Abstract
The process of propagation of shock waves in two-component mixtures is considered. The studies were performed within the framework of the two-velocity approximation of mechanics of heterogeneous media with account of different pressures of the components. The stability of propagation of all types of stationary shock waves (fully dispersed, frozen-dispersed, dispersed-frozen, and frozen shock waves of two-front configuration) to infinitesimal and finite perturbations is shown numerically, using the method of coarse particles. The problem of initiation of shock waves (the formation of different types of shock waves from stepwise initial data) is solved. Flows in the transonic range relative to the speed of sound in the first component are obtained.
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References
A. V. Fedorov, “Mathematical description of the flow of a mixture of condensed materials at high pressures,” in:Physical Gas Dynamics of Reactive Media [in Russian], Nauka, Novosibirsk (1990), pp. 119–128.
A. V. Fedorov, “Shock-wave structure in a mixture of two solids (a hydrodynamic approximation),”Model. Mekh.,5(22), No. 4, 135–158 (1991).
A. V. Fedorov, “Shock-wave structure in a heterogeneous mixture of two solids with equal pressures of the components,” in:Numerical Methods of Solving Problems of Elasticity and Plasticity (collection of scientific papers) [in Russian], Inst. of Theor. and Appl. Mech., Novosibirsk (1992), pp. 235–249.
E. V. Varlamov and A. V. Fedorov, “A traveling wave in a nonisothermal mixture of two solids,”Model. Mekh.,5(22), No. 3, 14–26 (1991).
A. V. Fedorov and N. N. Fedorova, “Structure, propagation and reflection of shock waves in a mixture of solids (the hydrodynamic approximation),”Prikl. Mekh. Tekh. Fiz., No. 4, 10–18 (1992).
A. A. Zhilin, A. V. Fedorov, and V. M. Fomin, “A traveling wave in a two-velocity mixture of compressible media with different pressures,”Dokl. Ross. Akad. Nauk,350, No. 2, 201–205 (1996).
A. A. Zhilin and A. V. Fedorov, “The shock-wave structure in a two-velocity mixture of compressible media with different pressures,”Prikl. Mekh. Tekh., Fiz. 39, No. 2, 10–19 (1998).
A. A. Gubaidullin, A. I. Ivandaev, and R. I. Nigmatulin, “The modified method of coarse particles for calculation of unsteady wave processes in multiphase dispersed media,”Zh. Vychisl. Mat. Mat. Fiz.,17, No. 6, 1531–1544 (1977).
A. I. Ivandaev and A. G. Kutushev, “Numerical simulation of unsteady wave flows of suspensions with identification of the boundaries of two-phase regions and contact discontinuities in the carrier gas,” in:Numerical Methods of Continuum Mechanics (collected, scientific papers) [in Russian], Vol. 14, No. 6, Inst. of Theor. and Appl. Mech.-Comput. Center, Novosibirsk (1983), pp. 58–82.
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Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 55–63, January–February 1999.
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Zhilin, A.A., Fedorov, A.V. Propagation of shock waves in a two-phase mixture with different pressures of the components. J Appl Mech Tech Phys 40, 46–53 (1999). https://doi.org/10.1007/BF02467971
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DOI: https://doi.org/10.1007/BF02467971