Methodology of numerical research of reflection of a shock wave from a solid surface in a dusty environment

Abstract

In this work, a mathematical model of the dynamics of a heterogeneous mixture was used to study shock-wave flows in dusty media. The heterogeneous mixture was assumed to consist of two components: the carrier component – gas and the dispersed component – solid particles. For each of the components of the medium, the complete system of equations of the continuum dynamics was solved, which included the continuity equation, the conservation equations for the spatial components of the momentum, and the energy conservation equation. The carrier medium was described as a viscous, compressible, heat-conducting gas. The mathematical model of the inter-component force interaction, which included the Stokes force, the dynamic force of Archimedes, the force of the added masses, as well as the heat exchange between the components of the mixture. The system of equations was solved using the Mac-Cormack explicit second-order finite-difference method using the splitting scheme in spatial directions. To obtain a monotonous solution to the grid function, a numerical solution correction scheme was applied, which allowed reducing local maxima and increasing local minima of the desired functions – overcoming numerical oscillation. Using the software code implementing the numerical algorithm for solving the equations of a mathematical model, the effect of particle dispersity on gas parameters during the reflection of a shock wave from a surface in a dusty medium was studied.