Model development and theoretical studies of viscoelastic flow instabilities are to be carried out. Domain decomposition and pseudospectral numerical codes will be used to explore the stability of flow configurations representative of polymer processing systems. The main focus will be on the coupling of such models to one simulating the near-wall region for polymers flowing past solid surfaces, based on simulated microstructures, to explore the effect of wall slip on flow instabilities. The work is expected to lead to more robust and realistic numerical modeling of complex polymer processes. The modeling also relates to drag reduction from fluids with polymer additives.