Mathematical Modeling of the Interaction of a Shock Wave with a Dense Cloud of Particles within the Framework of the Two-Fluid Approach

A parametric numerical study of the interaction of a shock wave with a dense cloud of particles is performed. The problem is solved in the framework of the two-fluid approach, with both the gas and dispersed phases are considered compressible media non-equilibrium in velocity and pressure. The system of governing hyperbolic equations was numerically solved using the Harten–Lax–van Leer method. The statement of the problem corresponds to the arrangement of natural experiments. The simulations revealed the main features of the process, such as the formation of transmitted and reflected waves, the movement of the cloud with a steep leading edge and a smeared tailing edge. The amplitudes of the transmitted and reflected waves, as well as the dynamics of the motion of the cloud, are compared to those observed in real experiments. The influence of the parameters of the equation of state of the dispersed phase and some properties of the computational algorithm on the characteristics of the process is examined.