Multiphase Flow Modeling via Hamilton’s Principle

作者: Sergey Gavrilyuk

DOI: 10.1007/978-3-7091-0983-0_4

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摘要: We present here a variational approach to derivation of multiphase flow models. Two basic ingredients this method are as follows. First, conservative part the model is derived based on Hamilton principle stationary action. Second, phenomenological dissipative terms added which compatible with entropy inequality. The technique shown up, and mathematical models (classical non-classical) describing fluid-fluid fluid-solid mixtures interfaces derived.

参考文章(35)
Richard Saurel, Rémi Abgrall, A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows Journal of Computational Physics. ,vol. 150, pp. 425- 467 ,(1999) , 10.1006/JCPH.1999.6187
M.R. Baer, J.W. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials International Journal of Multiphase Flow. ,vol. 12, pp. 861- 889 ,(1986) , 10.1016/0301-9322(86)90033-9
Smadar Karni, Multicomponent Flow Calculations by a Consistent Primitive Algorithm Journal of Computational Physics. ,vol. 112, pp. 31- 43 ,(1994) , 10.1006/JCPH.1994.1080
S.L. Gavrilyuk, N. Favrie, R. Saurel, Modelling wave dynamics of compressible elastic materials Journal of Computational Physics. ,vol. 227, pp. 2941- 2969 ,(2008) , 10.1016/J.JCP.2007.11.030
R. Saurel, O. Le Métayer, J. Massoni, S. Gavrilyuk, Shock jump relations for multiphase mixtures with stiff mechanical relaxation Shock Waves. ,vol. 16, pp. 209- 232 ,(2007) , 10.1007/S00193-006-0065-7
N. Favrie, S.L. Gavrilyuk, R. Saurel, Solid-fluid diffuse interface model in cases of extreme deformations Journal of Computational Physics. ,vol. 228, pp. 6037- 6077 ,(2009) , 10.1016/J.JCP.2009.05.015
Henri Gouin, Sergey Gavrilyuk, A new form of governing equations of fluids arising from Hamilton's principle International Journal of Engineering Science. ,vol. 37, pp. 1495- 1520 ,(1999) , 10.1016/S0020-7225(98)00131-1
Yi A. Li, Linear stability of solitary waves of the Green-Naghdi equations Communications on Pure and Applied Mathematics. ,vol. 54, pp. 501- 536 ,(2001) , 10.1002/CPA.1
S. L. Gavrilyuk, V. M. Teshukov, Linear Stability of Parallel Inviscid Flows of Shallow Water and Bubbly Fluid Studies in Applied Mathematics. ,vol. 113, pp. 1- 29 ,(2004) , 10.1111/J.1467-9590.2004.01486.X