The objective of this work is to study the role of some wavelike motion observed in the interior of a conical hydrocyclone used in mineral processing operations. In this paper, we obtained a stable numerical solution of the equations of motion, using a streamfunction-vorticity formulation on non-structured mesh. The numerical solution is obtained in a finite element context, where a stabilization is imposed through an unusual finite element method (USFEM) scheme. Finally, an adaptive mesh refinement is used for to enhance the solution. (c) 2005 Published by Elsevier B.V.