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Applied Physics and Mathematics

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Analytical solutions for problems of adiabaticcompress ion and extension of spherical andcylindrical layers from incompress ible viscous fluid
Kiselev A.B.

In paper present analytical solutions for one-dimensional dynamical
problems of adiabatic compression and extension of spherical and
cylindrical layers from viscous fluid Navier-Stokes type. Solutions
obtained in Lagrangian coordinates and at hypothesis that in
initial moment distributions of radial velocity satisfy condition
of incompressibility. These solutions, in particular, can be used
for testing programs of computing calculations and for estimate
of effectiveness of new numerical methods. In addition, solution
for spherical layer can be useful for sampling kinetic equation
for porosity (or volume damage parameter under modeling socalled
viscous fracture) of material. Previously similar results were
obtained for thick-walled shells from incompressibility viscoplastic
material Socolovsky-Perzyna type (Kiselev A.B. Analytical solutions
for problems of adiabatic compression of thick-walled spherical
and cylindrical shells from incompressibility viscoplastic material //
J. of Appl. Math. and Mech. 2012. Vol. 76. № 4. PP. 675...679; Kiselev
A.B. To investigation of process of no stationary extension of thickwalled
spherical and cylindrical viscoplastic shells // Moscow Univ.
Mech. Bulletin. 2012. № 6. PP. 20...25).
Key words: spherical and cylindrical layers, viscous fluid, incompressibility,
adiabatically process.

Contacts: E-mail: akis2006@yandex.ru

Pp. 88-93.

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