The present study treats the calculation of the continuous phase of a multiphase flow, i.e. the numerical solution of the equations for a turbulent incompressible flow. An existing SIMPLE based Single–Grid algorithm is improved applying the Multi–Grid Method. Numerical experiments for two test cases with up to 3174 400 finite volumes show the features of the new algorithm, the effect of its parallelization and capability to solve real life problems from engineering on PC clusters. IEEE International Conference on Cluster Computing, CLUSTER 2000, November 28.–December 2., 2000, Chemnitz University of Technology, Saxony, Germany. 1 Motivation Disperse multiphase flows are very common for processes in mechanical and thermal process technology (e.g. gas–particle or gas–droplet flows, coal combustion, pneumatic conveying, erosion phenomena). Furthermore processes for the separation of solid particles from gases or fluids and for the classification and particle size analysi...