We present a high-order nonuniform sliding-mesh flux reconstruction (FR) method for studying flows about rotating geometries. This new method is an extension of our previous methods that require uniform meshes on a sliding interface. 1-3 It completely eliminates the uniform-mesh restriction and thus significantly simplifies mesh generation. Meanwhile, the nonuniform nature of this method gives the maximum flexibility on mesh points distribution along a sliding interface, which helps to achieve the best mesh resolution across the interface. This extension is also crucial to successfully apply it to complex threedimensional geometries where the meshes are usually very nonuniform. Numerical tests on both inviscid and viscous flows successfully demonstrate that the present method is able to retain the high-order accuracy of the FR method. Finally, we report our high-fidelity and high-order simulations of flows over rotating cylinders with different cross-section shapes. These simulation results can be used as benchmark test cases for future studies by the CFD community.

Summary We present a high‐order solver for simulating vortex‐induced vibrations (VIVs) at very challenging situations, for example, VIVs of a row of very closely placed objects with large relative displacements. This solver works on unstructured hybrid grids by employing the high‐order tensor‐product spectral difference method for quadrilateral grids and the Raviart‐Thomas spectral difference method for triangular grids. To deal with the challenging situations where a traditional conforming moving mesh is incapable, we split a computational domain into nonoverlapping subdomains, where each interior subdomain encloses an object and moves freely with respect to its neighbors. A nonuniform sliding‐mesh method that ensures high‐order accuracy is developed to deal with sliding interfaces between subdomains. A monolithic approach is adopted to seamlessly couple the fluid and solid vibration equations. Moreover, the solver is parallelized to further improve its efficiency on distributed‐memory computers. Through a series of numerical tests, we demonstrate that this solver is high‐order accurate for both inviscid and viscous flows and has good parallel efficiency, making it ideal for VIV studies.

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