Geodesic
Implicit schemes development on the basis of rupture decay and large particles methods
Matematičeskoe modelirovanie, Tome 16 (2004) no. 6, pp. 81-84.

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The implicitness in new schemes is provided with the record of rupture decay equations on cells boundaries. Here were used the parameters in the beginning and the end of computational step by time. The density change is taken into account when the cells boundaries deform at the first stage of physical processes splitting. In outcome the net number of the Courant of calculations is considerably increased by a stability limit. The application of rupture decay equations allows to eliminate computational oscillations during non-stationary flow simulation. 
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Yu. A. Grishin. Implicit schemes development on the basis of rupture decay and large particles methods. Matematičeskoe modelirovanie, Tome 16 (2004) no. 6, pp. 81-84. http://geodesic.mathdoc.fr/item/MM_2004_16_6_a18/

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[2] Belotserkovskii O. M., Davydov Yu. M., Metod krupnykh chastits v gazovoi dinamike, Nauka, M., 1982, 392 pp.

[3] Grishin Yu. A., “Novye skhemy metoda krupnykh chastits i ikh ispolzovanie dlya optimizatsii gazovozdushnykh traktov dvigatelei”, Matematicheskoe modelirovanie, 14:8 (2002), 51–55 | Zbl