  Journal of Applied Mathematics and Mechanics Russian Academy of Sciences   Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 00218928 (print version) 
Archive of Issues
Total articles in the database:   1813 
In Russian (ÏÌÌ):   1014

In English (J. Appl. Math. Mech.):   799 

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Kh.F. Valiyev and A.N. Kraiko, "Selfsimilar problems of the compression of an ideal gas and its dispersion from a point," J. Appl. Math. Mech. 79 (3), 237249 (2015) 
Year 
2015 
Volume 
79 
Issue 
3 
Pages 
237249 
DOI 
10.1016/j.jappmathmech.2015.09.004 
Title 
Selfsimilar problems of the compression of an ideal gas and its dispersion from a point 
Author(s) 
Kh.F. Valiyev (Baranov Central Institute of Aviation Motors, Moscow, Russia)
A.N. Kraiko (Baranov Central Institute of Aviation Motors, Moscow, Russia, akraiko@ciam.ru) 
Abstract 
Selfsimilar solutions describing onedimensional unsteady flows of an ideal (inviscid and nonheatconducting) perfect gas are considered. Whereas, in the wellknown problem of isentropically compressing a gas to a plane, axis or centre of symmetry (henceforth, to a centre of symmetry CS) with a unit selfsimilarity index, the result of compression is a uniform flow moving to the CS, the problem of the retardation of such a flow of a continuous centred wave and the shock wave adjacent to it (the one shock wave in the plane case) subsequently arises. The gas is at rest behind the shock wave travelling from the CS. The change in the signs of the time and velocity in the solutions describing the finite isentropic compression of the gas gives a representation of the evolution of the flow in the case of uniform dispersion of the gas from the CS. Other known selfsimilar solutions with unit selfsimilarity exponent give an unbounded isentropic compression of a finite mass of gas to the CS ("compression into a point"). For such a compression, the density, pressure, internal energy and velocity are infinite but the entropy is finite. The entropy is also finite after the gas has been arrested by the shock wave travelling from the CS. The new selfsimilar problem concerning the "dispersion from a point" (plane or CS) of a finite mass of "hot" gas with an infinite initial energy, zero velocity and finite entropy is solved. In the new solutions (with and without a void in the neighbourhood of the CS), by virtue of the "mass integral" (its role is similar to the role of the energy integral in the strong explosion problem), all the trajectories of the hot gas particles are isolines of the selfsimilar variable with a selfsimilarity index found by dimensional analysis. The effect of a finite initial density of the cold gas surrounding the compressed gas on the solutions found, the selfsimilar solution arising here, and the occasionally paradoxical features of the selfsimilar solutions in the case of dispersion into a vacuum are discussed. 
Received 
3 September 2014 
Link to Fulltext 
http://www.sciencedirect.com/science/article/pii/S0021892815001069 
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