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We study frequency responses of an inertialess two-dimensional channel flow of viscoelastic fluids. By rewriting the evolution equations in terms of low-pass filtered versions of the stream function, we show that strongly-elastic flows can be brought into a standard singularly perturbed form that exhibits a slow-fast decomposition. In high-Weissenberg number regime, which is notoriously difficult to study numerically, we demonstrate that the frequency responses are reliably captured by the dynamics of the fast subsystem. We use numerical computations to validate our theoretical findings and to illustrate that our formulation does not suffer from spurious numerical instabilities. [ABSTRACT FROM PUBLISHER]

Simulating the flows of viscoelastic fluids under industrially relevant conditions requires robust numerical techniques. Thus far, Newton-Krylov methods have not been widely employed in practical applications. This is because their rate of failure is too high unless they are used together with some preconditioner. A robust general-purpose preconditioner has not been developed to this day, and the development of such preconditioners is a subject of intensive research. A new multilevel incomplete lower-upper (ILU) factorization has recently been proposed. We demonstrate that Newton-Krylov methods can be successfully applied in combination with this novel preconditioner to calculate the benchmark flows of viscoelastic fluids. [ABSTRACT FROM AUTHOR]

In this contribution, the results of experimental determination of the drag coefficient correction factor for spherical particles moving slowly through a Carreau viscosity model fluid are presented. The experimental values of the correction factor, which were evaluated from measurements of terminal falling velocity of seventeen types of spherical particles in viscoelastic polymer solutions, are compared with those calculated numerically using a finite elements method. The results obtained confirm that in the case of shear thinning concentrated polymer solutions the viscoelastic effects are only of minor significance. However, in the case of less concentrated high-molecular polymer solutions in polyalkylene glycol Emkarox an evident drag enhancement has been observed. [ABSTRACT FROM AUTHOR]

This study discusses the capability of the constitutive laws for the matrix logarithm of the conformation tensor (LCT model) within the framework of the spectral elements method. The high Weissenberg number problems (HWNP) usually produce a lack of convergence of the numerical algorithms. Even though the question whether the HWNP is a purely numerical problem or rather a breakdown of the constitutive law of the model has remained somewhat of a mystery, it has been recognized that the selection of an appropriate constitutive equation constitutes a very crucial step although implementing a suitable numerical technique is still important for successful discrete modeling of non-Newtonian flows. The LCT model formulation of the viscoelastic equations originally suggested by Fattal and Kupferman is applied for 2-dimensional (2D) FENE-CR model. The Planar Poiseuille flow is considered as a benchmark problem to test this representation at high Weissenberg number. The numerical results are compared with numerical solution of the standard constitutive equation. [ABSTRACT FROM AUTHOR]