Numerical modeling of the shock and detonation waves interaction with particles on microlevel
I. A. Bedarev

References
1.	Kuznetsov O.M, Stulov V.P., “Supersonic flow around two spheres with a line of centers across the stream”, Aerodynamics of the entrance of bodies into the atmospheres of the planets, ed. G.F. Telenin, Moscow State University, Moscow, 1983, 12–16 (In Russ.)
2.	Lyagushin E.E., Stulov V.P., Yushkov A.Yu., “Experimental study of the interaction of shock waves in the flow around two cylinders”, Investigation of gas dynamics and heat transfer of complex flows of homogeneous and multiphase media, ed. V.P. Stulov, Moscow State University, Moscow, 1990, 26–29 (In Russ.)
3.	Blagosklonov V.I., Kuznetsov V.M., Minailos A.N., Stasenko A.L., Chekhovskii V.F., “Interaction of hypersonic multiphase flows”, Journal of Applied Mechanics and Technical Physics, 20:5 (1979), 571–578
4.	Andreev A.A., Kholodov A.S., “On three-dimensional supersonic flow past blunt bodies when interference is present”, USSR Computational Mathematics and Mathematical Physics, 29:1 (1989), 103–107
5.	Dubrovina I.A., Stulov V.P., “Determination of the greatest distance of the aerodynamic interaction of a pair of spheres and cylinders in a supersonic flow”, Bulletin of Moscow University. Series 1. Mathematics and Mechanics, 1989, no. 5, 46–49 (In Russ.)
6.	Zhdan I.A., Stulov V.P., Stulov P.V., “Aerodynamic interaction of two bodies in a supersonic flow”, Doklady Physics, 49:5 (2004), 315–317
7.	N. A. Artem'eva, V. V. Shuvalov, “Interaction of shock waves during the passage of a disrupted meteoroid through the atmosphere”, Shock waves, 5:6 (1996), 359–367
8.	Zhdan I.A., Stulov V.P., Stulov P.V., “Characteristic elements of a fractured solid in supersonic flow”, Doklady Physics, 49:11 (2004), 680–682
9.	Zhdan I.A., Stulov V.P., Stulov P.V., Turchak L.I., “Drag coefficients for bodies of meteorite-like shapes”, Solar System Research, 41:6 (2007), 505–508
10.	H. Naiman, D. D. Knight, “The effect of porosity on shock interaction with a rigid, porous barrier”, Shock Waves, 16:4 (2007), 321–337
11.	Barri N.G., “Aerodynamic interaction of meteor-body fragments: The collimation effect”, Doklady Physics, 54:9 (2009), 423–425
12.	Maksimov F.A., “Supersonic flow of bodies system”, Computer Research and Modeling, 5:6 (2013), 969–980 (In Russ.)
13.	Guvernyuk S.V., Maksimov F.A., “Supersonic flow past a flat lattice of cylindrical rods”, Computational Mathematics and Mathematical Physics, 56:6 (2016), 1012–1019
14.	B. W. Skews, M. A. Draxl, L. Felthun, M. W. Seitz, “Shock wave trapping”, Shock Waves, 8:1 (1998), 23–28
15.	Boiko V.M., Klinkov K.V., Poplavskii S.V., “Collective bow shock ahead of a transverse system of spheres in a supersonic flow behind a moving shock wave”, Fluid Dynamics, 39:2 (2004), 330–338
16.	Boiko V.M., Kiselev V.P., Kiselev S.P., Papyrin A.N., Poplavskii S.V., Fomin V.M., “Interaction of a shock wave with a cloud of particles”, Combustion, Explosion and Shock Waves, 32:2 (1996), 191–203
17.	J. D. Regele, J. Rabinovitch, T. Colonius, G. Blanquart, “Unsteady effects in dense, high speed, particle laden flows”, International Journal of Multiphase Flow, 61 (2014), 1–13
18.	D. Igra, J. Falcovitz, “Lift and drag on a sphere above ground by a sliding shock”, Proceedings of the Institution of Mechanical Engineers. Part G. Journal of Aerospace Engineering, 226:5 (2012), 550–560
19.	P. Sridharan, T. L. Jackson, J. Zhang, S. Balachandar, “Shock interaction with one-dimensional array of particles in air”, Journal of Applied Physics, 117 (2015), 1–18
20.	P. Sridharan, T. L. Jackson, J. Zhang, S. Balachandar, S. Thakur, “Shock interaction with deformable particles using a constrained interface reinitialization scheme”, Journal of Applied Physics, 119 (2016), 1–18
21.	L. T. Zhang, H. H. Shi, C. Wang, R. L. Dong, H. X. Jia, X. N. Zhang, S. Y. Yue, “Aerodynamic characteristics of solid particles’ acceleration by shock waves”, Shock Waves, 21 (2011), 243–252
22.	R. R. Nourgaliev, T. N. Dinh, L. Nguyen, T. G. Theofanous, “Treatment of particle collisions in direct numerical simulations of high speed compressible flows”, Proceedings of IUTAM Symposium on Computational Approaches to Disperse Multiphase Flow, eds. S. Balachandar, A. Prosperetti, Springer, Dordrecht, 2006, 247–259
23.	C. Lu, S. Sambasivan, A. Kapahi, H. S. Udaykumar, “Multiscale modeling of shock interaction with a cloud of particles using an artificial neural network for model representation”, Procedia IUTAM, 3 (2012), 25–52
24.	Bedarev I.A., Fedorov A.V., Fomin V.M., “Numerical analysis of the flow around a system of bodies behind the shock wave”, Combustion, Explosion, and Shock Waves, 48:4 (2012), 446–454
25.	Bedarev I.A., Fedorov A.V., “Computation of wave interference and relaxation of particles after passing of a shock wave”, Journal of Applied Mechanics and Technical Physics, 56:5 (2015), 750–760
26.	Bedarev I.A., Fedorov A.V., “Direct simulation of the relaxation of several particles behind transmitted shock waves”, Journal of Engineering Physics and Thermophysics, 90:2 (2017), 423–429
27.	Bedarev I.A., Fedorov A.V., Rylova K.V., “Application of detailed and reduced kinetic schemes for the description of detonation of diluted hydrogen-air mixtures”, Combustion, Explosion and Shock Waves, 51:5 (2015), 528–539
28.	V. M. Boiko, K. V. Klinkov, S. V. Poplavski, “On a mechanism of intraphase interaction in nonrelaxing two-phase flow”, Procedings of 11th International Conference on Methods of Aerophysical Research, ICMAR'2002 (Novosibirsk, 28 June — 3 July, 2002), Novosibirsk, 2002, 24–27
29.	I. A. Bedarev, A. V. Fedorov, “Mathematical modeling of the detonation wave and inert particles interaction at the macro and micro levels”, Journal of Physics: Conference Series, 894:1 (2017), 012008