The present work investigates the dynamics and stability of shock waves in granular gases. The problem was modelled for a piston propagating into a system of disks that can undergo inelastic collisions if an impact threshold is exceeded. The model was addressed numerically at the microscopic and macroscopic levels. The molecular dynamics methodology employed the Event-Driven Molecular Dynamics method, and the continuum model was formulated using the Navier-Stokes equations for granular gases with the transport terms of Jenkins and Richman and a modified cooling rate term. The inviscid steady state shock structure was derived and analyzed. The results indicated that a relaxing shock structure is expected for sufficiently strong shock waves. Beyond this limit the structure was shown to be independent of the initial energy, a finding similar to the strong shock approximation in molecular gases. One-dimensional simulations demonstrated that the molecular dynamics and continuum models yield similar evolutions and structures of the shock wave, validating the continuum description of this study. Two-dimensional results showed that sufficiently strong shock waves can exhibit multi-dimensional instability with high density non-uniformities and convective rolls within the structure, with the size of instabilities shown to scale with the relaxation length of the shock structure. Instabilities were observed with the continuum description only with the inclusion of statistical fluctuations to density mimicking the molecular model. The cases that were unstable were shown to be in a regime whereby statistical fluctuations can become important, following the description for this regime by Bird. Based on these findings, it is proposed that unstable shock behaviour can be observed for highly dissipative shock waves that yield short relaxation length scales, where fluctuations become important. The current work may shed light on unstable shock behaviour observed in dissipative gases, having implications for both granular media and molecular gases.

The current study addresses the stability of shock waves propagating through dissipative media, analogous to both granular media and molecular gases undergoing endothermic reactions. In order to investigate the stability, a simple molecular dynamics model was developed to observe shock waves and their structures with the inclusion of energy dissipation. For this, an Event Driven Molecular Dynamics model was implemented in a 2D environment, where a molecule is represented by a disk. The simulations addressed the formation of a shock wave in a gas by the sudden acceleration of a piston. Inelastic collisions were assumed to occur only if an impact velocity threshold is surpassed, representing the activation energy of the dissipative reactions. Parametric studies were conducted for this molecular model, by varying the strength of the shock wave, the activation threshold and the degree of inelasticity in the collisions. The resulting simulations showed that a shock structure does indeed become unstable with the presence of dissipative collisions. This instability manifests itself in the form of distinctive high density non-uniformities behind the shock wave, which take the form of convective rolls. The spacing and size of this ``finger-like" unstable pattern was shown to be dependent on the degree of inelasticity, the activation energy, and the strength of the driving piston. The mechanism responsible for the instability was addressed by studying the time evolution of the material undergoing the shock wave compression and further relaxation. It is found that the gas develops the instability on the same time scales as the clustering instability in homogeneous gases, first observed by Goldhirsch and Zanetti in granular gases. This confirmed that the clustering instability is the dominant mechanism.

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The current study addresses the stability of shock waves propagating through dissipative media, analogous to both granular media and molecular gases undergoing endothermic reactions. In order to investigate the stability, a simple molecular dynamics model was developed to observe shock waves and their structures with the inclusion of energy dissipation. For this, an Event Driven Molecular Dynamics model was implemented in a 2D environment, where a molecule is represented by a disk. The simulations addressed the formation of a shock wave in a gas by the sudden acceleration of a piston. Inelastic collisions were assumed to occur only if an impact velocity threshold is surpassed, representing the activation energy of the dissipative reactions. Parametric studies were conducted for this molecular model, by varying the strength of the shock wave, the activation threshold and the degree of inelasticity in the collisions. The resulting simulations showed that a shock structure does indeed become unstable with the presence of dissipative collisions. This instability manifests itself in the form of distinctive high density non-uniformities behind the shock wave, which take the form of convective rolls. The spacing and size of this ``finger-like" unstable pattern was shown to be dependent on the degree of inelasticity, the activation energy, and the strength of the driving piston. The mechanism responsible for the instability was addressed by studying the time evolution of the material undergoing the shock wave compression and further relaxation. It is found that the gas develops the instability on the same time scales as the clustering instability in homogeneous gases, first observed by Goldhirsch and Zanetti in granular gases. This confirmed that the clustering instability is the dominant mechanism.

The current study addresses the stability of shock waves propagating through dissipative media, analogous to both granular media and molecular gases undergoing endothermic reactions. In order to investigate the stability, a simple molecular dynamics model was developed to observe shock waves and their structures with the inclusion of energy dissipation. For this, an Event Driven Molecular Dynamics model was implemented in a 2D environment, where a molecule is represented by a disk. The simulations addressed the formation of a shock wave in a gas by the sudden acceleration of a piston. Inelastic collisions were assumed to occur only if an impact velocity threshold is surpassed, representing the activation energy of the dissipative reactions. Parametric studies were conducted for this molecular model, by varying the strength of the shock wave, the activation threshold and the degree of inelasticity in the collisions. The resulting simulations showed that a shock structure does indeed become unstable with the presence of dissipative collisions. This instability manifests itself in the form of distinctive high density non-uniformities behind the shock wave, which take the form of convective rolls. The spacing and size of this ``finger-like" unstable pattern was shown to be dependent on the degree of inelasticity, the activation energy, and the strength of the driving piston. The mechanism responsible for the instability was addressed by studying the time evolution of the material undergoing the shock wave compression and further relaxation. It is found that the gas develops the instability on the same time scales as the clustering instability in homogeneous gases, first observed by Goldhirsch and Zanetti in granular gases. This confirmed that the clustering instability is the dominant mechanism.