# Simulation of the Marangoni Effect and Phase Change Using the Particle Finite Element Method
## 1 Introduction
There, the yield stress reduces to zero in the fluid and powder regions. This means that the fluids can deform without any resistance, while the actual solid around the melt pool deforms elasto-plasticly. To our best knowledge, this is the only approach that incorporates both the convective flow in the melt pool (to obtain a realistic heat transfer) and the elasto-plastic solid (to obtain residual stresses) in one single simulation method. [PERSON] obtains excellent agreement with experimental results. The main drawbacks of this method are the complex and expensive coupling and the necessity of using the level set interface tracking, which further increases cost and complexity. As an alternative approach we use the Particle Finite Element Method (PFEM), which can be described as a Lagrangian FEM with frequent and automatic remeshing to avoid mesh distortions, even when simulating fluid flow [8]. The Lagrangian description allows the free surface to deform without the need for an interface tracking technique. The remeshing algorithm also includes the alpha shape technique [9], which makes the remeshing fully automatic even when large or chaotic deformations of the free surface occur (e.g., sloshing, breaking waves, splashing etc.). The main advantage of the PFEM is its proven capability to simulate fluids [10], thermo-fluids [11; 12], solids [13] and thermo-solids [14; 15; 16]. A further advantage is its robustness, as it is based on the mature FEM. It has also been shown that free surface deformation and surface tension can easily be included in the PFEM [17]. Many works focus on fluid-structure interaction (FSI) using the PFEM [18; 19; 20; 21], and one work that we are aware of includes phase change, in which [PERSON] et al. [22] simulate a core melt accident in a nuclear power station using the PFEM. Other than this, PFEM has not been utilized for phase change problems, despite its unique capability to simulate fluids and solids equally well. An extensive yet concise review on PFEM was recently publishedby [PERSON] et al. [17], where more details are explained and the different directions of recent research into PFEM are outlined. In this work, we aim to show the general suitability of PFEM in the context of additive manufacturing and welding at the mesoscale. The focus lies on the evolution of the melt pool and the physics that drive fluid flow, such as buoyancy and the Marangoni effect. Two main simplifications are made at this stage of our in-house PFEM code development. First, the solid material is replaced by a fluid with a momentum sink term that prevents further deformation upon freezing, instead of using an elasto-plastic solid. Secondly, all simulations use the 2D plain strain assumption. These simplifications are planned to be abandoned in the future to arrive at a simulation method that can simulate both phase change, convective flows in the melt pool and residual stresses in the solid in 3D. To demonstrate the suitability of the method for simulations with phase change and fluid dynamics, three validation test cases are presented and compared against the results from the literature. Known limitations of PFEM include the increased computational cost due to the frequent remeshing when compared with traditional FEM. Furthermore, with the connectivity changing constantly, parallelization of the solving process is difficult and is not included in the present code. Other than that, the limitations are those of traditional FEM. The novelty of this work lies in the utilization of PFEM for phase change, which has only been published once before and that with limited focus on the intricacies of latent heat and the transition from solid to fluid. Applications such as welding and additive manufacturing are characteristically sensitive to accurate representation of the phase transition. This work serves as validation for the simulation of welding and additive manufacturing applications in the future.