The Taylor Vortex and the Driven Cavity Problems in the Stream Function-Vorticity Formulation

Blanca Bermúdez Juárez; René Posadas Hernández; Wuiyevaldo Fermín Guerrero Sánchez

doi:doi:10.11648/j.acm.20140306.18

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The Taylor Vortex and the Driven Cavity Problems in the Stream Function-Vorticity Formulation

Blanca Bermúdez Juárez, René Posadas Hernández, Wuiyevaldo Fermín Guerrero Sánchez

Received: 15 December 2014 Accepted: 24 December 2014 Published: 4 January 2015

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Abstract

In this work, two problems will be presented: The Taylor Vortex problem and the Driven Cavity problem. Both problems are solved using the Stream function-Vorticity formulation of the Navier-Stokes equations in 2D. Results are obtained using two methods: A fixed point iterative method and another one working with matrixes A and B resulting from the discretization of the Laplacian and the advective term, respectively. This second method resulted faster than the fixed point iterative one.

DOI	10.11648/j.acm.20140306.18
Published in	Applied and Computational Mathematics (Volume 3, Issue 6, December 2014)
Page(s)	337-342
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Taylor Vortex Problem, Driven Cavity Problem, Navier-Stokes Equations, Stream Funtion-Vorticity Formulation

References

[1]	Nicolás A., A finite element approach to the Kuramoto-Sivashinski equation, Advances in Numerical Equations and Optimization, Siam (1991).
[2]	Bermúdez B. and Juárez L., Numerical solution of an advection-diffusion equation, Información Tecnológica (2014) 25(1):151-160
[3]	Bermúdez B., Nicolás A., Sánchez F. J., Buendía E., Operator Splitting and upwinding for the Navier-Stokes equations, Computational Mechanics (1997) 20 (5): 474-477
[4]	Nicolás A., Bermúdez B., 2D incompressible viscous flows at moderate and high Reynolds numbers, CMES (2004): 6(5): 441-451.
[5]	Nicolás A., Bermúdez B., 2D Thermal/Isothermal incompressible viscous flows, International Journal for Numerical Methods in Fluids (2005) 48: 349-366
[6]	Bermúdez B., Nicolás A., Isothermal/Thermal Incompressible Viscous Fluid Flows with the Velocity-Vorticity Formulation, Información Tecnológica (2010) 21(3): 39-49.
[7]	Bermúdez B. and Nicolás A., The Taylor Vortex and the Driven Cavity Problems by the Velocity-Vorticity Formulation, Procedings 7th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics (2010).
[8]	Goyon, O., High-Reynolds numbers solutions of Navier-Stokes equations using incremental unknowns, Comput. Methods Appl. Mech. Engrg. 130, (1996) pp. 319-335.
[9]	Glowinski R., Finite Element methods for the numerical simulation of incompressible viscous flow. Introduction to the control of the Navier-Stokes equations, Lectures in Applied Mathematics (1991), AMS, 28.
[10]	Ghia U., Guia K. N. and Shin C. T., High-Re Solutions for Incompressible Flow Using the Navier-Stokes equations and a Multigrid Method, Journal of Computational Physics (1982): 48, 387-411.
[11]	Anson D. K., Mullin T. & Cliffe K. A. A numerical and experimental investigation of a new solution in the Taylor vortex problemJ. Fluid Mech, (1988) 475 – 487.
[12]	Adams, J.; Swarztrauber, P; Sweet, R. 1980: FISHPACK: A Package of Fortran Subprograms for the Solution of Separable Elliptic PDE`s, The National Center for Atmospheric Research, Boulder, Colorado, USA, 1980.
[13]	Nicolás-Carrizosa, A. and Bermúdez-Juárez, B., Onset of two-dimesional turbulence with high Reynolds numbers in the Navier-Stokes equations, Coupled Problems 2011.

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APA Style

Blanca Bermúdez Juárez, René Posadas Hernández, Wuiyevaldo Fermín Guerrero Sánchez. (2015). The Taylor Vortex and the Driven Cavity Problems in the Stream Function-Vorticity Formulation. Applied and Computational Mathematics, 3(6), 337-342. https://doi.org/10.11648/j.acm.20140306.18

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ACS Style

Blanca Bermúdez Juárez; René Posadas Hernández; Wuiyevaldo Fermín Guerrero Sánchez. The Taylor Vortex and the Driven Cavity Problems in the Stream Function-Vorticity Formulation. Appl. Comput. Math. 2015, 3(6), 337-342. doi: 10.11648/j.acm.20140306.18

