Overset methods are commonly employed to enable the effective simulation of problems involving complex geometries and moving objects such as rotorcraft. This paper presents a novel overset domain connectivity algorithm based upon the direct cut approach suitable for use with GPU-accelerated solvers on high-order curved grids. In contrast to previous methods it is capable of exploiting the highly data-parallel nature of modern accelerators. Further, the approach is also substantially more efficient at handling the curved grids which arise within the context of high-order methods. An implementation of this new algorithm is presented and combined with a high-order fluid dynamics code. The algorithm is validated against several benchmark problems, including flow over a spinning golf ball at a Reynolds number of 150,000.problems of engineering interest, including entire rotorcraft configurations with relative motion between one or more rotors in addition to a fixed fuselage.One of the many advantages of this approach, compared with say deforming grids, is that it is possible to employ multiple solvers: an unstructured near-body solver to allow for easier mesh generation around each body, and a high-order Cartesian off-body solver with adaptive mesh refinement (AMR) for speed and simplicity. In most production codes used for complex geometries, such as the CREATE-AV HELIOS software [2], the near-body solvers are typically 2nd or 3rd order accurate in space. Higherorder near-body solvers are available, but only for (multi-block) structured grids currently, such as with the OVERFLOW code using 5th order accurate finite differences [3,4]. For the best possible performance, accuracy, and applicability to a wide range of complex geometries, however, a higherorder unstructured near-body solver is preferable. As shown by Wissink [5] and by Nastase et al. [6], without a high-order near body solver, vortical structures and other flow features incur high amounts of diffusion before (or while) passing into the high-order off-body solver, causing a large increase in error.High order methods have a number of attractive attributes. Not only are they less dissipative, enabling the simulation of vortex-dominated flows with fewer degrees of freedom than a lower-order method, but they have also been shown to give remarkably good results when used to perform implicit large eddy simulations (ILES) and direct numerical simulations (DNS) [7,8]. Popular examples of high-order schemes for unstructured grids include the discontinuous Galerkin finite element method, first introduced by Reed and Hill [9], and spectral difference (SD) methods originally proposed under the moniker 'staggered-grid Chebyshev multidomain methods' by Kopriva and Kolias in 1996 [10] and later popularized by Sun et al. [11]. In 2007 Huynh proposed the flux reconstruction (FR) approach [12]; a unifying framework for high-order schemes for unstructured grids that encompasses both the nodal DG schemes of Hesthaven and Warburton [13] and, at least for a linear flux functi...