Volume 6, no. 1Pages 72 - 84

The New Hyperbolic Models of Heterogeneous Environments

V.S. Surov, I.V. Berezansky
Invention mathematically and physically correct models multiphase environment is an important problem, since many of the available models of heterogeneous environment are not such. In this paper, for multi-component environment offers two new models - single- and multi-velocity approximations. The models are based on the laws of conservation. Viscous and heat-conducting properties of the mixture are considered. For the described models is constructed automodels solution kind of traveling wave. On the example of a binary mixture have done of calculations for single- and multi-velocity approximations. It is shown that, if the use of the relaxation of the laws for the dissipative processes then the system of equations are hyperbolic.
Full text
multicomponent viscous heat-conducting mixture, singlevelocity and multivelocity multicomponent medium, hyperbolic systems of partial differential equations, automodel solutions.
1. Surov V.S. Reflection of the Air Shock Wave from the Foam Layer. High Temperature, 2000, vol. 38, no. 1, pp. 101-110.
2. Surov V.S. Calculation of Shock Wave Propagation in Bubbly Liquids. Technical Physics. The Russian J. of Applied Physics, 1998, vol. 68, no. 11, pp. 12-19.
3. Surov V.S. Localization of Contact Surfaces in Multifluid Hydrodynamics. J. of Engineering Physics and Thermophysics, 2010, vol. 83, no. 3, pp. 518-527.
4. Surov V.S. Single Velocity Model of Heterogeneous Media with Hyperbolic Adiabatic Core. Computational Mathematics and Mathematical Physics, 2008, vol. 48, no. 6, pp. 1111-1125.
5. Wackers J.A., Koren B. Fully Conservative Model for Compressible Two-Fluid Flow. J. Numer. Meth. Fluids, 2005, vol. 47, pp. 1337-1343.
6. Murrone A.A., Guillard H. Five Equation Reduced Model for Compressible Two Phase Flow Problems. J. Comput. Phys., 2005, vol. 202, pp. 664 - 698.
7. Kreeft J.J., Koren B.A. New Formulation of Kapila's Five-Equation Model for Compressible Two-Fluid Flow, and its Numerical Treatment. J. Comput. Phys, 2010, vol. 229, pp. 6220-6242.
8. Cattaneo C. Sur une forme de l'equation de la chaleur elinant le paradoxe d'une propagation instantance. CR. Acad. Sci., 1958, vol. 247, pp. 431-432.
9. Dai W., Wang H., Jordan P.M. A Mathematical Model for Skin Burn Injury Induced by Radiation Heating. Int. J. Heat and Mass Transfer, 2008, vol. 51, pp. 5497-5510.
10. Surov, V.S. Hyperbolic Model Single-Velocity Multi-Component Heat Conductive Medium. High Temperature, 2009, vol. 47, no. 6, pp. 905 - 913.
11. Samarskiy A.A., Popov U.P. Difference Methods for Solving Problems of Gas Dynamics. Moscow, Nauka, 1980. (in Rusian)
12. Lodge A.S. Elastic Fluids. Moscow, Nauka, 1969.(in Rusian)
13. Surov V.S. Hyperbolic Model Single Velocity Heterogeneous Environment. J. of Engineering Physics and Thermophysics, 2012, vol. 85, no. 3, pp. 495-502.
14. Kaminski W. Hyperbolic Heat Conduction Equation for Materials with a Non-homogeneous Inner Structure. Trans. of the ASME. J. of Heat Transfer, 1990, vol. 112, pp. 555.