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Numerical simulation of a viscoelastic fluid with a preconditioned Schwarz method

Luís Borges, Adélia Sequeira (2008)

Banach Center Publications

In this paper we apply a domain decomposition method to approach the solution of a non-Newtonian viscoelastic Oldroyd-B model. The numerical scheme is based on a fixed-point argument applied to the original non-linear system of partial differential equations decoupled into a Navier-Stokes system and a tensorial transport equation. Using a modified Schwarz algorithm, involving block preconditioners for the Navier-Stokes equations, the decoupled problems are solved iteratively. Numerical simulations...

Numerical simulation of generalized Newtonian fluids flow in bypass geometry

Keslerová, Radka, Řezníček, Hynek, Padělek, Tomáš (2019)

Programs and Algorithms of Numerical Mathematics

The aim of this work is to present numerical results of non-Newtonian fluid flow in a model of bypass. Different angle of a connection between narrowed channel and the bypass graft is considered. Several rheology viscosity models were used for the non-Newtonian fluid, namely the modified Cross model and the Carreau-Yasuda model. The results of non-Newtonian fluid flow are compared to the results of Newtonian fluid. The fundamental system of equations is the generalized system of Navier-Stokes equations...

On bounded channel flows of viscoelastic fluids

Marshall J. Leitman, Epifanio G. Virga (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We show that the smooth bounded channel flows of a viscoelastic fluid exhibit the following qualitative feature: Whenever the channel is sufficiently wide, any bounded velocity field satisfying the homogeneous equation of motion is such that if the flow stops at some time, then the flow is never unidirectional throughout the channel. We first demonstrate the qualitative property of the bounded channel flows. Then we show explicitly how a piecewise linear approximation of a relaxation function can...

On implicit constitutive theories

Kumbakonam R. Rajagopal (2003)

Applications of Mathematics

In classical constitutive models such as the Navier-Stokes fluid model, and the Hookean or neo-Hookean solid models, the stress is given explicitly in terms of kinematical quantities. Models for viscoelastic and inelastic responses on the other hand are usually implicit relationships between the stress and the kinematical quantities. Another class of problems wherein it would be natural to develop implicit constitutive theories, though seldom resorted to, are models for bodies that are constrained....

On the global existence for a regularized model of viscoelastic non-Newtonian fluid

Ondřej Kreml, Milan Pokorný, Pavel Šalom (2015)

Colloquium Mathematicae

We study the generalized Oldroyd model with viscosity depending on the shear stress behaving like μ ( D ) ∼ | D | p - 2 (p > 6/5), regularized by a nonlinear stress diffusion. Using the Lipschitz truncation method we prove global existence of a weak solution to the corresponding system of partial differential equations.

On the local strong solutions for a system describing the flow of a viscoelastic fluid

Ondřej Kreml, Milan Pokorný (2009)

Banach Center Publications

We consider a model for the viscoelastic fluid which has recently been studied in [4] and [1]. We show the local-in-time existence of a strong solution to the corresponding system of partial differential equations under less regularity assumptions on the initial data than in the above mentioned papers. The main difference in our approach is the use of the L p theory for the Stokes system.

On uniqueness for bounded channel flows of viscoelastic fluids

Marshall J. Leitman, Epifanio G. Virga (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

It was conjectured in [1] that there is at most one bounded channel flow for a viscoelastic fluid whose stress relaxation function G is positive, integrable, and strictly convex. In this paper we prove the uniqueness of bounded channel flows, assuming G to be non-negative, integrable, and convex, but different from a very specific piecewise linear function. Furthermore, whenever these hypotheses apply, the unbounded channel flows, if any, must grow in time faster than any polynomial.

Path following methods for steady laminar Bingham flow in cylindrical pipes

Juan Carlos De Los Reyes, Sergio González (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper is devoted to the numerical solution of stationary laminar Bingham fluids by path-following methods. By using duality theory, a system that characterizes the solution of the original problem is derived. Since this system is ill-posed, a family of regularized problems is obtained and the convergence of the regularized solutions to the original one is proved. For the update of the regularization parameter, a path-following method is investigated. Based on the differentiability properties...

Path following methods for steady laminar Bingham flow in cylindrical pipes

Juan Carlos De Los Reyes, Sergio González (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is devoted to the numerical solution of stationary laminar Bingham fluids by path-following methods. By using duality theory, a system that characterizes the solution of the original problem is derived. Since this system is ill-posed, a family of regularized problems is obtained and the convergence of the regularized solutions to the original one is proved. For the update of the regularization parameter, a path-following method is investigated. Based on the differentiability properties...

Simulation of the Three-Dimensional Flow of Blood Using a Shear-Thinning Viscoelastic Fluid Model

T. Bodnár, K.R. Rajagopal, A. Sequeira (2011)

Mathematical Modelling of Natural Phenomena

This paper is concerned with the numerical simulation of a thermodynamically compatible viscoelastic shear-thinning fluid model, particularly well suited to describe the rheological response of blood, under physiological conditions. Numerical simulations are performed in two idealized three-dimensional geometries, a stenosis and a curved vessel, to investigate the combined effects of flow inertia, viscosity and viscoelasticity in these geometries....

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