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Preconditioned conjugate gradient methods for the Navier-Stokes equationsA preconditioned Krylov subspace method (GMRES) is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux-split formulation. Several preconditioning techniques are investigated to enhance the efficiency and convergence rate of the implicit solver based on the GMRES algorithm. The superiority of the new solver is established by comparisons with a conventional implicit solver, namely line Gauss-Seidel relaxation (LGSR). Computational test results for low-speed (incompressible flow over a backward-facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade), and hypersonic flow (shock-on-shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the Mach 0.1 case, overall speedup factors of up to 17 (in terms of time-steps) and 15 (in terms of CPU time on a CRAY-YMP/8) are found in favor of the preconditioned GMRES solver, when compared with the LGSR solver. The corresponding speedup factors for the transonic flow case are 17 and 23, respectively. The hypersonic flow case shows slightly lower speedup factors of 9 and 13, respectively. The study of preconditioners conducted in this research reveals that a new LUSGS-type preconditioner is much more efficient than a conventional incomplete LU-type preconditioner.
Document ID
19950031605
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Ajmani, Kumud
(Virginia Polytechnic Institute, Blacksburg, VA, United States)
Ng, Wing-Fai
(Virginia Polytechnic Institute, Blacksburg, VA, United States)
Liou, Meng-Sing
(NASA Lewis Research Center Cleveland, OH, United States)
Date Acquired
August 16, 2013
Publication Date
January 1, 1994
Publication Information
Publication: Journal of Computational Physics
Volume: 110
Issue: 1
ISSN: 0021-9991
Subject Category
Fluid Mechanics And Heat Transfer
Accession Number
95A63204
Distribution Limits
Public
Copyright
Other

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