  In this work, a non-equilibrium wall model is proposed for the prediction of
turbulent flows experiencing adverse pressure gradients, including separated
flow regimes. The mean-flow nonequilibrium is identified by comparing two
characteristic velocities: the friction velocity (u_tau) and the
viscous-pressure gradient velocity (up). In regions where the pressure gradient
velocity is comparable to the friction velocity (up \sim u_tau, the near-wall
turbulent closure is modified to include the effect of the pressure-gradient
and convective terms. The performance of this wall model is evaluated in two
canonical flows experiencing smooth body separation: the NASA-Boeing speed bump
and the Bachalo-Johnson bump. Improvements in the predictive capabilities of
the proposed model for the conventional equilibrium wall model are theorized
and then demonstrated through numerical experiments. In particular, the
proposed wall model can capture the onset of boundary layer separation observed
in experiments or DNS calculations at resolutions where the equilibrium wall
model fails to separate.
