Solidification cracking is a common problem in laser-based powder bed fusion (PBF-LB/M) of many metallic alloys of industrial relevance, such as Ni-based superalloys. A common strategy of reducing crack densities is to increase heat input by, e.g., the means of a secondary laser beam. However, increased heat input can lead to the development of process defects that are, e.g., keyhole-instability-induced, or surface-tension-force-induced. These defects often only develop after processing multiple tracks or even several layers. Therefore, physics-based models capable of accurately resolving melt pool fluid flow, including evaporation and keyhole formation are needed, not only at the scale of single scan tracks, but also going towards part scale. To enable such simulations, PBF-LB/M is modelled using a compressible multiphase fluid mechanical model. The compressible Navier-Stokes Equations, in combination with a suitable equation of state based on the Tait equation and a porous bed model for the mushy zone are used to predict an isotropic, thermoelastic stress analogue during solidification and within the solid material. Therefore, no additional partial differential equation needs to be solved, making the residual stress model computationally cheap (essentially, “for free”). This novel model enables the prediction of residual stresses and thus defects such as solidification cracking, while at the same time fully resolving the fluid mechanical process, making it interesting for simulation-based process optimization within a single model. Furthermore, this approach enables the application of solidification cracking criteria that require information on both shrinkage and stress evolution within the solid material, as well as the feeding of liquid material. The set of equations is solved using the Finite Volume method within the open-source framework OpenFOAM. Simulation results of applying the model to the simulation of a PBF-LB/M process on the scale of several tracks and layers are shown. Additionally, an insight into currently ongoing work on incorporating a grain growth model into the here presented multiphysical model is given.