Computational fluid dynamics (CFD) simulations in the context of single-phase mixing remain challenging notably due the presence of a complex rotating geometry within the domain. In this work, we develop a parallel semi-implicit immersed boundary method based on Open. FOAM, which is applicable to unstructured meshes. This method is first verified on academic test cases before it is applied to single phase mixing. It is then applied to baffled and unbaffled stirred tanks equipped with a pitched blade impeller. The results obtained are compared to experimental data and those predicted with the single rotating frame and sliding mesh techniques. The proposed method is found to be of comparable accuracy in predicting the flow patterns and the torque values while being straightforwardly applicable to complex systems with multiples impellers for which the swept volumes overlap. (C) 2015 Elsevier Ltd. All rights reserved.