Analysis of the Invariance Under the Galilean Transformation of Some Mathematical Models of Multicomponent Media

The analysis of the invariance under the Galilean transformation of the mathematical model of 'frozen', gas suspension is done. It was shown that the equation of the total energy density of the gas phase in the model of 'frozen', gas suspension was not invariant under Galilean transformations. This leads to appearance of the total energy density equation of the fictitious source term, which determines the growth of entropy. An additional increase of entropy leads to a violation of the second law of thermodynamics. In this paper a modification of the equation of the total energy density of the gas phase was proposed. The modification consisted in the fact that the right-hand side of the equation of conservation of total energy density was subtracted the work of interfacial forces. The analysis of this equation showed that the equation of the total energy density of the gas phase was invariant under Galilean transformations, and the equation for the entropy production didn't contradict the second law of thermodynamics.

Keywords

mathematical model, invariance, multi-component mixture.

References

1. Nigmatulin R.I. Fundamentals of Mechanics of Heterogeneous Media. Moscow, Nauka, 1978. - 336 p.
2. Kuropatenko V.F. New Models of Continuum Mechanics. Ukrainian Journal of Physics, 2011, vol. 84, no. 1, pp. 74-92.
3. Shestakov A.L., Sviridyuk G.A., Zakharova E.V. Dynamic Measurements as an Optimal Control. Obozrenie prikladnoy i promyshlennoy matematiki - Review of Industrial and Applied Mathematics, 2009, vol. 16, no. 4, pp. 732-733.
4. Shestakov A.L., Keller A.V., Nazarova E.I. Numerical Solution of Optimal Measurement [Chislennoe reshenie zadachi optimal'nogo izmerenija]. Automatics and Telemechanics, 2012, no. 1, pp. 107-115.
5. Kruglikov B.S., Kutushev A.G. Attenuation of air Shock Waves Louvre. Combustion, Explosion and Shock Waves, 1988, no. 1, pp. 115-117.
6. Kruglikov B.S., Kutushev A.G. Attenuation of air shock layers of dust and gas grills. J. of Applied Mechanics and Technical Physics, 1988, no. 1, pp. 51-57.