In this paper, we proposed a new solver for the Navier-Stokes equations coming from the channel flow with high Reynolds number. We use the preconditioned Krylov subspace iterative methods such as Generalized Minimum Residual Methods (GMRES). We consider the variation of the Hermitian and Skew-Hermitian splitting to construct the preconditioner. Convergence of the preconditioned iteration is analyzed. We can show that the proposed preconditioner has a robust behavior for the Navier-Stokes problems in variety of models. Numerical experiments show the robustness and efficiency of the preconditioned GMRES for the Navier-Stokes problems with Reynolds numbers up to ten thousands.
| Published in | Applied and Computational Mathematics (Volume 6, Issue 4) |
| DOI | 10.11648/j.acm.20170604.18 |
| Page(s) | 202-207 |
| 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), 2017. Published by Science Publishing Group |
Preconditioning, GMRES, Navier-Stokes, High Reynolds Number, Iterative Methods
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APA Style
Josaphat Uvah, Jia Liu, Lina Wu. (2017). A Robust Preconditioned Iterative Method for the Navier-Stokes Equations with High Reynolds Numbers. Applied and Computational Mathematics, 6(4), 202-207. https://doi.org/10.11648/j.acm.20170604.18
ACS Style
Josaphat Uvah; Jia Liu; Lina Wu. A Robust Preconditioned Iterative Method for the Navier-Stokes Equations with High Reynolds Numbers. Appl. Comput. Math. 2017, 6(4), 202-207. doi: 10.11648/j.acm.20170604.18
AMA Style
Josaphat Uvah, Jia Liu, Lina Wu. A Robust Preconditioned Iterative Method for the Navier-Stokes Equations with High Reynolds Numbers. Appl Comput Math. 2017;6(4):202-207. doi: 10.11648/j.acm.20170604.18
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Download@article{10.11648/j.acm.20170604.18,
author = {Josaphat Uvah and Jia Liu and Lina Wu},
title = {A Robust Preconditioned Iterative Method for the Navier-Stokes Equations with High Reynolds Numbers},
journal = {Applied and Computational Mathematics},
volume = {6},
number = {4},
pages = {202-207},
doi = {10.11648/j.acm.20170604.18},
url = {https://doi.org/10.11648/j.acm.20170604.18},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170604.18},
abstract = {In this paper, we proposed a new solver for the Navier-Stokes equations coming from the channel flow with high Reynolds number. We use the preconditioned Krylov subspace iterative methods such as Generalized Minimum Residual Methods (GMRES). We consider the variation of the Hermitian and Skew-Hermitian splitting to construct the preconditioner. Convergence of the preconditioned iteration is analyzed. We can show that the proposed preconditioner has a robust behavior for the Navier-Stokes problems in variety of models. Numerical experiments show the robustness and efficiency of the preconditioned GMRES for the Navier-Stokes problems with Reynolds numbers up to ten thousands.},
year = {2017}
}
TY - JOUR T1 - A Robust Preconditioned Iterative Method for the Navier-Stokes Equations with High Reynolds Numbers AU - Josaphat Uvah AU - Jia Liu AU - Lina Wu Y1 - 2017/08/14 PY - 2017 N1 - https://doi.org/10.11648/j.acm.20170604.18 DO - 10.11648/j.acm.20170604.18 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 202 EP - 207 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20170604.18 AB - In this paper, we proposed a new solver for the Navier-Stokes equations coming from the channel flow with high Reynolds number. We use the preconditioned Krylov subspace iterative methods such as Generalized Minimum Residual Methods (GMRES). We consider the variation of the Hermitian and Skew-Hermitian splitting to construct the preconditioner. Convergence of the preconditioned iteration is analyzed. We can show that the proposed preconditioner has a robust behavior for the Navier-Stokes problems in variety of models. Numerical experiments show the robustness and efficiency of the preconditioned GMRES for the Navier-Stokes problems with Reynolds numbers up to ten thousands. VL - 6 IS - 4 ER -
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