"The high Weissenberg number problem"
Most fluids we are accustomed to are Newtonian: their internal state of stress only depends on their instantaneous local distortion (in other words they have no memory). Water and air are examples of Newtonian fluids. Complex fluids, such as corn syrup, blood, and molten plastics have memory: their state of stress is a function of their entire deformation history. Computational rheology is concerned with the development of numerical methods for predicting flows of such fluids.
Since the early 1970's this field has been haunted by the so-called high Weissenberg number problem---the breakdown of ALL computational methods at parameter regimes in which memory is manifest. Recent work sheds light on the origin of this breakdown, which has remained of a mystery for over 3 decades. In fact, this breakdown can be remedied by a simple change of variables.
Joint work with Raanan Fattal