A three-dimensional local unstructured mesh refinement strategy was developed to model viscous fluid flows in complex moving geometries in the context of the fictitious domain method. Two subdivision patterns were implemented in three dimensions and a numerical study done for a simple benchmark suggests that only the non-standard subdivision is suitable as a refinement strategy. To avoid the presence of discontinuous nodes in the mesh, an additional mesh refinement procedure was devised, which is analogous to the so-called red-green refinement strategy used in 2D. Fluid flow in a helical ribbon mixer for which experimental data are available was used to assess the performance of the proposed refinement strategy. By refining the elements that contain the control points of the fictitious domain, a significant improvement of the solution was obtained. The local subdivision of elements, which was also used as a tool to control the number of control points, also gives the possibility to increase this number of points to better describe the moving parts of a geometry. (c) 2005 Elsevier Ltd. All rights reserved.