Microscopic defects may occur during powder-bed fusion processes which originate from molten pool instabilities. To investigate this issue, a numerical model focusing on the interaction between laser and powder, melt pool formation and thermodynamics effects is on development. The approach used in the model assumes an incompressible Newtonian flow based on an enthalpy-porosity method for solid/liquid metal transition. The jump conditions at the liquid-solid interface for the energy equation are included through the modification of the enthalpy which incorporates the latent heat of fusion. A Carman-Kozeny porosity method is implemented in the momentum equation to penalize the flow in the solid phase. Molten flows are driven by natural and thermocapillary convection which are modelled using Boussinesq approximation and Marangoni free-surface stresses respectively. This numerical model is implemented within a Discontinuous Galerkin (DG) finite element formulation which ensures high order convergence on unstructured mesh [1]. In this work, a sharp interface method is integrated into the three dimensional high-order DG code Argo [2] to capture the free surface of the melt pool. This method allows to keep the high-order of convergence of the DG scheme even near the interface not conforming with the mesh. This is essential to capture the thermo-hydrodynamics phenomena during powder-bed fusion with accuracy. Current effort is dedicated to improve the model accounting for physical phenomena such as surface tension and vaporization. The main purpose is to investigate the occurrence of discontinuities in fused powder tracks depending on material properties and process parameters.