Additive manufacturing (AM) is becoming increasingly popular on an industrial level, as it allows for components to be designed much more freely than with conventional methods. For example, additive manufacturing can be used to produce topologically optimized parts or components with internal structures such as cooling channels. The most widely used process is Selective Laser Melting (SLM), a process in which a powder bed is applied and melted layer by layer to create the component generatively. At the time of this work, components manufactured with additive manufacturing methods are, however, significantly more expensive than conventionally manufactured components. This is in large extent due to a comparatively high scrap rate, which is taken into account in the price calculation. The sources for poor part quality are on the part level, where thermal distortion leads to scrap, as well as on powder level, where incomplete melting or an unstable melt pool can affect the inner structure of the component in a negative way. In this thesis, the development of the melt pool at the powder level is considered in detail in order to predict the melt pool geometry as well as the cooling. In order to predict flow conditions in the melt pool, the mesh-free Smoothed Particle Hydrodynamics (SPH) method is used. With this method, the melting of the solid powder and the rapidly changing free surfaces of the melt pool can be represented in a numerically efficient way. This follows from the fact that in such multi-phase systems (solid powder - liquid melt - gaseous atmosphere) the description of the interfaces is based on the particle distribution without the need for additional surface meshing or detection. By neglecting the gas phase and the mechanical deformation in the powder bed, a performant method is created, which captures the decisive thermal and fluid mechanical phenomena during melt pool development. The second focus is the implementation of the incompressible SPH method (ISPH). The implicit calculation of the particle pressures results in significant advantages in terms of stability and computing time compared to the explicit, weakly compressible SPH method (WCSPH), which are discussed in this thesis. This is possible due to the parallel solution of the equation system on a graphics card (GPU, Graphics Processing Unit) based on the PARALUTION library and the DualSPHysics Framework. The performance of the presented framework will be demonstrated on academic examples from fluid dynamics as well as on the example of the SLM powder bed. Comparisons with experimental and simulative results are carried out. Despite a resolution of 3 micrometers, the simulation time of a laser transition (0.8 mm length) with the incompressible SPH method is only 3.5 to 11.3 hours, simulated on a mid-range graphics card (NVIDIA GTX 1660 Ti).