Abstract:The Oldroyd-B equations model the flow of fluids containing rod-like elastic molecules. This model couples the momentum equation with an equation governing the evolution of the elastic components, and numerical simulation is notoriously difficult (the high Weisenberg problem). This system of partial differential equations can be derived from Hamilton's principle which reveals a subtle balance between inertia, transport, and dissipation effects. This talk will focus on the structural properties of these equations which provide insight into why naive numerical schemes may fail, and the ingredients required to construct stable numerical schemes.