Time-dependent shear flow of a non-Newtonian fluid. (English) Zbl 0683.76003

Current progress in hyperbolic systems: Riemann problems and computations, Proc. AMS-IMS-SIAM Jt. Summer Res. Conf., Brunswick/ME (USA) 1988, Contemp. Math. 100, 91-109 (1989).
[For the entire collection see Zbl 0683.00014.]
This paper presents results obtained using three numerical methods that accurately represent the flow dynamics for a particular viscoelastic model, and surveys analytical results for related models. The computations reproduce experimental measurements of non-Newtonian “spurt” in shearing flow through a slit die and predict related phenomena associated with a non-monotone relation between the shear stress and shear strain-rate. Experiments are suggested to verify these predictions.


76A05 Non-Newtonian fluids
74Hxx Dynamical problems in solid mechanics
35L65 Hyperbolic conservation laws
65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs


Zbl 0683.00014