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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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Online
ISSN
1609-9389
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Volume 11, Issue 1 (Jan 2011)

Issues

On an Efficient Finite Element Method for Navier-Stokes-ω with Strong Mass Conservation

Carolina C. Manica
  • Departmento de Matematica Pura e Aplicada, Universidade Federal do Rio Grande do Sul.
  • Email:
Monika Neda
  • Department of Mathematics, University of Nevada, Las Vegas.
  • Email:
Maxim Olshanskii
  • Department of Mechanics and Mathematics, M. V. Lomonosov Moscow State University, Moscow 119899, Russia.
  • Email:
Leo G. Rebholz
  • Department of Mathematical Sciences, Clemson University, Clemson, SC 29634.
  • Email:
Nicholas E. Wilson
  • Email:

Abstract

We study an efficient finite element method for the NS-ω model, that uses van Cittert approximate deconvolution to improve accuracy and Scott-Vogelius elements to provide pointwise mass conservative solutions and remove the dependence of the (often large) Bernoulli pressure error on the velocity error. We provide a complete numerical analysis of the method, including well-posedness, unconditional stability, and optimal convergence. Additionally, an improved choice of filtering radius (versus the usual choice of the average mesh width) for the scheme is found, by identifying a connection with a scheme for the velocity-vorticity-helicity NSE formulation. Several numerical experiments are given that demonstrate the performance of the scheme, and the improvement offered by the new choice of the filtering radius.

Keywords: Navier-Stokes-alpha; Navier-Stokes-omega; approximate deconvolution; Scott-Vogelius elements

About the article

Received: 2011-02-25

Revised: 2011-03-18

Accepted: 2011-03-25

Published in Print:


Citation Information: Computational Methods in Applied Mathematics Comput. Methods Appl. Math., ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.2478/cmam-2011-0001. Export Citation

© Institute of Mathematics, NAS of Belarus. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY-NC-ND 4.0)

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Mine A. Belenli, Songül Kaya, Leo G. Rebholz, and Nicholas E. Wilson
International Journal of Computer Mathematics, 2013, Volume 90, Number 7, Page 1506
[2]
Benjamin R. Cousins, Sabine Le Borne, Alexander Linke, Leo G. Rebholz, and Zhen Wang
Numerical Methods for Partial Differential Equations, 2013, Volume 29, Number 4, Page 1217
[3]
Tae-Yeon Kim, Monika Neda, Leo G. Rebholz, and Eliot Fried
Computer Methods in Applied Mechanics and Engineering, 2011, Volume 200, Number 41-44, Page 2891
[4]
Keith J. Galvin, Leo G. Rebholz, and Catalin Trenchea
SIAM Journal on Numerical Analysis, 2014, Volume 52, Number 2, Page 678
[5]
Eleanor W. Jenkins, Chris Paribello, and Nicholas E. Wilson
Numerical Methods for Partial Differential Equations, 2014, Volume 30, Number 2, Page 625
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