The Immersed Boundary Surface Method (IBS) is a novel variant of the Immersed Boundary Method (IBM) and is based on an advanced finite volume cut-cell approach. IBS was developed by H. Jasak at the University of Zagreb, Croatia, and is implemented in the open source simulation package foam-extend, which is a community driven branch of the object-oriented C++ library OpenFOAM. IBS can predict the flow behavior in plastics processing easily and realistically without major simplifications of the geometries and process conditions of the real process. This is particularly advantageous when simulating moving intermeshing elements, such as twin screw extruders. This study deals with numerical three-dimensional (3D) simulation of a co-rotating twin-screw extruder using IBS. Since 3D simulation models usually become very extensive, especially for time-dependent (transient) calculations, the parallelization possibilities of IBS on a high performance cluster (hpc) will also be addressed here. The results demonstrate that twin-screw extruders can be simulated in full 3D using IBS without the need of complex re-meshing mechanisms or simplified geometries and simulation models. Furthermore, a performance study outlines the possibilities and importance of parallelizing the simulations in order to speed up the calculations and/or to investigate even larger models. The results of the numerical simulation are compared with experimental investigations carried out on a twin-screw extruder. It could be shown that the simulation reflects the tendencies of the experimental investigations well.