Isogeometric Variational Multiscale Large-Eddy Simulation of Fully-developed Turbulent Flow over a Wavy Wall

Abstract We report on the isogeometric residual-based variational multiscale (VMS) large eddy simulation of a fully developed turbulent flow over a wavy wall. To assess the predictive capability of the VMS modeling framework, we compare its predictions against the results from direct numerical simulation (DNS) and large eddy simulation (LES) and, when available, against experimental measurements. We use C 1 quadratic B-spline basis functions to represent the smooth geometry of the sinusoidal lower wall and the solution variables. The Reynolds numbers of the flows considered are 6760 and 30,000 based on the bulk velocity and average channel height. The ratio of amplitude to wavelength ( α/λ ) of the sinusoidal wavy surface is set to 0.05. The computational domain is 2 λ  × 1.05 λ  ×  λ in the streamwise, wall-normal and spanwise directions, respectively. For the Re  = 6760 case, mean averaged quantities, including velocity and pressure profiles, and the separation/reattachment points in the recirculation region, are compared with DNS and experimental data. The turbulent kinetic energy and Reynolds stress are in good agreement with benchmark data. Coherent structures over the wavy wall are observed in isosurfaces of the Q-criterion and show similar features to those previously reported in the literature. Comparable accuracy to DNS solutions is obtained with at least one order of magnitude fewer degrees of freedom. For the Re  = 30,000 case, good agreement was obtained for mean wall shear stress and velocity profiles compared with available LES results reported in the literature.

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