Toward a solution to the high Weissenberg number problem

We present results of a numerical study of high Weissenberg number flows using the method of Trebotich, Colella and Miller, J. Comput. Phys. vol. 205 (2005). We consider benchmark viscoelastic flow of an Oldroyd‐B fluid in four to one sudden contractions for We = 1, 10, Re = 1. We conclude that (i) underlying wave behavior in the solution for flows at critical and supercritical elastic Mach number prevents the solution from reaching a steady‐state; and (ii) high resolution is needed to resolve structure in the solution downstream from the re‐entrant corner in order to determine convergence. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)