The modeling of welding and additive manufacturing processes is a crucial area of industrial research when striving to improve components quality and to optimize manufacturing control. Indeed, direct energy deposition (DED) processes usually involve numerous phenomena acting across several spatial and temporal scales. In this context, the development of a new multi-scale modeling method for fluid interface tracking for generic DED processes is realised here. In this work we focus on the modeling of the shielding gas and drop interactions with the melt pool. The underlying dominant fluid phenomena are known to strongly influence the manufactured products. Using the finite element method and focusing on fluid mechanics, our model decomposes the system into two subdomains: the shielding gas and the falling metallic drop subdomain, and the metallic melt pool subdomain. The mechanics of each subdomain exhibits a different spatial and temporal scale, which justifies the use of an adapted and specific numerical method per subdomain. The Level-Set Method (LS) is used to model the drop falling through the shielding gas as it is adapted to the capture of highly deformable volumes in multiphase systems, but does not easily conserve mass and requires very small time steps. Furthermore, the Arbitrary Lagrangian-Eulerian Method (ALE) is used for the melt pool, as it can strongly conserve mass and interfaces but remains unsuitable to strong interface deformation phenomena, such as coalescence and/or splashing . However the long living melt pool interface can be considered to be quasi-stationary in the hydrodynamic regimes of industrial interest and the ALE method is therefore adapted. Lastly, hypotheses based on strong surface tension arguments are used to justify the coupling approach at the common LS-ALE fluid interface.