Volume 6, Issue 4, August 2017, Page: 202-207
A Robust Preconditioned Iterative Method for the Navier-Stokes Equations with High Reynolds Numbers
Josaphat Uvah, Department of Mathematics and Statistics, University of West Florida, Pensacola, USA
Jia Liu, Department of Mathematics and Statistics, University of West Florida, Pensacola, USA
Lina Wu, Department of Mathematics, Borough of Manhattan Community College, The City University of New York, New York, USA
Received: Aug. 13, 2017;       Published: Aug. 14, 2017
DOI: 10.11648/j.acm.20170604.18      View  609      Downloads  53
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.
Keywords
Preconditioning, GMRES, Navier-Stokes, High Reynolds Number, Iterative Methods
To cite this article
Josaphat Uvah, Jia Liu, Lina Wu, A Robust Preconditioned Iterative Method for the Navier-Stokes Equations with High Reynolds Numbers, Applied and Computational Mathematics. Vol. 6, No. 4, 2017, pp. 202-207. doi: 10.11648/j.acm.20170604.18
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