# Multi-Resolution SPH Simulation of a Laser Powder Bed Fusion Additive Manufacturing Process
## 5 Conclusions  
This paper developed an efficient multi-resolution SPH framework for numerical simulation of the LPBF process. Analytical and experimental validations were carried out to ensure the correct working of the code in a liquid droplet and laser spot welding test. The numerical results demonstrate the capability of the presented method in simulating the melt pool dynamics and capturing the relevant physics in an LPBF process. By enabling dynamic particle refinement within the SPH simulation, the proposed approach reduced the calculation time remarkably and facilitated further explorations such as parameter study and fine discretization. The results from this improvement are promising: Showcased for a 2D single-track LPBF case, almost 35% of the computational cost of SPH was saved without using the optimized neighbor-list algorithm. Using an optimized neighbor-search scheme resulted in a 15% additional saving and led to a 2\(\times\) faster code with the same result. In brief, a 2D LPBF simulation of a 1-mm long track using SPH particles of 4 \(\upmu\)m diameter can now be completed in 90 min. The use of SPH for AM simulation is a young but rapidly growing area of research, which opens up multiple new avenues for future developments. It is of utmost importance to strengthen the numerical model validation against physical experiments where more measurement data are available. The proposed scheme was presented for a 2D LPBF simulation but can be easily extended to 3D applications. Furthermore, the achieved saving in runtime is convincing to incorporate the dynamic refinement algorithm into the parallel SPH codes running on both CPUs and GPUs. Figure 15: Runtime performance comparison. The proposed multi-resolution model (with optimized neighbor list) outperforms the other models by reducing approximately 50% of the computational cost of the reference model (i.e., single high resolution with \(dx=4\)\(\upmu\)m). The total number of SPH particles used by the multi-resolution model is 3668 at the beginning and 7658 at the end of the simulation, significantly lower than a total of 11,800 particle used by the reference model 1. **Supplementary Materials:** The following are available at [[https://www.mdpi.com/2076-3417/11](https://www.mdpi.com/2076-3417/11)]([https://www.mdpi.com/2076-3417/11](https://www.mdpi.com/2076-3417/11)) //7/2962/s1. The software used for producing the results in this paper follows the implementation given in the following public source codes: \"MFree IWF Cut Refine\" (link: [[https://github.com/iwf-inspire/mfree_iwf-ul-cut-refine](https://github.com/iwf-inspire/mfree_iwf-ul-cut-refine)]([https://github.com/iwf-inspire/mfree_iwf-ul-cut-refine](https://github.com/iwf-inspire/mfree_iwf-ul-cut-refine)) (accessed on 24 March 2021)) and \"MFree IWF Thermal\" (link: [[https://github.com/iwf-inspire/thermal_iwf](https://github.com/iwf-inspire/thermal_iwf)]([https://github.com/iwf-inspire/thermal_iwf](https://github.com/iwf-inspire/thermal_iwf)) (accessed on 24 March 2021)). **Author Contributions:** M.A. : conceptualization, methodology, software, validation, formal analysis, investigation, data curation, visualization, writing, original draft preparation, and writing, review and editing. C.L. : software, data curation. M.B. : supervision, revision, project administration. K.W. : supervision, revision, project administration, and funding acquisition. All authors read and agreed to the published version of the manuscript. **Funding:** The authors received no specific funding for this work. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Acknowledgments:** The authors thank [PERSON], [PERSON], and [PERSON] for their support and invaluable discussions during this research project. **Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; nor in the decision to publish the results.