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AMA Style

Blanca Bermúdez Juárez, René Posadas Hernández, Wuiyevaldo Fermín Guerrero Sánchez. The Taylor Vortex and the Driven Cavity Problems in the Stream Function-Vorticity Formulation. Appl Comput Math. 2015;3(6):337-342. doi: 10.11648/j.acm.20140306.18

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@article{10.11648/j.acm.20140306.18,
  author = {Blanca Bermúdez Juárez and René Posadas Hernández and Wuiyevaldo Fermín Guerrero Sánchez},
  title = {The Taylor Vortex and the Driven Cavity Problems in the Stream Function-Vorticity Formulation},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {6},
  pages = {337-342},
  doi = {10.11648/j.acm.20140306.18},
  url = {https://doi.org/10.11648/j.acm.20140306.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140306.18},
  abstract = {In this work, two problems will be presented: The Taylor Vortex problem and the Driven Cavity problem. Both problems are solved using the Stream function-Vorticity formulation of the Navier-Stokes equations in 2D. Results are obtained using two methods: A fixed point iterative method and another one working with matrixes A and B resulting from the discretization of the Laplacian and the advective term, respectively. This second method resulted faster than the fixed point iterative one.},
 year = {2015}
}

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TY  - JOUR
T1  - The Taylor Vortex and the Driven Cavity Problems in the Stream Function-Vorticity Formulation
AU  - Blanca Bermúdez Juárez
AU  - René Posadas Hernández
AU  - Wuiyevaldo Fermín Guerrero Sánchez
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VL  - 3
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Author Information

Blanca Bermúdez Juárez

Faculty of Computer Science, Autonomous University of Puebla (BUAP), Puebla, México
René Posadas Hernández

Faculty of Physics and Mathematics, Autonomous University of Puebla (BUAP), Puebla, México
Wuiyevaldo Fermín Guerrero Sánchez

Faculty of Physics and Mathematics, Autonomous University of Puebla (BUAP), Puebla, México

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APA Style

Blanca Bermúdez Juárez, René Posadas Hernández, Wuiyevaldo Fermín Guerrero Sánchez. (2015). The Taylor Vortex and the Driven Cavity Problems in the Stream Function-Vorticity Formulation. Applied and Computational Mathematics, 3(6), 337-342. https://doi.org/10.11648/j.acm.20140306.18

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ACS Style

Blanca Bermúdez Juárez; René Posadas Hernández; Wuiyevaldo Fermín Guerrero Sánchez. The Taylor Vortex and the Driven Cavity Problems in the Stream Function-Vorticity Formulation. Appl. Comput. Math. 2015, 3(6), 337-342. doi: 10.11648/j.acm.20140306.18

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AMA Style

Blanca Bermúdez Juárez, René Posadas Hernández, Wuiyevaldo Fermín Guerrero Sánchez. The Taylor Vortex and the Driven Cavity Problems in the Stream Function-Vorticity Formulation. Appl Comput Math. 2015;3(6):337-342. doi: 10.11648/j.acm.20140306.18

Copy | Download

@article{10.11648/j.acm.20140306.18,
  author = {Blanca Bermúdez Juárez and René Posadas Hernández and Wuiyevaldo Fermín Guerrero Sánchez},
  title = {The Taylor Vortex and the Driven Cavity Problems in the Stream Function-Vorticity Formulation},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {6},
  pages = {337-342},
  doi = {10.11648/j.acm.20140306.18},
  url = {https://doi.org/10.11648/j.acm.20140306.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140306.18},
  abstract = {In this work, two problems will be presented: The Taylor Vortex problem and the Driven Cavity problem. Both problems are solved using the Stream function-Vorticity formulation of the Navier-Stokes equations in 2D. Results are obtained using two methods: A fixed point iterative method and another one working with matrixes A and B resulting from the discretization of the Laplacian and the advective term, respectively. This second method resulted faster than the fixed point iterative one.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - The Taylor Vortex and the Driven Cavity Problems in the Stream Function-Vorticity Formulation
AU  - Blanca Bermúdez Juárez
AU  - René Posadas Hernández
AU  - Wuiyevaldo Fermín Guerrero Sánchez
Y1  - 2015/01/04
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20140306.18
DO  - 10.11648/j.acm.20140306.18
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 337
EP  - 342
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140306.18
AB  - In this work, two problems will be presented: The Taylor Vortex problem and the Driven Cavity problem. Both problems are solved using the Stream function-Vorticity formulation of the Navier-Stokes equations in 2D. Results are obtained using two methods: A fixed point iterative method and another one working with matrixes A and B resulting from the discretization of the Laplacian and the advective term, respectively. This second method resulted faster than the fixed point iterative one.
VL  - 3
IS  - 6
ER  -

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