POLYFLOW  need of a viscosity ratio of 1/9 in viscoelastic flow simulation
Should one always select a viscosity ratio of 1/9 for a viscoelastic fluid model? Actually, it is not always necessary. A bit of historical and rheological background may help for this. * First simulations of 2D extrusion flow (free surface) with a Maxwell model (thus an Oldroyd model without this viscosity ratio): results were obtained at a modest level of elasticity; * Simulations were then carried out with a single mode PTT model, originally without viscosity ratio; it gave rather poor results, but improvement was found when a ratio of 1/9 was introduced. Actually, this value 1/9 guarantees that the shear stress remains a monotonic increasing function of shear rate. A nonzero value of this ratio is also needed for a single mode Giesekus model when alpha is larger than 0.5. * This ratio 1/9 has been subsequently applied to the Oldroyd model: results were obtained at a higher level of elasticity. As can be seen, for the PTT model, this viscosity ratio was needed for reasons of rheological stability; it provided some stability of the sovler for the Oldroyd model. If one focuses on the stability from the point of view of rheology, this ratio may decrease when the number of modes increase, as the limit of stability (or the onset of instability in the viscosity curve) is pushed towards large shear rates. From the point of view of the momentum equation, things that are viscous are interesting (diffusive term in the momentum equation). The EVSS method helps for that, but one must also make sure that the rheology is stable. POLYMAT does not consider stability issues, but the user may decide a particular value for this ratio. 

