Turbulent and transitional channel flow simulations have been performed in order to assess the differences concerning speed and accuracy in the pseudo-spectral code simson and the spectral-element code nek5000. The results indicate that the pseudo-spectral code is 4–6 times faster than the spectral-element code in fully turbulent channel flow simulations, and up to 10–20 times faster when taking into account the more severe CFL restriction in the spectral-element code. No particular difference concerning accuracy could be noticed either in the turbulent nor the transitional cases, except for the pressure fluctuations at the wall which converge slower for the spectral-element code.

The effect of over-integration and filter-based stabilization in the spectral-element method is investigated. There is a need to stabilize the SEM for flow problems involving non-smooth solutions, e.g., turbulent flow simulations. In model problems such as the Burgers’ equation (similar to Kirby and Karniadakis, J. Comput. Phys. 191:249–264, 2003) and the scalar transport equation together with full Navier–Stokes simulations it is noticed that over-integration with the full 3/2-rule is not required for stability. The first additional over-integration nodes are the most efficient to remove aliasing errors. Alternatively, filter-based stabilization can in many cases alone help to stabilize the computation.

LES and no-model LES (coarse-grid DNS) have been performed of turbulent flow in a plane asymmetric diffuser by the Spectral-Element Method (SEM). Mean profile and turbulent stresses compare well to LES results from Herbst e, however the SEM generally predicts a later (i.e. further downstream) separation. It can be concluded that the use of a high-order method is advantageous for flows featuring pressure-induced separation.

A direct numerical simulation (DNS) of turbulent flow in a three-dimensional diffuser at Re = 10 000 (based on bulk velocity and inflow-duct height) was performed with a massively parallel high-order spectral element method running on up to 32 768 processors. Accurate inflow condition is ensured through unsteady trip forcing and a long development section. Mean flow results are in good agreement with experimental data by Cherry et al. (Intl J. Heat Fluid Flow, vol. 29, 2008, pp. 803-811), in particular the separated region starting from one corner and gradually spreading to the top expanding diffuser wall. It is found that the corner vortices induced by the secondary flow in the duct persist into the diffuser, where they give rise to a dominant low-speed streak, due to a similar mechanism as the 'lift-up effect' in transitional shear flows, thus governing the separation behaviour. Well-resolved simulations of complex turbulent flows are thus possible even at realistic Reynolds numbers, providing accurate and detailed information about the flow physics. The available Reynolds stress budgets provide valuable references for future development of turbulence models.