Moving Least‐Squares Aided Finite Element Method: A Powerful Means to Evaluate Distributive and Dispersive Mixing

ABSTRACT Employing the Moving Least‐Squares Aided Finite Element Method (MLS‐FEM), we present a robust computational technique that effectively evaluates the flow field parameters and subsequently analyzes the evolution of the mixing process, using different criteria for distributive and dispersive mixing in an internal mixer. By enhancing classical finite element shape functions using MLS interpolation, the method allows accurate simulation of velocity and pressure fields on a fixed background mesh, eliminating the need for remeshing despite rotor movement. We validate MLS‐FEM against classical boundary‐fitted FEM and demonstrate that it achieves comparable accuracy while significantly reducing pre‐processing effort and its computational complexity. The method retains the symmetric structure of the finite element system and introduces no additional unknowns. Using particle tracking and deformation‐based metrics, we further show that MLS‐FEM reliably captures both distributive and dispersive mixing behavior under various rotor configurations and fluid rheologies. These findings highlight MLS‐FEM as a practical and powerful alternative to traditional mesh‐dependent methods for analyzing complex mixing flows.