We demonstrate the ability to simulate complex flows of entangled polymer melts using a high-fidelity slip-link model. Given the strong connections of the underlying molecular model to an atomistic description, nearly ab initio predictions of complex processing are feasible. Moreover, the method retains sufficient information which might allow extraction of detailed polymer chain conformations imposed by the flow. The macroscopic transport equations are solved using smoothed-particle hydrodynamics consistently with the stresses calculated using stochastic simulation of an ensemble of polymer chains in each particle. The polymer model uses only a single adjustable parameter whose value is determined from equilibrium stress relaxation. All other parameters are determined from atomistic simulation. Thereafter, nonlinear rheology predictions are made without any parameter adjustment. As a demonstration, we simulate journal-bearing flow of a moderately entangled polymer. Although the flows considered here are two dimensional, the required computational resources demonstrate that three dimensional flow calculations are accessible.