A Numerical Technique for Solving the Maxwell Model for Free Surface Flows
DOI:
https://doi.org/10.5540/tema.2004.05.02.0195Abstract
This work is concerned with the development of a numerical technique for solving free surface flows of a Maxwell fluid. The governing equations for the flow of a Maxwell type fluid together with appropriate boundary conditions are given. The free surface stress conditions are treated in details. A novel formulation for calculating the extra stress components on rigid boundaries is given. The numerical technique presented in this work employs the finite difference method on a staggered grid and employs the ideas of the MAC (Marker-and-Cell) method. Numerical results demonstrating that this numerical technique can solve viscoelastic flows governed by the Maxwell model are presented. Moreover, validation results are presented.References
[1] A.A. Amsden and F.H. Harlow, “The SMAC method: a numerical technique for calculating incompressible fluid flow”, Los Alamos Scientific Laboratory, Report LA, 4370, 1970.
M.J. Crochet and R. Keunings, Die swell of a Maxwell fluid - numerical prediction, J. Non-Newtonian Fluid Mech., 7 (1980), 199-212.
J.O. Cruickshank, Low-Reynolds-number instabilities in stagnating jet flows, J. Fluid. Mech., 193 (1988), 111-127.
M. Griebel, T. Dornseifer and T. Neunhoeffer, “Numerical Simulation in Fluid Dynamics: a practical introduction”, SIAM publications, 1997.
G. Mompean and M. Deville, Unsteady finite volume of Oldroyd-B fluid through a three-dimensional planar contraction, J. Non-Newtonian Fluid Mech., 72 (1997), 253-279.
M.F. Tomé, N. Mangiavacchi, J.A. Cuminato, A. Castelo and S. Mckee, A finite difference technique for simulating unsteady viscoelastic free surface flows, J. Non-Newtonian Fluid Mech, 106 (2002), 61-106.
A. Varonos and G. Bergeles, Development and assessment of a variable-order non-oscillatory scheme for convection term discretization, Intern. J. Numer. Meth. Fluids, 26 (1998), 1-16.
J.Y. Yoo and Y. Na, A numerical study of the planar contraction flow of a viscoelastic fluid using the SIMPLER algorithm, J. Non-Newtonian Fluid Mech., 30 (1991), 89-106.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish in this journal agree to the following terms:
Authors retain copyright and grant the journal the right of first publication, with the work simultaneously licensed under the Creative Commons Attribution License that allows the sharing of the work with acknowledgment of authorship and initial publication in this journal.
Authors are authorized to assume additional contracts separately, for non-exclusive distribution of the version of the work published in this journal (eg, publish in an institutional repository or as a book chapter), with acknowledgment of authorship and initial publication in this journal.
Authors are allowed and encouraged to publish and distribute their work online (eg, in institutional repositories or on their personal page) at any point before or during the editorial process, as this can generate productive changes as well as increase impact and the citation of the published work (See The effect of open access).
This is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the
author. This is in accordance with the BOAI definition of open access
Intellectual Property
All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License under attribution BY.
