A spectral-element/Fourier smoothed profile method for large-eddy simulations of complex VIV problems

An accurate, fast and robust spectral-element/Fourier smoothed profile method (SEF-SPM) for turbulent flow past 3D complex-geometry moving bluff-bodies is developed and analyzed in this paper. Based on the concept of momentum thickness δ2, a new formula for determining the interface thickness parameter ξ is proposed. In order to overcome the numerical instability at high Reynolds number, the so-called Entropy Viscosity Method (EVM) is introduced in the framework of large-eddy simulation. To overcome resolution constraints pertaining to moving immersed bodies, the Coordinate Transformation Method (Mapping method) is incorporated in the current implementation. Moreover, a hybrid spectral-element method using mixed triangular and quadrilateral elements is employed in conjunction with Fourier discretization along the third direction to efficiently represent a body of revolution or a long-aspect ratio bluff-body like risers and cables. The combination of the above algorithms results in a robust method which we validate by several prototype flows, including flow past a stationary sphere at 200 ≤ Re ≤ 1000, as well as turbulent flow past a stationary and moving cylinder at 80 ≤ Re ≤ 10, 000. Finally, we apply the new method to simulate a self-excited rigidly moving dual-step cylinder and demonstrate that SEF-SPM is an efficient method for complex VIV problems.