The separation of finely dispersed particles from liquids is a basic operation in mechanical process engineering. On an industrial scale, continuously operating decanter centrifuges are often used, whose separation principle is based on the density difference between the solid and the liquid phase due to high g-forces acting on both phases. The design of centrifuges is based on the experience on the individual manufacturer or simplified black box models, which only consider a stationary state. Neither the physical behavior of the separation process nor the sediment formation and its transport is considered. In this work, a computationally-efficient approach is proposed to simulate the separation process in decanter centrifuges. Thereby, the open-source computation software OpenFOAM was used to simulate the multiphase flow within the centrifuge. Sedimentation, consolidation of the sediment, and its transport are described by material functions which are derived from experiments. The interactions between the particles and the fluid are considered by locally defined viscosity functions. This work shows that the simulation method is suitable for describing the solid-liquid separation in a simplified test geometry of a decanter centrifuge. In addition, the influence of the rheological behavior on the flow in the test geometry can be observed for the first time.