Shock Wave Dynamics in Non-Ideal Gases

Shock waves represent supersonic disturbances that induce abrupt changes in pressure, density and velocity as they propagate through a medium. In non-ideal gases, intermolecular forces and finite molecular volumes give rise to deviations from the ideal gas law, thereby altering shock structure, compression ratios and post-shock thermodynamic states. Real-gas equations of state, such as the van der Waals model, introduce additional parameters that modulate wave thickness, shock speed and the coupling between leading discontinuities and trailing rarefactions or contact waves. Mathematical tools—including singular surface theory, truncated transport equations and self-similarity techniques—have yielded exact and approximate solutions for converging and diverging shocks in spherical, cylindrical and planar geometries. These advances underpin accurate modelling of high-pressure phenomena in inertial confinement fusion, detonation propulsion, astrophysical blast waves and materials science, where real-gas effects critically influence energy deposition, shock focusing and stability under extreme conditions.

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Shock Wave Dynamics in Non-Ideal Gases publication trend

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Technical terms

Shock wave: A propagating disturbance characterised by near-instantaneous jumps in flow variables that travels faster than the local speed of sound.

Non-ideal gas: A gas whose pressure–volume–temperature relationship deviates from the ideal gas law due to intermolecular attractions and finite molecular volume.

Similarity solution: A reduction of governing partial differential equations to ordinary differential equations by exploiting scaling symmetries, yielding self-similar flow profiles.

Van der Waals equation of state: A real-gas model incorporating parameters for molecular attraction (A) and excluded volume (B) to describe non-ideal pressure–volume–temperature behaviour.

Rankine–Hugoniot conditions: The conservation relations across a shock front that determine jumps in pressure, density and velocity between pre-shock and post-shock states.

Adiabatic index (γ): The ratio of specific heats at constant pressure and constant volume, governing compressibility and shock strength in a gas.

References

1. Similarity solutions for strong shocks in a non-ideal gas. Mathematical Modelling and Analysis (2012).
2. Kinematics of a shock wave of arbitrary strength in a non-ideal gas. Quarterly of Applied Mathematics (2009).
3. Detonation in van der Waals Gas. Fluids (2023).