An overlapping mesh methodology that is spectrally accurate in space and up to third-order accurate in time is developed for solution of unsteady incompressible flow equations in three-dimensional domains. The ability to decompose a global domain into separate, but overlapping, subdomains eases mesh generation procedures and increases flexibility of modeling flows with complex geometries. The methodology employs implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrallyaccurate spatial interpolation and high-order accurate temporal extrapolation, and requires few, if any, iterations, yet maintains the global accuracy and stability of the underlying flow solver. The overlapping mesh methodology is thoroughly validated using two-dimensional and three-dimensional benchmark problems in laminar and turbulent flows. The spatial and temporal convergence is documented and is in agreement with the nominal order of accuracy of the solver. The influence of long integration times, as well as inflow-outflow global boundary conditions on the performance of the overlapping grid solver is assessed. In a turbulent benchmark of fully-developed turbulent pipe flow, the turbulent statistics with the overlapping grids is validated against published available experimental and other computation data. Scaling tests are presented that show near linear strong scaling, even for moderately large processor counts.

The development of a three dimensional spectrally accurate moving overlapping grid technique that is utilized to solve for the flow around complex moving geometries opens doors to various practical applications that have previously been difficult to model. This method provides a straightforward approach to managing grid resolution near moving structures without the need for mesh restructuring techniques. Building upon our previously validated overlapping mesh methodology, we have developed a moving overlapping mesh method in a high-order spectral element computational fluid dynamics solver. Current validation tests on the two dimensional moving overlapping grid methodology have shown spectral accuracy of the coupled solution for both translating and rotating meshes, and results for fluid interactions with translating structures that correlate well with experimental and other computational data. A three dimensional simulation demonstrates robustness of the method and the ability to represent flow around complex structures moving in complex ways, paving the way to accurately model the flow through a rotating wind turbine.

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Dynamically moving airfoils are encountered in helicopter rotors, wind-turbine blades, and maneuvering aircraft. A clearer understanding of how freestream disturbances affect the aerodynamic forces on pitching airfoils leads to improved designs. In the present study, the authors' recently validated spectrally accurate moving overlapping mesh methodology is used to perform a direct numerical simulation of a NACA 0012 airfoil pitching with oscillatory motion in the presence of a turbulent wake created by an upstream solid cylinder. The global computational domain is decomposed into a stationary background mesh, which contains the solid cylinder, and a mesh constructed around the airfoil that is constrained to pitch with predetermined reduced frequency k 0.16. Present simulations are performed with chord-based Reynolds number Re c 44;000. Aerodynamic forces and vortex-shedding properties are compared between the pitching airfoil simulations with and without upstream disturbances. Power spectral density functions of the aerodynamic forces and moments are investigated to further determine the effect of a turbulent wake on a pitching airfoil.

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