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This paper presents an analytical investigation into the propagation of a normal shock wave in Van der Waals gas flow, employing the Buongiorno model. It explores the dynamics of this flow type under a shock wave, considering modified Rankine–Hugoniot (RH) jump conditions within the Buongiorno model framework. By solving the RH conditions, this study provides a solution for gas flows with varying nanoparticle concentrations, facilitating an examination of parameter variations under discontinuity. The abstract further emphasizes the graphical representation of velocity coefficient and pressure in adiabatic gas flow during a shock wave, considering compressive and exponential waves. The analysis accounts for nanoparticle concentration and non-ideal parameters. [ABSTRACT FROM AUTHOR]

In the present study, the phenomena of concentration and cavitation in the Riemann solution for the non-homogeneous hyperbolic system with logarithmic equation of state and magnetic field is analyzed. Firstly, we introduced new state variable for the velocity to modify the non-conservative system into conservative system and solved the Riemann problem for modified system constructively. Further, the Riemann solutions for the transport equations is investigated as pressure and magnetic field vanish. It is proved that the Riemann solution for the non-homogeneous hyperbolic system with logarithmic equation of state and magnetic field having two shock waves converges to the delta shock wave solution of the transport equations as pressure and magnetic field vanish. It is also proved that the Riemann solution for the non-homogeneous hyperbolic system with logarithmic equation of state and magnetic field having two rarefaction waves converges to the contact discontinuity solution of the transport equations as pressure and magnetic field vanish. [ABSTRACT FROM AUTHOR]

The present study uses the theory of weakly nonlinear geometrical acoustics to derive the high-frequency small amplitude asymptotic solution of the one-dimensional quasilinear hyperbolic system of partial differential equations characterizing compressible, unsteady flow with generalized geometry in ideal gas flow with dust particles. The method of multiple time scales is applied to derive the transport equations for the amplitude of resonantly interacting high-frequency waves in a dusty gas. These transport equations are used for the qualitative analysis of nonlinear wave interaction process and self-interaction of nonlinear waves which exist in the system under study. Further, the evolutionary behavior of weak shock waves propagating in ideal gas flow with dust particles is examined here. The progressive wave nature of nonresonant waves terminating into the shock wave and its location is also studied. Further, we analyze the effect of the small solid particles on the propagation of shock wave. [ABSTRACT FROM AUTHOR]