  This paper presents a simple, efficient, and high-order accurate sliding-mesh
interface approach to the spectral difference (SD) method. We demonstrate the
approach by solving the two-dimensional compressible Navier-Stokes equations on
quadrilateral grids. This approach is an extension of the straight mortar
method originally designed for stationary domains by Kopriva, it employs curved
dynamic mortars on sliding-mesh interfaces to couple rotating and stationary
domains. On the nonconforming sliding-mesh interfaces, the related variables
are first projected from cell faces to mortars to compute common fluxes, and
then the common fluxes are projected back from the mortars to the cell faces to
ensure conservation. To verify the spatial order of accuracy of the
sliding-mesh spectral difference (SSD) method, both inviscid and viscous flow
cases are tested. It is shown that the SSD method preserves the high-order
accuracy of the SD method. Meanwhile, the SSD method is found to be very
efficient in terms of computational cost. This novel sliding-mesh interface
method is very suitable for parallel processing with domain decomposition. It
can be applied to a wide range of problems, such as the aerodynamics of
rotorcraft, wind turbines, and oscillating wing wind power generators, etc.
