This work focuses on the development of a general finite element code devoted to the three-dimensional direct simulation of mixing processes of complex fluids. The code, developed from the CimLib (c) Library, is based oil a domain immersion method coupled with a "level-set" approach to represent the rigid moving boundaries, Such as screws and rotors, as well as free surfaces. These techniques, combined with the use of automatized parallel computing, allow calculating the time-dependent flow of generalized Newtonian fluids in large and complex processes, involving moving free surfaces which are treated by a level-set/Hamilton-Jacobi method. Three examples of flow case studies are presented in this paper: the flow within the mixing section of a twin-screw extruder, the flow in an internal mixer and the flow in a batch mixer.