Summary: The use of a high-performance parallel computer system has been investigated to compute the incompressible flow and mixing efficiency of a static mixer. The flow computation is performed using a conventional Eulerian approach, by resolving the governing flow equations on a block-structured computational mesh. To examine the mixing process, we emply a Lagrangian approach involving particle tracking. We describe the parallelization of both the flow computation and particle tracking phases of the numerical simulation, which are performed independently. It is shown that a high-performance parallel computer system provides a possibility for more detailed and accurate simulations, leading to greater insights into the flow behaviour and mixing properties.