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JOURNALS // Applied Mathematics & Physics // Archive

Applied Mathematics & Physics, 2019, Volume 51, Issue 4, Pages 565–576 (Mi pmf35)

MATHEMATICAL PHYSICS. MATHEMATICAL MODELING

Numerical modeling of reflection of a shock wave in a gas suspension for various parameters of a dispersed component of a dusted medium

D. A. Tukmakov

IME - Deoartment of FIC KazanSC of RAS

Abstract: In this paper, the process of reflection of a direct shock wave from a solid surface numerically modeled. The system of equations of dynamics of both the carrier medium and the dispersed component included the continuity equation, the momentum conservation equation, and the energy conservation equation. The mathematical model took into account the viscosity, compressibility and thermal conductivity of the carrier medium, the interaction force between component, which includes the Stokes force, the dynamic force of Archimedes, the strength of the attached masses; also the mathematical model took into account inter-component heat transfer. The numerical solution carried out using an explicit finite-difference method, followed by the application of a nonlinear correction scheme for the numerical solution. In the problem under study, a shock wave propagates from a pure gas and moves through a dusty medium with subsequent reflection from a solid surface. The calculation results of the parameters of the reflected shock wave in a dusty medium compared with a numerical solution for a homogeneous viscous gas and an analytical solution known from the literature. The regularities of the effect of the parameters of the dispersed phase on the intensity of a courageous shock wave revealed.

Keywords: mathematical modeling of physical processes, multiphase media, Navier-Stokes equation, shock waves.

UDC: 533.2, 51-72

DOI: 10.18413/2075-4639-2019-51-4-565-576



© Steklov Math. Inst. of RAS, 2026