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Deflated preconditioned conjugate gradients applied to a Petrov-Galerkin generalized least squares finite element formulation for incompressible flows with heat transfer

Deflated preconditioned conjugate gradients applied to a Petrov-Galerkin generalized least... Purpose – The purpose of this paper is to show benefits of deflated preconditioned conjugate gradients (CG) in the solution of transient, incompressible, viscous flows coupled with heat transfer. Design/methodology/approach – This paper presents the implementation of deflated preconditioned CG as the iterative driver for the system of linearized equations for viscous, incompressible flows and heat transfer simulations. The De Sampaio-Coutinho particular form of the Petrov-Galerkin Generalized Least Squares finite element formulation is used in the discretization of the governing equations, leading to symmetric positive definite matrices, allowing the use of the CG solver. Findings – The use of deflation techniques improves the spectral condition number. The authors show in a number of problems of coupled viscous flow and heat transfer that convergence is achieved with a lower number of iterations and smaller time. Originality/value – This work addressed for the first time the use of deflated CG for the solution of transient analysis of free/forced convection in viscous flows coupled with heat transfer. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat & Fluid Flow Emerald Publishing

Deflated preconditioned conjugate gradients applied to a Petrov-Galerkin generalized least squares finite element formulation for incompressible flows with heat transfer

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References (21)

Publisher
Emerald Publishing
Copyright
Copyright © Emerald Group Publishing Limited
ISSN
0961-5539
DOI
10.1108/HFF-12-2012-0272
Publisher site
See Article on Publisher Site

Abstract

Purpose – The purpose of this paper is to show benefits of deflated preconditioned conjugate gradients (CG) in the solution of transient, incompressible, viscous flows coupled with heat transfer. Design/methodology/approach – This paper presents the implementation of deflated preconditioned CG as the iterative driver for the system of linearized equations for viscous, incompressible flows and heat transfer simulations. The De Sampaio-Coutinho particular form of the Petrov-Galerkin Generalized Least Squares finite element formulation is used in the discretization of the governing equations, leading to symmetric positive definite matrices, allowing the use of the CG solver. Findings – The use of deflation techniques improves the spectral condition number. The authors show in a number of problems of coupled viscous flow and heat transfer that convergence is achieved with a lower number of iterations and smaller time. Originality/value – This work addressed for the first time the use of deflated CG for the solution of transient analysis of free/forced convection in viscous flows coupled with heat transfer.

Journal

International Journal of Numerical Methods for Heat & Fluid Flow – Emerald Publishing

Published: Mar 2, 2015

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