# Benchmarking Numerical Methods for Impact and Cratering Applications
## 5 Conclusions  
This work presented a code-to-code comparison between a modern hydrodynamics code, FLAG, and an FDEM code, HOSS. This study successfully benchmarked both numerical methods for impact cratering simulations. This work explored multiple Al-Al impact scenarios, in both 2D and 3D, in order to evaluate the differences each numerical method had on the overall solution obtained. Both numerical methods produced qualitatively similar velocity contours and predicted similarly sized craters in the early stages of crater formation. From a quantitative point of view, both codes produced maximum pressures with lower relative errors than previously published results of the same simulations using different hydrocodes. In addition, both FLAG and HOSS demonstrated abilities to incorporate strength and damage processes into impact simulations, key components to modeling strength-dominated crater formation. One notable difference in these two approaches is the meshing strategies used. FLAG employs an ALE strategy that allows for deformation of the mesh and also transport of material through the mesh, but ultimately the mesh remains connected and cannot break apart. Conversely, HOSS allows for elements in the mesh to both deform and break away from the initial configuration, disconnecting along element edges. Partially as a result of these mesh strategies, primary differences in results are apparent in damage evolution and computational expense. HOSS shows more damage evolution in the system, particularly at early times, resolved to a level in which individual cracks can form and evolve. This meshing strategy also allows for more distributed ejecta coming from the impact crater. While FLAG does not have the ability to resolve damage in the same way at early simulation times, it is more computationally efficient, requiring fewer cores and less computation time to achieve the similar if not longer simulation times. At later times, the extent of damage in FLAG simulations more closely resembles the extent of damage in HOSS simulations, as shown in Appendix A. Overall, both approaches appropriately capture the impact cratering process at different impact velocities and impact trajectories. Major aspects of the cratering process,  
Figure 14: Continuum and discrete damage measures from a \(5\times 10^{3}\) m/s normal impact in which strength and damage are considered in the material models. Snapshots are shown at 0.4 s (**a,b**) and 0.8 s (**c,d**) and are calculated from 3D simulations from FLAG and HOSS. (**a,c**) show continuum damage from 3D FLAG simulations, and (**b,d**) show discrete damage from 3D HOSS simulations. The length of the horizontal green bar shown inside the crater represents a distance of 1000 m.  
including shock wave propagation, shock pressure decay, and crater profiles, are captured with reasonable accuracy determined through comparison between the codes and to previous published simulated data. Conceptualization, W.K.C., B.E., C.S.P., C.L., Z.L., E.E.K., E.R. and A.H.; methodology, W.K.C. and B.E. ; software, W.K.C. and B.E. ; validation, W.K.C. and B.E. ; formal analysis, W.K.C., B.E., C.S.P., C.L., Z.L., E.E.K., E.R. and A.H.; writing--original draft preparation, W.K.C., B.E., E.R. and A.H.; writing--review and editing, W.K.C., B.E., C.S.P., C.L., Z.L., E.E.K., E.R. and A.H.; visualization, W.K.C., B.E., E.R. and A.H.; supervision, C.S.P., E.R. and A.H. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The data presented in this study are subject to release restrictions and are not publicly available. Requests for these data can be made to the corresponding author(s). We.K.C. acknowledges the Advanced Simulation and Computing (ASC)--Integrated Codes (IC) program through the Lagrangian Applications Project (LAP) at Los Alamos National Laboratory (LANL) and the ASC--Threat Reduction (TR) program at LANL. B.E. would like to thank the LANL Institutional Computing program for their support in generating these data.