Without linearization of the diffusive equation or the adiabatic approximation, we have numerically solved the two-fluid model to study dynamic phase separation of a binary polymer liquid with asymmetric composition under shear flow in the infinite Peclet number regime. The details of the model and the simulation technique are presented. The simulations reproduce shear-induced demixing, i.e., the shift of the position of the phase boundary from the equilibrium phase diagram, reported in literature. Our results show that the theological signature of demixing fluids under shear is the change from non-linear to linear of the dependence of the steady-state shear stress on shear rate within that range of shear rates in which the demixing takes place. We have also observed an interesting mechanism by which the stable band structure is reached; there is a transition from fine bands to waves, then to droplets, and finally to much coarser bands. (C) 2004 Elsevier B.V. All rights reserved.