# Multi-Resolution SPH Simulation of a Laser Powder Bed Fusion Additive Manufacturing Process
## 1 Introduction
A year ago, [PERSON] and [PERSON] [14] published a comprehensive review paper, where they cross-compare the individual capabilities of different methods in AM modeling and simulation. It turns out that most CFD codes for AM process simulation are based on either FVM or FEM tools. A few recent publications are mentioned in the following. [PERSON] and [PERSON] [15] combined a DEM powder-bed model with the melt pool CFD simulation using the package Flow-3D to model an LPBF process for IN718--a nickel-based superalloy. Ansys Fluent(r) is another commercial software employed by the AM community for PBF simulation, e.g., in [16; 17]. There are also some studies on solving the melt pool CFD equations by applying the open-source CFD software OpenFOAM, e.g., by [18]. Despite the excellent insights generated by these developments into the AM process simulation, the issue with their computational effort and parallelization capability is still an open question. Figure 1: Main physical processes in melt-pool region during powder bed fusion of LPBF. In addition to the broad class of mesh-based techniques, mesh-free particle methods have also been attempted in simulating the LPBF process. Specifically, a growing share of interest in using the Smoothed Particle Hydrodynamics (SPH) method for such applications can be noticed in the literature. In essence, SPH is a purely Lagrangian method, introduced by [PERSON] [19] and [PERSON] and [PERSON] [20], that can efficiently handle large deformations, violent free surface movements, and multiphase material boundaries. For the adoption of SPH in various multi-physics and manufacturing processes, see in [21; 22; 23; 24; 25]. These attractive features of SPH have convinced the AM research community to apply this method to laser-based processes such as LPBF. In 2016, [PERSON] and [PERSON] [26] demonstrated promising SPH results in simulating a laser spot welding process of aluminum and suggested that SPH can offer great potential for large-scale manufacturing simulations. [PERSON] et al. [27] presented a 3D SPH model of Tungsten Inert Gas (TIG) welding and validated their numerical results with experiments. The applicability of SPH to high-fidelity modeling of AM processes like LPBF is still being explored, but [PERSON] et al. [28] have made important headway in this area. They present a robust SPH framework for modeling a 2D LPBF track, where the most important thermal-mechanical-material aspects of the process were included. This method achieves excellent results at the powder scale but suffers from the calculation effort for simulations on a large scale or 3D. In another effort to develop SPH for AM simulations, [PERSON] and [PERSON] [29] proposed coupling of SPH and FEM for thermomechanical simulation of droplet-based AM processes. [PERSON] et al. [30] studied the material removal simulation in laser drilling and then extended this approach to 3D in [31]. However, they accounted only for the thermal aspect of the process. More recently, [PERSON] et al. [32] developed a GPU-accelerated 3D SPH model of LPBF. These authors demonstrate high-resolution SPH simulation using a discretization size of 1 \(\upmu\)m, which is the finest particle size to date. Despite these incremental improvements of SPH AM simulations from both algorithmic and computational perspectives, all recent developments overlook the topic of adaptivity. In other words, state-of-the-art SPH models of AM use a uniform resolution for their spatial discretization. Therefore, a significant amount of SPH calculation time is wasted on unimportant regions with no (or negligible) physical contribution to the solution. In an LPBF process, for instance, the mechanism decisive for the outcome of the process occurs under the laser beam and in the vicinity of the melt pool. Consequently, the need for an efficient SPH model of LPBF within a multi-resolution framework motivates this study. To fill the research gap identified above, an enhanced dynamic refinement algorithm via particle splitting is developed.