Propagation of strong shock waves in a non-ideal gas

On kinematics of one‐dimensional radially symmetric shocks in non‐ideal reacting gases

“…Taking into account the complexity of the system, it gives rise to the difficulty in analyzing relevant wave patterns. The Guderley's solution for a blast wave with similarity variable 𝜉 = x∕(−t) 𝛿 3 along with 𝜉 ∈ [1, ∞) and t ∈ (−∞, 0] is taken into account as follows [22]:…”

“…Taking into account the complexity of the system, it gives rise to the difficulty in analyzing relevant wave patterns. The Guderley's solution for a blast wave with similarity variable $$$ \xi =x/{\left(-t\right)}^{\delta_3} $$$ along with $$$ \xi \in \left[1,\infty \right) $$$ and $$$ t\in \left(-\infty, 0\right] $$$ is taken into account as follows [22]: $$$$ \rho ={\rho}_0\mathcal{S}\left(\xi \right),\kern9.24774pt u=\frac{\delta_3x}{t}\mathcal{U}\left(\xi \right),\kern9.24774pt p={\rho}_0{\left(\frac{\delta_3x}{t}\right)}^2\mathcal{P}\left(\xi \right),z={\left(\frac{\delta_3x}{t}\right)}^2\mathcal{Z}\left(\xi \right),\kern9.24774pt r=\frac{{\delta_3}^2{x}^2}{t^3}\mathcal{R}\left(\xi \right). $$$$ Using equations () in equations (), we obtain the following system of ordinary differential equations …”

Kinematics of spherical shock waves in an interstellar ideal gas clouds with dust particles

“…12 Toward the study of shock phenomena, we mention the works by many researchers. [13][14][15][16][17][18][19] Across the wave (a wave may be considered as the moving surface), some of the flow variables or their derivatives, describing the material medium, undergo certain kinds of discontinuities that are carried along by the surface. On both sides of the discontinuity surface, the flow variables or their derivatives are connected by a relation, which is known as compatibility condition.…”

Propagation of a spherical wave in elastoplastic medium with complex equations of state

“…In [3][4][5][6], the propagation of a strong spherical shock wave in a dusty gas with or without self-gravity effects in the case of isothermal and adiabatic flows was investigated. It is assumed that the dusty gas is a mixture of fine solid particles and ideal gas.…”