## 5 Conclusions  
The present manuscript lays out two open problems (namely, what incident overpressure and impulses are felt at given distances from relatively small hemispherical ground charges, and how well can certain types of boundaries mitigate the incident overpressure below a certain threshold). It then describes the results of numerical investigations to attempt to answer these questions. A major motivating factor in this research is the uncertainty in the available empirical curve fits (e.g., Kingery-Bulmash). The source of this uncertainty is twofold: there is relatively large error between some of the original data and the available fitting curves, and the original data were taken for explosions that were many orders of magnitude larger than the charges investigated here. A major unknown remains the extent to which the assumed scaling described by Equation 1 (distance by the cubed root of charge weight) holds as weights become small. The free-field blast simulations presented here indicate that the strong shock of the initial blast smoothed out within the distance simulated and continued to propagate near the sound speed. The slowing of the wave speed is in fact predicted by the empirical Swisdak (KB) equations, but there remains uncertainty into how this change in the physics regime and the shape of the waveform effects the ultimate impulse at different scales. A benefit of the direct numerical calculations is the availability of the full waveforms in time at all distances in the simulation domain; this was further leveraged in the subsequent mitigation simulations. The ultimate shape of the incident pressure wave may be another degree of freedom which is not fully captured by the \(K\) factor scaling. This may explain why the simulations agree well with the peak overpressure and the slope of the impulse curves from Swisdak, but seem to consistently predict slightly smaller impulse magnitudes. It was never assumed that the empirical curves would or should be \"exact\" predictors of incident overpressure and impulse for a given case. While this was a primary motivator for the present attempts for a direct physics-based prediction, it is also not assumed that these predictions will correspond exactly to any field case. Ultimately, the analyst, engineer, or responsible person must weigh uncertainty and risk to assess a given scenario. It is hoped that the present simulations (or others like them) could be used in uncertainty quantification efforts for blasts effects in wider-varying scenarios. The blast-barrier mitigation simulations presented here were also motivated by this desire to mitigate risk and uphold safety standards. The \"Public Withdrawal Distance\" or \"K328\" threshold was taken as a more-or-less arbitrary datum against which to gauge effectiveness. The findings of this work should not be used to indicate whether a given scenario is \"safe\", but rather to elucidate some of the physical mechanisms of mitigation in a dynamic blast event. Safety standards and acceptable risk vary from scenario to scenario; this work provides a methodology of analyzing the effectiveness of hypothetical tools to decrease risk. The specific barrier designs presented here were somewhat ad hoc and experimental. The fairings were designed to reflect incident waves and further mitigate overpressure from wraparound over the top. The double fairing was intended to facilitate mitigation further by partially reflecting the incident wave from the backward-facing fairing. The \"deep roof\" concept was designed to provide even further mitigation. Each subsequent design was found to enhance mitigation. The results indicate that these types of simple barriers are in fact effective at mitigating incident pressure and impulse. They do not, however, eliminate these risks. Ultimately, distance from the source is the surest form of mitigation.