The primary objective of this study is to develop a sliding interface method for simulations involving relative rotational grid motion suitable for unstructured grid topologies. The present method alleviates computationally expensive grid deformation, remeshing, and hole cutting procedures. Rotational motion is accomplished by rigidly rotating a subdomain representing the moving component. At the subdomain interface boundary, the faces along the interfaces are extruded into the adjacent subdomain to create new volume elements and provide a one-cell overlap. These new volume elements close the control volumes for the nodes on the interface surface and allow a flux to be computed across the subdomain interface. An interface flux is computed independently for each subdomain. The values of the solution variables and other quantities for the nodes created by the extrusion process are found by interpolation. The extrusion is done so that the interpolation will maintain information as localized as possible. A parallel implementation of the neighbor search is used to find the extruded points in the adjacent subdomain. The method has been implemented in a parallel, node-centered finite volume, high-resolution viscous flow solver. The method does not impose any restrictions on the subdomain interface aside from the axisymmetric limitation required for rotational motion. In addition, the grid on the subdomain interface is arbitrary. The boundary surfaces between the two subdomains can have independent grids from one another. They do not have to connect in a one-to-one manner and there are no symmetry or pattern restrictions placed on the surface grid. A variety of numerical simulations were performed on several small-scale model problems to examine conservation of the interface flux. Overall flux conservation errors were found to be comparable to that for fully connected and fully conservative simulations. In addition, excellent agreement was obtained with both theoretical and experimental results. Three large-scale applications were also used to validate the method and highlight some of the advantages of the sliding interface method compared to the current state-of- the-art for unstructured grid applications. This sliding interface method requires no geometric modifications and has significantly shorter run times Furthermore, there were no apparent adverse effects on the numerical solutions by not strictly enforcing flux conservation at the subdomain boundary.