Geodesic
Rarefaction shock waves in gas dynamics numerical solutions
Matematičeskoe modelirovanie, Tome 20 (2008) no. 1, pp. 48-60.

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Properties of various gas dynamics difference schemes (conservative, nonconsevative and completely conservative) are investigated on the basis of a classical moving piston problem. It's shown that shock wave can appears in rarefaction wave solution for piston moving out of gas. Shocks appear when low stability schemes are used for these tasks. Explanation of this effect and possible ways of its elimination are proposed. 
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M. V. Abakumov; S. I. Mukhin; Yu. P. Popov; D. V. Rogozhkin. Rarefaction shock waves in gas dynamics numerical solutions. Matematičeskoe modelirovanie, Tome 20 (2008) no. 1, pp. 48-60. http://geodesic.mathdoc.fr/item/MM_2008_20_1_a3/

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

[2] Popov Yu. P., Samarskii A. A., “Polnostyu konservativnye raznostnye skhemy”, ZhVM i MF, 9:4 (1969), 953–958 | MR | Zbl

[3] Samarskii A. A., Popov Yu. P., Raznostnye metody resheniya zadach gazovoi dinamiki, Nauka, M., 1992 | MR

[4] Tikhonov A. N., Samarskii A. A., “Ob odnorodnykh raznostnykh skhemakh”, ZhVM i MF, 1:1 (1961), 5–63 | MR | Zbl

[5] Kuznetsov O. A., Chislennoe issledovanie skhemy Rou s modifikatsiei Einfeldta dlya uravnenii gazovoi dinamiki, Preprint, IPM AN SSSR, M., 1998

[6] Abakumov M. V., Issledovanie i modifikatsiya raznostnykh skhem metoda krupnykh chastits, Preprint, IPM RAN, M., 1998

[7] Landau L. D., Lifshits E. M., Gidrodinamika, Nauka, M., 1988

[8] Sedov L. I., Metody podobiya i razmernosti v mekhanike, Fizmatgiz, M., 1962

[9] Troschiev V. E., “O divergentnosti skhemy “krest” chislennogo resheniya uravnenii gazovoi dinamiki”, Chislennye metody mekhaniki sploshnoi sredy, 1, no. 5, Nauka, Novosibirsk, 1970, 87–93

[10] Davydov Yu. M., “Primenenie metoda differentsialnogo priblizheniya dlya issledovaniya i postroeniya nelineinykh raznostnykh skhem”, ChM MSS, 11, no. 4, Novosibirsk, 1980, 41–59 | MR

[11] Shokin Yu. I., Metod differentsialnogo priblizheniya, Nauka, Novosibirsk, 1979 | MR

[12] Mukhin S. I., Popov S. B., Popov Yu. P., “O raznostnykh skhemakh s iskusstvennoi dispersiei”, ZhVM i MF, 23:6 (1983), 1355–1363 | MR | Zbl

[13] Davydov Yu. M., Skotnikov V. P., Differentsialnye priblizheniya raznostnykh skhem, VTs AN SSSR, M., 1978 | MR

[14] Ivanov M. Ya., Koretskii V. V., Kurochkina N. Ya., “Issledovanie svoistv raznostnykh skhem skvoznogo scheta vtorogo poryadka approksimatsii”, ChM MSS, 11, no. 2, Novosibirsk, 1980, 41–63 | MR

[15] Ardelyan N. V., Gulin A. V., K obosnovaniyu ustoichivosti raznostnykh skhem dlya uravnenii akustiki, Preprint No 96, IPM AN SSSR, M., 1978 | MR

[16] Gelfand I. M., “Nekotorye zadachi teorii kvazilineinykh uravnenii”, UMN, 14:2(86) (1959), 87–158 | MR