FALSE BIFURCATIONS AND INSTABILITY OF A MAXWELL FLUID IN FULLY-DEVELOPED FLOW

The viscoelastic flow problem in two-dimensions is difficult to solve numerically because either inaccurate solutions are found or the iterations do not converge to a solution at all. This statement is true regardless of the physical problem being solved, the method being used, or the rheological model being used. Here a simple problem is solved: fully-developed flow of an upper-convected Maxwell fluid between two flat plates or in a tube. The presence of bifurcations in the numerical approximation is examined, and the effect of mesh refinement, trial functions, problem formulation, and boundary conditions on the bifurcations is elucidated. Transient simulations emphasize the presence of false eigenmodes that are highly oscillatory.