Three-dimensional (3-D) computational modeling approach of mold insert injection molding is developed to build a more robust and complete simulation solution of polymer melt flow in a mold cavity considering the effects of process conditions oil non-isothermal, viscous, compressible and non-Newtonian flow behavior. The changes it? viscosity and density in the polymer melt flow are successfully modeled within a volume of fluid (VOF) method coupled with a finite volume approach to generate more realistic melt flow physics during filling stage of injection molding under different process conditions. The Pressure Implicit with Splitting Operators (PISO) pressure velocity coupling algorithm is employed to enable higher degree of approximate relation between corrections for pressure and velocity, and a comprehensive high-resolution differencing scheme (CICSAM) is successfully utilized to capture moving interfaces. The present developed numerical approach is verified for a box shape mold insert injection molding process of melt flow polypropylene (PP) and comparisons are made with a well-known commercial software program and the experimental data available it? the open literature in terms of basic flow features. The numerical results are also compared with each other for each process condition to predict the evolution of a few flow parameters such as temperature and pressure field distributions in the selected regions of the mold cavity to optimize the polymer melt flow during the filling stage of injection molding. The present study is later extended to simulate the filling process of the injection molding for a mold insert PP pipe fitting model for further assessment of the modeling capabilities of the present numerical modeling methodology in injection molding of complex geometrical configurations.