The search continues for accurate and efficient 3D computational fluid dynamics algorithms for hydrocyclone flows. A review of recent work and new developments are presented. This contribution is based on the authors' past experience both in creating their own specialized numerical approaches and using commercial packages for simulating swirling flow. In particular, the paper presents the application of the developed 3D finite element code to hydrocyclone modelling. Some important factors in the numerical solution of the model equations, namely proper representation of geometry, imposition of boundary conditions and the choice of turbulence model, are discussed. Numerical results indicate the versatility and the effectiveness of the new approaches. A scheme that utilizes numerical results in the multi-objective design is also suggested. Remaining technical difficulties are highlighted in order to suggest key directions for future work. (C) 2004 Elsevier Ltd. All rights reserved.