An empirical strategy for improving modeling of the energy dissipation
rate epsilon(ij) and the velocity-pressure gradient Pi(ij) terms in t
he transport equations for the Reynolds stresses is proposed on the ba
sis of available direct numerical simulations of the turbulent boundar
y layer and fully developed turbulent channel flow. The dissipation-ra
te model takes into account the anisotropy of the dissipation rate not
only near the wall but elsewhere in the flow as well. When modeling t
he velocity-pressure gradient term, the usual split between pressure-t
ransport and redistributive terms is avoided, One consequence of this
strategy is the elimination of wall reflection or near wall correction
terms. Wall-topography parameters, such as the distance to the wall a
nd wall normal vectors, are also absent. Calculations of a turbulent b
oundary layer over a smooth wall confirm the potential improvements th
at can be achieved with this approach.