A WALL-MODELED LARGE EDDY SIMULATION METHOD FOR HIGH-ORDER SPECTRAL ELEMENT SOLVERS

A new method for implementation of wall-modeled large eddy simulation (WMLES) for use with high-order spectral element methods is introduced. Spectral element methods present unique challenges for wall modeling, specifically related to the application of appropriate wall boundary conditions and the specification of modeled fluxes in the near-wall region. The new method addresses these difficulties through the use of an assumed wall function velocity profile in the first layer of near-wall elements, which is used to determine the wall shear stress as well as appropriate pseudo-fluxes to be summed and implemented as source terms at each grid point located in the near-wall elements. Furthermore, the method ensures that the mean velocity field is C-1 continuous at the interface between the wall- modeled region and the outer region. Simulations are performed using the spectral element solver Nek5000, and results are compared to high-fidelity DNS data. The test cases considered are fully developed channel flow and flow over a backward- facing step with separation and reattachment. Variations are investigated including different values of the subgrid stress model coefficients for the baseline LES method used. The results show that the new wall function methodology produces results in close agreement with more fully resolved LES for attached channel flow and produces good agreement with field quantities for the backward facing step. The magnitude of wall shear stress in the separated/reattaching flow is underpredicted, and potential reasons for this are discussed. Because WMLES provides a savings in computational cost that scales with Reynolds number, further improvements to the new wall-modeling strategy can potentially lead to significant savings in computational effort for scale-resolving simulations using spectral element numerical methods.