Solid bowl centrifuges are applied for the separation of small particles in a variety of industries. However, the particles accumulate at the rotor wall, which leads to a time-dependent separation efficiency. A numerical approach for spatial and time-resolved simulations of the separation process in a tube centrifuge is developed and some numerical results are presented. The back coupling of the dispersed and sedimented particles is realized by locally defined viscosity functions. The open source computation software OpenFOAM was used to simulate the turbulent multiphase flow within the centrifuge. The numerical investigations demonstrate the significant influence of the growing sediment on the flow conditions and of the rheological behavior of the sediment on the sediment shape.