## 2 Materials and Methods
### Blast-Barrier Interaction  
Simulations of the interaction of incident overpressure waves and lightweight Lexan barriers were performed to gauge the effectiveness of simple modular structures to maintain \"Public Withdrawal Distance\" conditions where incident overpressures are already quite low. The 2D plane strain simulations were performed, given the assumption that multiple barriers could be placed alongside each other to minimize any edge effects. Further larger 3D cases of interest were explored to visualize and quantify the effects of lateral wraparound for standalone barriers.  
Figure 6 presents a \"cartoon\" depiction of these simulations with labeled boundary conditions. Again the lower boundary is taken as a symmetry plane to estimate ground interactions as perfect reflections. The upper and outer boundaries have pressure continuous non-reflecting conditions. The \(x=0\) plane is given a pressure load curve corresponding to the pressure tracer time histories derived from the free-field blast simulations (Figure 4). It is assumed that in the far field the incident waves are planar. A problem arose in earlier simulations where reflections off of the barrier reached the \(x=0\) plane a re-reflected back into the problem domain before the relevant dynamic events could conclude, causing undesirable boundary effects. It was found that the non-reflecting boundary conditions did not coexist well with the pressure load curves and thus caused numerical issues with the incident pressure waves. To avoid these issues, the barrier was placed at a distance \(d=\frac{1}{2}ct_{wave}\), where \(c\) is the speed of sound in air (approximately 343 m/s) and \(t_{wave}\) is the wavelength (in time) of the incident pressure wave, including positive and negative overpressure phases. Because the far-field waves are traveling at approximately the speed of sound, under these conditions the entire incident wave enters the domain before reflections can return to the boundary. Then, at time \(t_{wave}\), the pressure load curve boundary conditions are replaced with pressure continuous, non-reflecting conditions which eliminate the problem of reflection. The 3D simulations were performed in half-symmetry, so that the \(y=0\) plane was a symmetry plane and the \(y_{max}\) also had pressure continuous and non-reflecting conditions.  
Figure 5: Snapshots of the pressure wave from explosion of a detonation cord (**a**) 0.27 ms, (**b**) 0.7 ms, (**c**) 4.6 ms, and (**d**) 12 ms after programmed detonation.  
Various simple designs of mitigation barriers were studied. These included three major types: single fairing, compound fairing, and deep-roof (Figure 7). The barriers are all 1.2 m wide, and 3.8 cm thick. The total height varies with the length and angle of the fairing, but the bases are approximately 2.2 m high.  
Figure 6: A “cartoon” depiction of the setup of the blast-structure interactions simulations with materials and boundary conditions labeled. (Not to scale)  
Figure 7: Representative cross-sections of the types of mitigation barriers studied: (**a**) Single-fairing barrier. (**b**) Compound-fairing barrier. (**c**) Barrier with deep roof.  
All calculations utilized a graded mesh which was most refined in the area around the mitigation barrier. The 2D plane strain simulations ultimately contained around 1.2 million zones. The 3D simulations in general utilized a coarser mesh that was graded more aggressively, but still contained on the order of 10 million zones per simulation. Figures 8 and 9 show snapshots of the pressure fields in representative 2D and 3D simulations, respectively.  
Figure 8: Images from a representative 2D plane strain blast-barrier mitigation simulation: (**a**) at arrival time of wave at barrier. (**b**) During dynamic interaction event.  
Figure 9: Images from a representative 3D blast-barrier mitigation simulation: (**a**) at arrival time of wave at barrier. (**b**) During dynamic interaction event.