Geodesic
Computation of discontinuous solutions of fluid dynamics equations with entropy nondecrease guarantee
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 6, pp. 1008-1021
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A new formulation of the Godunov scheme with linear Riemann problems is proposed that guarantees a nondecrease in entropy. The new version of the method is described for the simplest example of one-dimensional gas dynamics in Lagrangian coordinates. 
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S. K. Godunov; I. M. Kulikov. Computation of discontinuous solutions of fluid dynamics equations with entropy nondecrease guarantee. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 6, pp. 1008-1021. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_6_a11/

[1] Godunov S. K., “Raznostnyi metod chislennogo rascheta razryvnykh reshenii uravnenii gidrodinamiki”, Matem. sbornik, 47:3 (1959), 271–306 | MR | Zbl

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

[3] Toro E. F., Riemann solvers and numerical methods for fluid dynamics, Springer-Verlag, Heidelberg, 1999 | MR | Zbl

[4] Courant R., Isaacson E., Rees M., “On the solution of nonlinear hyperbolic differential equations by finite difference”, Commun. Pure and Appl. Math., 5:3 (1952), 243–255 | DOI | MR | Zbl

[5] Roe P., “Approximate Riemann solvers, parameter vectors, and difference schemes”, J. Comput. Phys., 135:2 (1997), 250–258 | DOI | MR | Zbl

[6] Engquist B., Osher S. J., “One-sided difference approximations for nonlinear conservation laws”, Math. Comput., 36:154 (1981), 321–351 | DOI | MR | Zbl

[7] Harten A., Lax P. D., van Leer B., “On upstream differencing and Godunov-type schemes for hyperbolic conservation laws”, Soc. Industrial and Appl. Math. Review, 25:1 (1983), 35–61 | MR | Zbl

[8] Einfeld B., “On Godunov-type methods for gas dynamics”, Soc. Industrial and Appl. Math. J. Numerical Analys., 25:2 (1988), 294–318 | MR | Zbl

[9] Batten P., Clarke N., Lambert C., Causon D. M., “On the choice of savespeeds for the HLLC Riemann solver”, Soc. Industrial and Appl. Math. J. Comput., 18:6 (1997), 1553–1570 | MR | Zbl

[10] Toro E. F., Spruce M., Speares S., “Restoration of the contact surface in the HLL Riemann solver”, Shock Waves, 4:1 (1994), 25–34 | DOI | Zbl

[11] Safronov A. V., “Raznostnyi metod resheniya nestatsionarnykh uravnenii gazodinamiki na osnove sootnoshenii na razryvakh”, Kosmonavtika i raketostroenie, 2006, no. 2(43), 152–158 | MR

[12] Prokopov G. P., O priblizhennykh realizatsiyakh metoda Godunova, Preprint No 14, IPM, M., 2007

[13] Prokopov G. P., Kontrol entropii v algoritmakh i raschetakh gazodinamicheskikh techenii, Preprint No 84, IPM, M., 2006

[14] Prokopov G. P., Severin A. V., Ekonomichnaya realizatsiya metoda Godunova, Preprint No 29, IPM, M., 2009

[15] Zabrodin A. V., Sofronov I. D., Chentsov N. N., “Adaptivnye raznostnye metody matematicheskogo modelirovaniya nestatsionarnykh gazodinamicheskikh techenii”, obzor, Vopr. atomnoi nauki i tekhn. Seriya: Metodiki i programmy chisl. resheniya zadach matem. fiz., 4, 1988, 3–22 | MR

[16] Godunov S. K., “Problema obobschennogo resheniya v teorii kvazilineinykh uravnenii i v gazovoi dinamike”, Uspekhi matem. nauk, 17:3 (1962), 147–158 | MR | Zbl

[17] Prokopov G. P., “Neobkhodimost kontrolya entropii v gazodinamicheskikh raschetakh”, Zh. vychisl. matem. i matem. fiz., 47:9 (2007), 1591–1601 | MR

[18] Godunov S. K., Peshkov I. M., “Simmetricheskie giperbolicheskie uravneniya nelineinoi teorii uprugosti”, Zh. vychisl. matem. i matem. fiz., 48:6 (2008), 1034–1055 | MR | Zbl

[19] Godunov S. K., Peshkov I. M., “Termodinamicheski soglasovannaya nelineinaya model uprugoplasticheskoi sredy Maksvella”, Zh. vychisl. matem. i matem. fiz., 50:8 (2010), 1481–1498 | MR | Zbl

[20] Godunov S. K., Kiselev S. P., Kulikov I. M., Mali V. I., “Chislennoe i eksperimentalnoe modelirovanie obrazovaniya voln pri svarke vzryvom”, Trudy MIAN, 281, 2013, 16–31 | Zbl