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 JAMP  Vol.5 No.2 , February 2017
Dispersion Effects in the Falkner-Skan Problem and in the Kinetic Theory
Abstract: The conservation laws of continuum mechanics and of the kinetic theory with the influence of the angular momentum and associated with its rotation of the elementary volume are considered, the variant of accounting lag is investigated for discrete environment. The analysis of the recording of the Lagrangian function for the collective interaction of the particles with the change of the center of inertia of the moving particles and the effect influence of the angular momentum were used. The equations for gas are calculated from the modified Boltzmann equation and the phenomenological theory. For a rigid body the equations were used of the phenomenological theory, but their interpretation was changed. The nonsymmetric stress tensor was obtained. The Boltzmann equation is written with an additional summand. This situation is typical for discrete environment as the transition from discrete to continuous environment is a key to the issue of mechanics. Summary records of all effects lead to a cumbersome system of equations and therefore require the selection of main effects in a particular situation. The Hilbert paradox was being solved. The simplest problem of the boundary layer continuum (the Falkner-Skan task) and the kinetic theory are discussed. A draw attention at the delay process would be suggested for the description of discrete environment. Results are received for some special cases.
Cite this paper: Galaev, O. and Prozorova, E. (2017) Dispersion Effects in the Falkner-Skan Problem and in the Kinetic Theory. Journal of Applied Mathematics and Physics, 5, 522-537. doi: 10.4236/jamp.2017.52045.
References

[1]   Prozorova, E.V. (2014) Influence of Mathematical Models in Mechanics. Problems of Nonlinear Analysis in Engineering Systems, 20, 78-86.

[2]   Prozorova, E.V. (2012) The Effect of Dispersion in Nonequilibrium Continuum Mechanics Problems Environment. Physico-Chemical Kinetics in Gas Dynamics, 13. (In Russian)
http://www.chemphys.edu.ru/pdf/2012-10-30-001.pdf

[3]   Prozorova, E.V. (2014) Influence of the Delay and Dispersion In mechanics. Journal of Modern Physics, 5, 1796-1805.
https://doi.org/10.4236/jmp.2014.516177

[4]   Cosserat, E. and Cosserat, F. (1909) Theories des corps deformables. Hermann, Paris.

[5]   Efendiev, Y., Galvis, J. and Hou, T. (2013) Generalized Multiscale Finite Element Method. Journal of Computational Physics, V, 116-135.

[6]   Bulanov, E.A. (2012) The Momentum Tension on Mechanics of Solid, Free Flowing and Liquid Medium. College Book, Moment.

[7]   Elizarova, T.G. (2007) Guasi-Gasdynamic Equations and Numerical Methods for Viscous Flow Simulation. M.:Scientific Word, 352.

[8]   Cercignani, C. (1969) Mathematical Methods in Kinetic Theory. Macmillan, 148 p.
https://doi.org/10.1007/978-1-4899-5409-1

[9]   Ferziger, J.H. and Kaper, H.G. (1972) Mathematical Theory of Transport Processes in Gases. North-Holland Publishing Company, Amsterdam, London.

[10]   Hirschfelder, J.O., Curtiss, C.F. and Bird, R.B. (1954) The Molecular Theory of Gases and Liquids. New York.

[11]   Kogan, M.N. (1967) The Dynamics of the Rarefied Gases. M.: Nauka. (In Russian)

[12]   Loyotinskiy, L.G. (1970) Mechanics of Fluids and Gas. M.: Nauka. (In Russian)

[13]   Kameda, Y., Yoshino, J. and Ishihara, T. (2008) Examination of Kolmogorov’s 4/5 Law by High-Resolution Direct Numerical Simulation Data of Turbulence. Journal of the Physical Society of Japan, 77, Article ID: 064401.
https://doi.org/10.1143/JPSJ.77.064401

[14]   Adamian, D.Y., Strelets, M.K. and Travin, A.K. (2011) An Efficient Method of Synthetic Turbulence Generation at LES Inflow in Zonal RANS-LES Approaches to Computation Flows. Mathematical Modeling, 23. (In Russian)

[15]   Natrajan, V.K., Wu, Y. and Christensen, K.T. (2007) Spatial Signatures of Retrograde Spanwise Vortices in Wall Turbulence. Journal of Fluid Mechanics, 574, 155-167.
https://doi.org/10.1017/S0022112006003788

[16]   Guala, M., Liberzon, A., Tsinober, A. and Kinzelbach, W. (2007) An Experimental Investigation on Lagrangian Correlations of Small-Stale Turbulence at Law Reynolds Number. Journal of Fluid Mechanics, 574, 405-427.
https://doi.org/10.1017/S0022112006004204

[17]   Rashid, A. (2007) Numerical Solution of Korteweg-de Vries Equation by the Fourier Pseudospectral Method. Bulletin of the Belgian Mathematical Society—Simon Stevin, 14, 709-721.

[18]   Popov, S.P. (2015) Numerical Analysis of Soliton Solutions of the Modified Korteweg-de Vries-Sine-Gordon Equation. Computational Mathematics and Mathematical Physics, 55, 437-446.

[19]   Kononenko, V.A., Prozorova, E.V. and Shishkin, A.V. (2009) Influence Dispersion for Gas Mechanics with Great Gradients. 27th International Symposium on Shock Waves, St. Petersburg, 19-24 July 2009, 406-407.

[20]   Katasonov, M.M., Kozlov, V.V., Nikitin, N.V. and Sboev, D.C. (2015) Beginnings and Development of Localization Indignation in Circle Tube and Boundary Layer. Educational Text-Book, State University, Novosibirsk.

[21]   Babkin, V.A. and Nicholas, V.N. (2009) Turbulent Flow in Acircular Tubeanda Flat channel and model Mesoscale Turbulence. Engineering Physics Magazine, 84, 56-72.

[22]   Elsinga, G.E., Adrian, R.J., Van Oudhensden, B.W. and Scarano, F. (2010) Three-Dimensional Vortex Organization in a High-Reynolds-Number Supersonic Turbulent Boundary Layer. Journal of Fluid Mechanics, 644, 35-60.
https://doi.org/10.1017/S0022112009992047

[23]   Priezjev, N.V. and Trouan, S.M. (2006) Influence of Periodic Wall Roughness on Slip Behaviour at Liquid/Solid Interfaces: Molecular-Scale Simulations versus Continuum Predictions. Journal of Fluid Mechanics, 554, 25-47.

[24]   Batchelor, G.K. (1970) An Introduction to Fluid Dynamics. Cambridge of University Press, Cambridge.

 
 
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