Hydrodynamics of shock propagation in homogeneous and inhomogeneous gases [HBNI Th269]

Abstract

This thesis addresses the fundamental problem of shock propagation in both homogeneous and inhomogeneous media, with a focus on scenarios initiated by either intense explosions or continuous energy input. Classical descriptions based on the Taylor–von Neumann–Sedov (TvNS) theory and the Euler equation are evaluated against molecular dynamics (MD) simulations. While these models capture certain qualitative features, significant discrepancies arise, particularly near the shock center, due to their neglect of dissipative effects such as heat conduction and viscosity.

By incorporating these effects through the Navier–Stokes equations, this work demonstrates substantial improvement in reproducing MD results in both two and three dimensions. Heat conduction emerges as the dominant mechanism influencing shock structure and scaling, while viscosity plays a secondary role. In inhomogeneous media, the Navier–Stokes framework reliably captures shock dynamics across varying degrees of spatial density variation, outperforming the Euler-based predictions which are accurate only at specific parameter values. New scaling laws and characteristic length scales arise in regimes where heat conduction dominates.

The thesis also explores driven shock propagation under continuous energy input, both localized and global, where the system is far from equilibrium. Even in these complex conditions, the Navier–Stokes solutions remain consistent with MD simulations, whereas the Euler equation fails to capture essential features of the evolving shock. These findings underscore the importance of including dissipative processes in hydrodynamic models of shock propagation.