Igor V. Lebed

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Zhukovsky Central Institute of Aerohydrodynamics, Moscow, Russia.
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Abstract: The equations for the pair distribution functions are derived directly from the second equation of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. The derivation is fulfilled within the frameworks of the multiscale method. The equations for the pair distribution functions are the kinetic foundation for the multimoment hydrodynamics equations. Solutions to the equations for the pair distribution functions predetermine the possibility of constructing the hydrodynamics equations with an arbitrary number of principle hydrodynamic values specified beforehand. The tendency to increase the number of principal hydrodynamic values is caused by the necessity of interpreting the behavior of the system after the loss of stability. Solutions to the classic hydrodynamics equations constructed for only three principle hydrodynamic values are unable to predict the direction of instability evolution. Solutions to the multimoment hydrodynamics equations are capable of reproducing correctly the phenomenon of emergence and development of instability.

Keywords: Multimoment Hydrodynamics, Pair Functions, Instability

Cite this paper: Lebed, I. (2015) Kinetic Foundation for the Multimoment Hydrodynamics Equations. Open Journal of Fluid Dynamics, 5, 76-91. doi: 10.4236/ojfd.2015.51010.

References

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http://dx.doi.org/10.1134/S1990793107010071

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http://dx.doi.org/10.1134/S1990793112010204

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http://dx.doi.org/10.4236/ojfd.2013.33027

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http://dx.doi.org/10.4236/ojfd.2014.42015

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