A number of important technical applications rely on diffusers where the flow is decelerated in the presence of an associated adverse pressure gradient, resulting in rapid boundary layer growth, potentially flow separation, and unsteadiness (both, small and large scale turbulent motion). Simulations of high Reynolds number flows with strong adverse pressure gradient and flow separation are computationally challenging because standard turbulence models are difficult to calibrate for such flows and simulations that resolve all scales of the turbulent motion can become prohibitively expensive. For validation purposes we computed two well documented turbulent channel flow cases using steady Reynolds-averaged Navier-Stokes. In collaboration with J. Eaton at Stanford University we then started simulations of an asymmetric diffuser at an inflow Reynolds number based on channel height and bulk velocity of 10,000 using Reynolds-averaged Navier-Stokes, direct numerical simulations, and a hybrid turbulence modeling approach, the flow simulation methodology. The capability of the various approaches to accurately predict time-averaged properties of the flow are discussed. Although at this point none of the different approaches is entirely satisfactory, the current results provide valuable hints and insights of how to proceed with such flow simulations so that more reliable results can be obtained.