Elsevier

Applied Mathematics Letters

Volume 82, August 2018, Pages 1-7
Applied Mathematics Letters

Augmented Lagrangian-based preconditioners for steady buoyancy driven flow

https://doi.org/10.1016/j.aml.2018.02.013Get rights and content
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Abstract

In this paper, we apply the augmented Lagrangian (AL) approach to steady buoyancy driven flow problems. Two AL preconditioners are developed based on the variable’s order, specifically whether the leading variable is the velocity or the temperature variable. Correspondingly, two non-augmented Lagrangian (NAL) preconditioners are also considered for comparison. An eigenvalue analysis for these two pairs of preconditioners is conducted to predict the rate of convergence for the GMRES solver. The numerical results show that the AL preconditioner pair is insensitive with respect to the mesh size, Rayleigh number, and Prandtl number in terms of GMRES iterations, resulting in a significantly more robust preconditioner pair compared to the NAL pair. Accordingly, the AL pair performs much better than the NAL pair in terms of computational time. For the AL pair, the preconditioner with velocity as the leading variable gives slightly better efficiency than the one with temperature as the leading variable.

Keywords

Augmented Lagrangian preconditioners
Buoyancy driven flow problems
Finite element method
Eigenvalue analysis

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