TY - GEN

T1 - Numerical implementation of traveling-wave solutions in heterogeneous media with two pressures taking into account the volume concentration of particles

AU - Fedorov, A. V.

AU - Bedarev, I. A.

PY - 2017/10/26

Y1 - 2017/10/26

N2 - The motion of shock waves through a mixture of gas and fine solid particles is studied using a model of the mechanics of heterogeneous media taking into account the difference in phase velocities, the intergranular pressure of the particles, and their finite volume concentration. The equation of state includes the volume concentration of particles. For this model, we have analytically and numerically studied the question of what types of strong discontinuities (frozen, dispersive, frozen-dispersive, two-front) exist and are stable in the dispersed medium considered and under what conditions they occur. A numerical solution of initial-boundary-value problems is obtained using a third-order TVD scheme for approximation in space and a five-order Runge-Kutta scheme for time approximations. The corresponding solutions in the class of traveling waves are calculated. A map of flow regimes in the form of shock waves is constructed, which makes it possible to determine the final velocity of the mixture behind the shock wave as a function of its initial velocity and the relative mass concentration of the gas phase. The above-mentioned stationary solutions for various types of shock waves are found numerically. Their stability is investigated by solving the Cauchy problem for nonstationary one-dimensional equations of the mechanics of heterogeneous media.

AB - The motion of shock waves through a mixture of gas and fine solid particles is studied using a model of the mechanics of heterogeneous media taking into account the difference in phase velocities, the intergranular pressure of the particles, and their finite volume concentration. The equation of state includes the volume concentration of particles. For this model, we have analytically and numerically studied the question of what types of strong discontinuities (frozen, dispersive, frozen-dispersive, two-front) exist and are stable in the dispersed medium considered and under what conditions they occur. A numerical solution of initial-boundary-value problems is obtained using a third-order TVD scheme for approximation in space and a five-order Runge-Kutta scheme for time approximations. The corresponding solutions in the class of traveling waves are calculated. A map of flow regimes in the form of shock waves is constructed, which makes it possible to determine the final velocity of the mixture behind the shock wave as a function of its initial velocity and the relative mass concentration of the gas phase. The above-mentioned stationary solutions for various types of shock waves are found numerically. Their stability is investigated by solving the Cauchy problem for nonstationary one-dimensional equations of the mechanics of heterogeneous media.

UR - http://www.scopus.com/inward/record.url?scp=85034249169&partnerID=8YFLogxK

U2 - 10.1063/1.5007448

DO - 10.1063/1.5007448

M3 - Conference contribution

AN - SCOPUS:85034249169

VL - 1893

T3 - AIP Conference Proceedings

BT - Proceedings of the XXV Conference on High-Energy Processes in Condensed Matter, HEPCM 2017

A2 - Fomin, null

PB - American Institute of Physics Inc.

T2 - 25th Conference on High-Energy Processes in Condensed Matter, HEPCM 2017

Y2 - 5 June 2017 through 9 June 2017

ER -