In the present paper, we investigated the problem of the propagation of blast waves governed by a nonhomogeneous quasilinear hyperbolic system of partial differential equations (PDEs), describing one-dimensional unsteady motion with generalized geometries in a real gas flow (van der Waals gas) in which the influence of the dust particles is significant. An efficient analytical approach has been used to the governing hyperbolic system with respect to the Rankine-Hugoniot (RH) conditions to obtain an exact solution in terms of flow parameters density, velocity and the pressure, which exhibits space-time dependence. Further, an analytical expression for the total energy influenced by real gas effects (consisting of non-ideal gas and small solid dust-laden particles) is derived. The results obtained significantly explore the effect of dust-laden particles on the propagation of blast waves in a van der Waals gas.
The Riemann problem for a van der Waals fluid with entropy rate admissibility criterion—Nonisothermal case