The main objective of the present work is to modify the traditional mapping method for the simulation of distributive mixing of multiphase flows in geometries involving moving parts such as, internal mixers or twin-screw extruders without a limitation on their geometrical periodicity. The periodicity condition, limits the results of traditional mapping method to tracking mapping mesh between specific discrete time intervals or distances for that geometry is repeated, hence, result is only for fixed orientation of rotors. Imaginary domain method is introduced to track mapping mesh from one state to the next free of geometrical periodicity limitations. In this work the method is introduced and its applicability and accuracy is discussed in details. A two-dimensional (2D) simulation of mixing of two Newtonian fluids with different viscosities in an intermeshing internal mixer is used as a test case study. In this example the key issues of ability to predict mixing state in details for all orientations of rotors is presented. To reduce diffusion errors of mapping method in the boundaries of the rotors, mapping mesh refinement technique that relies upon one single reference mesh is also presented. (C) 2007 Elsevier Ltd. All rights reserved.