The suitability of spectral/h — p finite elements for large eddy simulation and the performance of the Smagorinsky eddy-viscosity model are investigated using isotropic flows, wall bounded flows and transitional flows. The two- dimensional spectral/h — p finite elements discretisation of Sherwin & Kar- niadakis (1995) is used, extended in the third direction using Fourier series. The scheme is integrated in time using the splitting scheme of Karniadakis et al. (1991), which is extended to allow for temporally and spatially varying viscosity whilst retaining the decoupling of the viscous term.
Muschinski’s (1996) concept of an LES-fluid is validated through numerical experiments by considering three test flows: isotropic turbulence decay at an initial Reynolds number Re\ = 245, channel flow at Reynolds numbers of ReT = 180 and 640, and cylinder flow at Re = 3900. Assuming the Smagorinsky length scale, tiles = cs A, as the LES-fluid counterpart of Kolmogorov’s dissipation length scale, it is shown that for a Smagorinsky length scale larger than the implicit or explicit filter width, the subfilter model damps motions smaller than tiles• If the width of the filter is larger than tiles, then the numerical discretisation determines the length scale of the model. This is often associated with a reduction of the Smagorinsky length scale in the wall region of channel flow simulations. It is concluded that the spectral element method may be succesfully applied to LES, if the Smagorinsky length scale is not based just on the grid size, but rather on the grid size and polynomial order of the expansion basis used. A new definition of the Smagorinsky length scale is proposed and tested, which is dependent on the cell dimensions and the polynomial order. It is shown that spectral elements may then be used in LES in an manner equivalent to any other discretisation. The added advantage of the method would be in the unstructured nature of the mesh, which allows flexibility in simulating complex geometries, and the arbitrary nature of the order of the discretisation.