A spectral vanishing viscosity for the LES of turbulent flows within rotating cavities

A spectral vanishing viscosity technique (SVV) is presented for the simulation of 3D turbulent incompressible flows within a rotor–stator cavity. One characteristic of this technique is that the SVV is active only for the short length scales, a feature which is reminiscent of Large Eddy Simulation models. The Spectral Vanishing Viscosity, first introduced by E. Tadmor for the inviscid Burgers equation [E. Tadmor, Convergence of spectral methods for nonlinear conservation laws, SIAM J. Numer. Anal. 26 (1) (1989) 30], is incorporated into the cylindrical Navier–Stokes equations written in velocity pressure formulation. The second-order operator involved in the SVV-method is implemented in a Chebyshev-collocation Fourier–Galerkin pseudo-spectral code. The SVV is shown to lead to stable discretizations without sacrificing the formal accuracy, i.e., exponential convergence, in the proposed discretization. LES results are presented here for rotational Reynolds numbers ranging from Re = 7 × 10 4 to Re = 7 × 10 5 . Turbulent quantities are shown to compare very favorably with results of direct numerical simulation (DNS) and experimental measurements.