A finite element method for liquid with memory
type: Item
instance of: scholarly article
title: A finite element method for liquid with memory
zbMATH Open document ID: 0616.76014
DOI: 10.1016/0377-0257(87)85020-6
author: A. C. Papanastasiou
author: L. E. Scriven
author: Christopher W. Macosko
published in: Journal of Non-Newtonian Fluid Mechanics
publication date: 1987-01-01T00:00:00Z
review text: Steady, two-dimensional flows of viscoelastic liquid with memory are analyzed by means of a nonlinear integral constitutive equation, novel streamlined finite elements, Galerkin's method of weighted residuals, and Newton iteration. By their relation to streamlines the new elements allow, for the first time, full Newton iteration of the algebraic equation set to which the governing integrodifferential system reduces. Streamlines are computed simultaneously with velocity components and pressure, the primary unknowns; to track the history of liquid particles the deformation equations are solved analytically in a Protean system of coordinates that conforms to the streamlines. In the cases studied the Newton iteration converges quadratically to a creeping flow state of Weissenberg number (product of upstream wall shear rate and relaxation time of the liquid) up to about 20 in channel flow, 10 in film flow, and 2 in die-swell flow. Shear-thinning shrinks the domain of convergence; it also reduces die-swell. A slip boundary condition in the vicinity of the contact line extends the domain of convergence.
Mathematics Subject Classification ID: 76A05
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 3999495
zbMATH Keywords: Steady, two-dimensional flows
zbMATH Keywords: viscoelastic liquid with memory
zbMATH Keywords: nonlinear integral constitutive equation
zbMATH Keywords: streamlined finite elements
zbMATH Keywords: Galerkin's method of weighted residuals
zbMATH Keywords: Newton iteration
zbMATH Keywords: history of liquid particles
zbMATH Keywords: Protean system of coordinates
MaRDI profile type: Publication
full work available at URL: 0377-0257(87)85020-6
OpenAlex ID: W2064833229
description: scientific article; zbMATH DE number 3999495