RT Journal Article
ID 4561e0f1548831ca
A1 Kirillov, Oleg Evguenievich
T1 ONE SOLUTION OF THE NAVIER−STOKES EQUATIONS: SPHERICALLY SYMMETRIC POINT SOURCE IN A COMPRESSIBLE PERFECT GAS
JF TsAGI Science Journal
JO TSAGI
YR 2015
FD 2016-07-22
VO 46
IS 7
SP 657
OP 670
K1 bulk viscosity
K1 irregular singularity
K1 convolution
K1 source
K1 Navier-Stokes equations
AB 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.
PB Begell House
LK http://dl.begellhouse.com/journals/58618e1439159b1f,3842901765b5ae64,4561e0f1548831ca.html