedov L. I., Metody podobiya i razmernosti v mekhanike, Nauka, M., 1977 | MR