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

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.

Citation

Kraft, R.A. and Coutinho, A.L.G.A. (2015), "Deflated preconditioned conjugate gradients applied to a Petrov-Galerkin generalized least squares finite element formulation for incompressible flows with heat transfer", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 25 No. 2, pp. 272-298. https://doi.org/10.1108/HFF-12-2012-0272