# Benchmarking Numerical Methods for Impact and Cratering Applications
## 4 Results and Discussion
### 3D Impact Cratering Simulations  
This section presents qualitative comparisons of the 3D simulations from both FLAG and HOSS. Figure 5 shows the particle velocity evolution in both codes at 0.5 s and 1.0 s after impact from a normal impact with a velocity of 20 km/s. Overall, the shock wave propagates similarly; however, there are some distinct differences. Within the target itself, both FLAG and HOSS simulations show the highest velocity occurs at the front of the shock,  
Figure 4: 2D mesh resolution study for FLAG and HOSS for (**a**) 5 km/s normal impact and (**b**) 20 km/s normal impact. Figure 3: HOSS 3D Simulation domain for an aluminum on aluminum impact, where (**a**) shows the full simulation domain, and (**b**) displays a zoomed in region where the impactor is initialized. as expected. In both codes, the highest particle velocities in the entire system appear in the crater ejecta. While both codes capture the ejecta, the ability for discrete elements to break away from the mesh in the FDEM approach allows for much more ejecta to appear within the crater in the HOSS simulations. However, it is worth noting that a considerable part of the material located inside the crater, shown in Figure 5b,d, corresponds to the impactor material. Also for consideration, the SESAME EOS used in the FLAG simulations allows for material vaporization. The resulting vapor plume of ejected material is significantly underdense and thus not visible in these figures, which have been thresholded on density to remove the surrounding air. The FLAG simulations appear to show interactions between waves, resulting in some variations in the velocity profiles. This behavior can be attributed to the shock reflection, regions of compression and tension, and the pressure differential between the target and ambient air. These effects, while visible in the velocity plots, do not affect the crater formation in a significant way. Figure 6 presents similar particle velocity plots for an oblique impact with a velocity of 5 km/s. Similar to the normal impact case, the highest velocities occur in the crater ejecta. Figures 7a,b and 8a,b directly overlay the crater profiles for both the normal and oblique impacts just discussed. The HOSS target is shown in green, on top of the FLAG target, which is shown in orange. The impactors themselves are also distinguished, where red indicates the FLAG impactor and dark green indicates the HOSS impactor. Overall, the HOSS simulations tend to predict slightly deeper craters than FLAG. In general, this is a result of the higher amount of ejecta/fragmentation accounted for within the crater in HOSS. Some of this ejecta will not leave the crater, but rather settle into the bottom, producing a crater depth closer to what FLAG predicts. The predicted crater diameters are similar b  
Figure 5: Particle velocity from a \(2.0\times 10^{4}\) m/s normal impact at 0.5 s (**a,b**) and 1.0 s (**c,d**) as calculated from 3D simulations from FLAG and HOSS. (**a,c**) show particle velocity from 3D FLAG simulations, and (**b,d**) show particle velocity from HOSS simulations. The length of the horizontal green bar shown inside the crater represents a distance of 1000 m.  
Figure 6: Particle velocity from a \(5\times 10^{3}\) m/s 45\({}^{\circ}\) oblique impact at 0.5 s (**a,b**) and 1.0 s (**c,d**) as calculated from 3D simulations from FLAG and HOSS. (**a,c**) show particle velocity for 3D FLAG simulations, and (**b,d**) show particle velocity for 3D Hoss simulations. The length of the horizontal green bar shown inside the crater represents a distance of 1000 m.  
Figure 7: FLAG and HOSS simulations overlaid to show differences in the crater profiles from a 20 km/s normal impact (**a,b**) at 0.5 s and 1.0 s. The FLAG simulations are represented with an orange target material and red impactor. HOSS simulations are shown with a green target material and dark green impactor. (**c–f**) show 3D cross-sections of the impact scenario at 0.5 s and 1.0 s, where dark blue and cyan represent the target and impactor, respectively.