On 3D numerical simulations of viscoelastic fluids

On 3D numerical simulations of viscoelastic fluids

Niedziela, D.
Iliev, O.
Latz, A.

2006-09-07

In this work we present and solve a class of non--Newtonian viscoelastic fluid flow problems. Models for non-Newtonian fluids can be classified into three large groups depending on the type of the constitutive relation used: algebraic, differential and integral. The first type of models are most simple one, the last are the most physically adequate ones. Here we consider some models from the first and the third groups, and present robust and efficient algorithms for their solution. We present new mathematical model, which belongs to the class of generalized Newtonian models and is able to account for the anisotropy of the viscosity tensor observed in many real liquids. In particular, we discuss a unified model that captures both shear thinning and extensional thickening for complex flows. The resulting large variations of the viscosity tensor in space and time are leading to a strong numerical coupling of the momentum equations due to the appearance of mixed derivatives in the discretization. To treat this strong coupling appropriately, we present two modifications of classical projection methods (like e.g. SIMPLE). In the first modification all momentum equations are solved coupled (i.e. mixed derivative are discretized implicitly) but still iterations are performed between the momentum equations and the continuity equation. The second one is a fully coupled method, where momentum and continuity equation are solved together using a proper preconditioner. The models involving integral constitutive relation which accounts for the history of deformations, result in a system of integro-differential equations. To solve it, we suggest a proper splitting scheme, which treats the integral and the differential parts consecutively. Integral Oldroyd B and Doi Edwards models are used to simulate flows of dilute and concentrated polymer solutions, respectively.

non-Newtonian fluids
anisotropic viscosity
integral constitutive equation

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Conference proceedings

conference paper

(c) 2006 Niedziela, D.; Iliev, O.; Latz, A.