Numerical modeling of multicomponent gas flows with strong discontinuities of medium properties
Matematičeskoe modelirovanie, Tome 19 (2007) no. 12, pp. 89-100.

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In this paper the numerical method of calculation of multicomponent gas flows with discontinuities of thermodynamic properties of medium and temperatures is described. The numerical method does not lead to occurrence pressure and velocity oscillations as the another of conservative methods.
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I. E. Ivanov; I. A. Kryukov. Numerical modeling of multicomponent gas flows with strong discontinuities of medium properties. Matematičeskoe modelirovanie, Tome 19 (2007) no. 12, pp. 89-100. http://geodesic.mathdoc.fr/item/MM_2007_19_12_a9/

[1] Abgrall R., “How to prevent pressure oscillations in multicomponent flow calculations a quasi conservative approach”, J. of Comput. Physics, 125 (1996), 150–160 ; INRIA Report de recherche, 1994, No 2372 | DOI | MR | Zbl

[2] Shue K.-M., “An effisient Schock-Capturing Algorithm for Compressible Multicomponent Problems”, J. of Comput. Physics, 142 (1998), 208–242 | DOI | MR

[3] Toro E. F., “Anomalies of conservative methods: analysis, numerical evidence and possible cures”, Computational Fluid Dynamics Journal, 11:2 (2002), 128–143

[4] Abgrall R., Karni S., “Computations of Compressible Multifluids”, Journal of Computational Physics, 169 (2001), 594–623 | DOI | MR | Zbl

[5] Larrouturou B., “How to preserve the mass fraction positivity when computing compressible multi-component flows”, J. of Comput. Physics, 95 (1991), 59–73 | DOI | MR

[6] Jenny P., Mueller B., Thomann H., “Correction of conservative Euler solvers for gas mixtures”, J. of Comput. Physics, 132 (1997), 91–112 | DOI | MR

[7] Fedkiw R. P., Aslam T., Merriman B., Osher S., “A Non-oscillatory Eulerian Approach to interfaces in multima-terial flows (the Ghost Fluid Metod), Multifluids”, J. of Comput. Physics, 152 (1999), 457–492 | DOI | MR | Zbl

[8] Godunov S. K., “Raznostnyi metod chislennogo rascheta razryvnykh reshenii uravnenii gidrodinamiki”, Matem. sb., 47(89):3 (1959), 271–306 | MR | Zbl

[9] Ivanov I. E., Kryukov I. A., “Kvazimonotonnyi metod povyshennogo poryadka tochnosti dlya rascheta vnutrennikh i struinykh techenii nevyazkogo gaza”, Matem. modelirovanie, 8:6 (1996), 47–55 | MR | Zbl

[10] Van-Leer B., Lectures Notes Phys., 170, 1982, 507–512

[11] Osher S., Fedkiw R. P., “A Level Set Method: An Overview and some recent results”, J. of Comput. Physics, 169 (2001), 463–502 | DOI | MR | Zbl

[12] Sethian J. A., Level set method and fast marching methods, University Press, Cambridge, 1999 | MR | Zbl

[13] Fares E., Schroder W., “A differential equation for approximate wall distance”, Int. J. Numer. Meth. Fluid, 39 (2002), 743–762 | DOI | MR | Zbl

[14] Tucker P. G., “Differential equation-based wall distance computation for DES and RANS”, J. Comput. Phys., 190 (2003), 229–248 | DOI | Zbl

[15] Kim S., “An $O(N)$ level set method for Eikonal equations”, SIAM J. Sci. Comput., 22 (2001), 2178–2193 | DOI | MR | Zbl

[16] Tsai Y. R., “Rapid and accurate computation of the distance function using grids”, J. Comput. Phys., 178:1 (2002), 175–195 | DOI | MR | Zbl

[17] Fedkiw R. P., Shapiro G., Shu C.-W., “Shock capturing Level sets and PDE based methods in computer vision and image processing: review of Osher's contributions”, J. Comp. Phys., 185 (2003), 309–343 | DOI | MR

[18] Falcone M. Ferretti, “Semi Lagrangian schemes for Hamilton–Jacobi equations, discrete representation formulae and Godunov methods”, J. Comput. Phys., 175:2 (2002), 559–575 | DOI | MR | Zbl

[19] Ivanov D. I., Ivanov I. E., Kryukov I. A., “Algoritmy priblizhennogo resheniya nekotorykh zadach prikladnoi geometrii, osnovannye na uravnenii tipa Gamiltona–Yakobi”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 45:8 (2005), 1345–1358 | MR | Zbl

[20] Grossman B., Walters R. W., “Analysis of flux-split algorithms for Euler's equations with real gases”, AIAA J., 27:5 (1989), 524–531 | DOI | MR | Zbl