# Modeling the dynamics of solid particles in the cloud formed at ground explosion booster

### Abstract

This work deals with the modelling of dynamics of solid soil particles in the cloud formed by ground explosion. Simulation for ground blast carrier phase is based on three-dimensional unsteady filtered Navier-Stokes equations for simulation and the dispersed phase particles is carried out by the equation of motion with regard explosion force. A numerical algorithm for solving the dynamics of the solid particles in the cloud formed by the explosion of the rocket carrier ground. The numerical solution of the equations for the motion of the particles using the finite difference method using a penta - diagonal matrix. To approximate the convective and diffusive terms of the equations the fourth order accuracy scheme O(t^3, h^4) is used. The pressure equation is solved by the Fourier method, in combination with the matrix sweep methods. A numerical algorithm is implemented in the form of programm code in Fortran. The results obtained by changing the trajectories of particles of time depending on the initial turbulent energy carrier rocket explosion (СR) allows to calculate accurately the dynamics of solids in time and determine their trajectory.### References

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[2] Edited by Avdeev F.A. Technical rules of blasting on the surface. - M.: Nedra, 1972. – 239 p.

[3] Edited by Orlenko L.P. Explosion Physics. - M.: FIZMATLIT, 2002. - T. 1. - 832 p.

[4] Edited by Sominskij E.M. Operation of Nuclear Weapons. - M.: Voenizdat, 1965. – 679 p.

[5] Yakush S.E. Hydrodynamics and burning of gas and two-phase emissions in an open atmosphere: dis. ... doctor of physico- mathematical Sciences: 01.02.05. - Moscow, 2000. – 336 p.

[6] Biryukov G. P., Smirnov V. I. Elements of design theory of rocket space systems. - M.: MAI, 2003. – 288 p.

[7] Lavrentiev M. A., Shabat B. V. Problems of hydrodynamics and their mathematical models. - M.: Nauka, 1973. – 416 p.

[8] Zhumagulov B.T., Zhakebayev D.B., Abdibekova A.U. The decay of mhd turbulence depending on the conducting properties of environment // Magnetohydrodynamics. - 2014. - No2(50). - P. 121–138.

Published

2017-11-24

How to Cite

АСКАРОВА, З. Б. et al.
Modeling the dynamics of solid particles in the cloud formed at ground explosion booster.

**KazNU Bulletin. Mathematics, Mechanics, Computer Science Series**, [S.l.], v. 89, n. 2, p. 41-54, nov. 2017. ISSN 1563-0277. Available at: <http://bm.kaznu.kz/index.php/kaznu/article/view/352>. Date accessed: 17 aug. 2018.
Section

Mathematics

**Keywords:**modeling, particles, explosion, booster, finite-difference method, turbulence