The Mathematical Institute, University of Oxford, Eprints Archive

Preconditioning harmonic unsteady potential flow calculations

Laird, Alistair L. and Giles, M. B. (2005) Preconditioning harmonic unsteady potential flow calculations. Technical Report. Unspecified. (Submitted)

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Abstract

This paper considers finite element discretisations of the Helmholtz equation and its generalisation arising from harmonic acoustics perturbations to a non-uniform steady potential flow. A novel elliptic, positive definite preconditioner, with a multigrid implementation, is used to accelerate the iterative convergence of Krylov subspace solvers. Both theory and numerical results show that for a model 1D Helmholtz test problem the preconditioner clusters the discrete system's eigenvalues and lowers its condition number to a level independent of grid resolution. For the 2D Helmholtz equation, grid independent convergence is achieved using a QMR Krylov solver, significantly outperforming the popular SSOR preconditioner. Impressive results are also presented on more complex domains, including an axisymmetric aircraft engine inlet with non-stagnant mean flow and modal boundary conditions.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1152
Deposited By:Lotti Ekert
Deposited On:13 May 2011 08:18
Last Modified:13 May 2011 08:18

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