|
Article information
2014 , Volume 19, ¹ 4, p.107-116
Surov V.S., Berezansky I.V.
The calculation of the flow of single-speed viscous and heat mixture by using the nodular method of characteristics
In this work we use single-speed model of viscous and heat heterogeneous media. For describing heat transfer we used Maxwell - Cattaneo law instead of Fourier law. The viscous stresses are described by means of a similar relaxation law. The account of viscosity and thermal conductivity is introduced for the equilibrium state of the whole mixture. Through using the relaxation laws for the source model is still hyperbolic, it allows us to use numerical methods for hyperbolic systems. We use nodular method of characteristics. This method proves to be effective during integration the equations for the single-speed model without considering the heat transfer and the viscosity. In this paper we describe a modification of the classical method of characteristics. We look for the parameters for a new time frame by means an iterative procedure. The calculated results are compared with results of single-speed model when the heat transfer and the viscosity are not considered. Received 12 September 2013.
[full text]
Keywords: Single-speed viscous and heat mixture, hyperbolic systems of partial differential equations, nodular method of characteristics, numerical modeling
Author(s):
Surov Victor Sergeevich
Dr. , Professor
Position: Professor
Office: South Ural State University
Address: 454080, Russia, Chelyabinsk, 76, Lenin prospekt
Phone Office: (951) 778 55 47
E-mail: surovvictor@gmail.com
SPIN-code: 9049-3366Berezansky Ivan Vladimirovich
Position: Student
Office: South Ural State University
Address: 454080, Russia, Chelyabinsk, Lenin Avenue, 76
E-mail: mynameivanych@gmail.com
References:
[1] Surov V.S. Ob otrazhenii vozdushnoj udarnoj volny ot sloja peny [The reflection of the shock wave from the foam layer]. Teplofizika vysokih temperatur. 2000; 38(1): 101-110.(In Russ.)
[2] Surov V.S. Raschjot vzaimodejstvija vozdushnoj udarnoj volny s poristym materialom [A calculation of the interaction of air shock waves in porous materials]. Vestnik Cheljabinskogo gos. un-ta. 1997; 1: 124-134.(In Russ.)
[3] Surov V.S. Analiz volnovyh javlenij v gazo-zhidkostnyh sredah [An analysis of wave phenomena in gas-liquid media].Teplofizika vysokih temperatur. 1998; 36(4): 624-630.(In Russ.)
[4] Surov V.S. O lokalizacii kontaktnyh poverhnostej v mnogozhidkostnoj gidrodinamike [On localization of contact surfaces in multifluid hydrodynamics ]. Inzhenerno-fizicheskij zhurnal. 2010; 83(3): 518-527.(In Russ.)
[5] Surov V.S. Uzlovoj metod harakteristik v mnogozhidkostnoj gidrodinamike [The nodular method of characteristics in multifluid hydrodynamics]. Inzhenerno-fizicheskij zhurnal. 2013; 86(5): 1080-1086.(In Russ.)
[6] Goncalves E. Numerical study of expansion tube problems: Toward the simulation of cavitation. Comput. & Fluids. 2013; 72: 1-19.
[7] Schoch S., Nikiforakis N., Lee B.J., Saurel R. Multi-phase simulation of ammonium nitrate emulsion detonations .Combustion and Flame. 2013; 160: 1883-1899.
[8] Surov V.S. Techenie Buzemana dlja odnoskorostnoj modeli geterogennoj sredy [The Busemann flow for a one-velocity model of a heterogeneous medium]. Inzhenerno-fizicheskij zhurnal. 2007; 80(4): 45-51.(In Russ.)
[9] Wackers J., Koren B. A fully conservative model for compressible two-fluid flow.J. Numer. Meth. Fluids. 2005; 47: 1337-1343.
[10] Murrone A., Guillard H. A five equation reduced model for compressible two phase flow problems. J. Comput. Phys. 2005; 202: 664-698.
[11] Deledicque V., Papalexandris M.V. A conservative approximation to compressible two-phase flow models in the stiff mechanical relaxation limit . J. Comput. Phys. 2008; 227: 9241-9270.
[12] Saurel R., Petitpas F. and Berry R.A. Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures . J. Comput. Phys. 2009; 228: 1678-1712.
[13] 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; 229: 6220-6242.
[14] Cattaneo C. Sur une forme de l’equation de la chaleur elinant le paradoxe d’une propagation instantance . CR. Acad. Sci. 1958; 247: 431-432.
[15] Samarskij A.A., Popov Yu.P. Raznostnye metody reshenija zadach gazovoj dinamiki [The difference methods for solving problems of gas dynamics]. Moscow: Nauka, 1980.(In Russ.)
[16] Lodzh A.S. Jelastichnye zhidkosti [The elastic fluids]. Moscow: Nauka, 1969.(In Russ.)
[17] Surov V.S. Ob odnom variante metoda harakteristik dlja raschjota techenij odnoskorostnoj mnogokomponentnoj smesi [A variant of the method of characteristics for computation the onespeed multicomponent mixtures]. Inzhenerno-fizicheskij zhurnal. 2010; 83(2): 345-350.(In Russ.)
[18] Surov V.S., Stepanenko E.N. Setochnyj metod harakteristik dlja raschjota techenij odnoskorostnoj mnogokomponentnoj teploprovodnoj sredy [The mesh method of characteristics to calculate the single-speed flows of multicomponent thermally conductive medium]. Vestnik Cheljabinskogo gos. un-ta. 2010; 24(205): 15-22.(In Russ.)
[19] Surov V.S. Odnoskorostnaja model’ mnogokomponentnoj teploprovodnoj sredy [One-velocity model of a multicomponent heat-conducting medium]. Inzhenerno-fizicheskij zhurnal. 2010; 83(1): 132-141.(In Russ.)
[20] Kulikovskij A.G., Pogorelov N.V., Semjonov A.Ju. Matematicheskie voprosy chislennogo reshenija giperbolicheskih sistem uravnenij [The mathematical complexities of numerical solving the hyperbolic systems]. Izd. 2-e, dopoln. i ispravl. Moscow: Fizmatlit; 2012. 656.
Bibliography link:
Surov V.S., Berezansky I.V. The calculation of the flow of single-speed viscous and heat mixture by using the nodular method of characteristics // Computational technologies. 2014. V. 19. ¹ 4. P. 107-116
|
