# Modification of Method of Large Particles for Research of Currents of Gas-Suspensions

D.S. Grishchenko, Yu.M. Kovalev, E.A. KovalevaIn this work a modification of the large particles method is given applications the study gas-suspensions flows. It is shown that the proposed modification of the large particlesFull text

method allows to carry out calculations of behavior of shock waves in gas-suspensions without insertion of artificial viscosity in an explicit form. It allows to avoid distortion of a physical picture of the gas-suspension flow connected with existence of the ostsillyation taking place at distribution of shock waves in non-homogeneous medium. In this work it was established that for carrying out of calculations of distribution of shock waves in gas-suspensions with large Courant the problem numbers an explicit modification of a large particles method can be used. It allow to reduce time of calculation of the problem and to avoid carrying out difficult iterative procedures inherent in implicit difference schemes. It was shown that the modification of large particles method offered in this work is effective and allows to carry out calculations for even strong shock waves in gas-suspensions.

- Keywords
- numerical method; mathematical model; gas-suspensions; conservation laws; shock waves; Courant number.
- References
- 1. Kuropatenko V.F. New Models of Continuum Mechanics. Journal of Engineering Physics and Thermophysics, 2011, vol. 84, no. 1, pp. 77-99. DOI: 10.1007/s10891-011-0457-0

2. Grishin A.M., Kovalev Yu.M. About Strengthening of Shock Waves at Their Interaction with the Front of Forest Fire. Doklady Akademii nauk, 1990, vol. 312, no. 1, pp. 50-54. (in Russian)

3. Kovalev Yu.M., Pigasov E.E. Mathematical Model of a Gas-Suspension with Chemical Transformations in Approach of Pair Interactions. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2014, vol. 7, no. 3, pp. 40-49. DOI: 10.14529/mmp140304 (in Russian)

4. Kovalev Yu.M., Kovaleva E.A. A Mathematical Study of the Conservation Equation for Two-Phase. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2014, vol. 7, no. 2, pp. 29-37. DOI: 10.14529/mmp140202 (in Russian)

5. Kovalev Yu.M., Kovaleva E.A. The Analysis of Some Numerical Methods Application for the Solvation of Multicomponents Media Mechanics. Bulletin of the South Ural State University. Series: Computer Technologies, Automatic Control & Radioelectronics, 2014, vol. 14, no. 1, pp. 57-62. (in Russian)

6. Belotserkovskiy O.M., Davydov Yu.M. Metod krupnykh chastits v gazovoy dinamike [Method of Large Particles in Gas Dynamics]. Moscow, Nauka, 1982. 392 p.

7. Grishin Yu.A. New Schemes of a Method of Large Particles and Their Use for Optimization of Air-Gas Paths of Engines. Matematicheskoe modelirovanie [Mathematical Models and Computer Simulations], 2002, vol. 14, no. 8, pp. 51-55. (in Russian)

8. Kruglikov B.S., Kutushev A.G. Attenuation of Shock Waves by Shielding Grids. Combustion, Explosion, and Shock Waves, 1988, vol. 24, no. 1, pp. 106-109. DOI: 10.1007/BF00749083

9. Kruglikov B.S., Kutushev A.G. Attenuation of Air Shock Waves by Layers of Dusty Gas and Lattices. Journal of Applied Mechanics and Technical Physics, 1988, vol. 29, no. 1, pp. 48-53. DOI: 10.1007/BF00909690

10. Ivandaev A.I., Kutushev A.G. Numerical Research of non-Stationary Wave Currents of Gas-Suspensions with Allocation of Borders of Two-Phase Areas and Contact Gaps in the Bearing Gas. Numerical Methods in Mechanics of Continuous Environments, 1983, vol. 14, no. 6, pp. 47-60. (in Russian)