Laser Powder Bed Fusion is a transformative additive manufacturing technique with the potential to revolutionize the production of complex, high-performance components for demanding applications. However, process-induced defects – such as evaporation-driven porosity and lack of fusion – can compromise part quality and reliability. The intricate interplay between process parameters and part quality remains incompletely understood. To address these challenges, we develop a high-fidelity simulation approach for compressible–incompressible two-phase flows with rapid evaporation, aiming to gain deeper insight into melt pool evaporation dynamics and vapor/gas flow behavior. We propose an efficient, robust, and accurate sharp-interface numerical method based on the cut discontinuous Galerkin (cutDG) formulation. We employ face-based ghost-penalty stabilization to handle small cut elements, Saye’s quadrature rule for numerical integration on cut elements, and explicit time-stepping to solve the compressible Navier-Stokes equations. The condensed metal phase is modeled as incompressible via appropriate equations of state, and moving interfaces are treated using a face-based ghost-penalty extrapolation technique. Additionally, we leverage highly efficient matrix-free solvers based on the finite element library deal.II. A key challenge in our numerical scheme is incorporating interface jump conditions across the Knudsen layer in non-equilibrium thermodynamics. In this talk, we compare different strategies, including strong enforcement in the weak formulation, penalty approaches, Nitsche-type weighted flux methods, and explicit approximate Riemann solvers. We assess the effectiveness of these strategies in simplified yet representative melt pool evaporation scenarios, highlighting their applicability, advantages and limitations.