For the simulations discussed in this paper two geometries are considered: A square-duct channel flow at a Reynolds number based on bulk velocity and hydraulic diameter of 10,000 (627 based on friction velocity and hydraulic diameter) and a 1:3.33 rectangular channel flow at a Reynolds number based on bulk velocity and channel height of 10,000 (909 based on friction velocity and hydraulic diameter). Reynolds-averaged Navier-Stokes (RANS) and hybrid turbulence model simulations based on the flow simulation methodology (FSM), filter-based RANS, and partially-averaged Navier-Stokes simulations were carried out. In addition, for the square-duct flow, as a reference, we also carried out direct numerical simulations (DNS). A new FSM contribution function is proposed and tested. It is also shown how hybrid RANS/LES models can be extended to allow for "turbulence seeding" ("backscatter") in regions of vanishing model contribution and energy transfer to the unresolved scales in regions with increasing model contribution. A comparison of the mean flow data obtained with the different methods for three different grid resolutions showed that FSM and filter-based RANS with variable filter width consistently yielded the best bulk velocity and velocity profile predictions. It remains to be investigated if these methods perform equally well for more complex flows, such as separated diffuser flows.