For several years, injection molding simulation softwares have proved to be indispensable tools to predict flow behavior through complex cavities. At first, these software were based on a 2.5D modeling that reveals to be very efficient in the case of simple, thin geometries. Nevertheless, these technologies are not able to describe realistic complex flows in a volumetric cavity, such as air entrapment or jet buckling. Multi materials simulation is yet much more critical in the way that only the filling rate can be computed, giving an imprecise idea of real interfaces' position and residual thicknesses. Therefore, several 3D simulation solutions appeared. However, considering the huge difference in terms of computational cost (especially for steady-isotropic meshes), a particular attention should be given to the employed numerical methods. In this paper, we propose an approach based on an improved level-set method with a multi-criteria adaptive meshing technology. Our level-set method uses an improved scheme that includes Hamilton-Jacobi reinitialization and reduces resolution time. Furthermore, it provides the high interface accuracy needed for multi-materials applications and complex flows. The error estimator technology provides a fully automatic and optimized metric to generate the part discretization. The mesh is refined only where high precision is needed (close to the interfaces, in high shear regions and close to the boundaries) in order to correctly describe strong coupling between different phases, heat transfers and rheology. Generated mesh is highly anisotropic and enables to run computations with much less nodes than an isotropic mesh with equivalent accuracy. Numerical results are also compared to an experimental industrial part. This part, obtained by water assisted injection molding, shows a complex geometry with narrow pin-points and complex fluid interfaces. Results show good agreement with experiments.