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TsAGI Science Journal

ISSN Print: 1948-2590
ISSN Online: 1948-2604

TsAGI Science Journal

DOI: 10.1615/TsAGISciJ.v46.i7.40
pages 657-670

ONE SOLUTION OF THE NAVIER−STOKES EQUATIONS: SPHERICALLY SYMMETRIC POINT SOURCE IN A COMPRESSIBLE PERFECT GAS

Oleg Evguenievich Kirillov
Central Aerohydrodynamic Institute (TsAGI), 1 Zhukovsky Str., Zhukovsky, 140180, Moscow Region, Russia

ABSTRACT

The solution of the Navier−Stokes equations for a spherically symmetric flow source is considered. Only the second (bulk) viscosity, in the absence of the first (shear) viscosity and thermal conductivity, is taken into account. This allows obtaining a solution in the form of a series in which the coefficients are expressed in terms of previously recurring convolution coefficients. The solution has two irregular singular points−in the center and at infinity−resulting in significant non-uniqueness of the solution; that is, the equations have many solutions that are physically indistinguishable at infinity. When the second viscosity tends to zero, the solution describes the inviscid limit of compressible flows. It records the second viscosity, followed by its aspiration to zero, which quickly allows physically solving the Navier−Stokes equations correctly for a compressible inviscid gas flow point source. Therefore, this method is called the method of correct compressibility. The results of the calculations and solutions that have physical meaning are presented.


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