Modeling viscoelastic flow with discrete methods

The hydrodynamics of viscoelastic materials (for example, polymer melts and solutions) presents interesting and complex phenomena, for example, instabilities and turbulent flow at very low Reynolds numbers due to normal stress effects and the existence of a finite stress relaxation time. This present work is motivated by renewed interest in instabilities in polymer flow. The majority of currently used numerical methods discretize a constitutive equation on a grid with finite difference or similar methods. We present work in progress in which we simulate viscoelastic flow with dissipative particle dynamics. The advantage of this approach is that many of the numerical instabilities of conventional methods can be avoided, and that the model gives clear physical insight into the origins of many viscoelastic flow instabilities.