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exploiting recursive properties of fixed point algorithms 485
function of CFD algorithms, restarted algorithm is used to make the algorithm
memory efficient and to rely on local linear properties of the restar ted Krylov
subspace to represent the solution correctly. The proposed algorithm is shown to
be nonintrusive and applicable to a wide range of solvers including explicit and
implicit formulations of pressure- and density-based algorithms. The RRE algo-
rithmrequiresonlythestorageofcorrectionvectorsanddoesnotrequireevaluation
of the residuals which makes this algorithm easy to implement for the solvers that
do not form residual vector. Improved coupling of the systems of equations when
used with the RRE algorithm is demonstrated and shown to improve convergence
properties of segregated solvers.
References
[1] Wesseling, P. Principles of Computational Fluid Dynamics, Springer-Verlag, New
York, 2000.
[2] Patankar, S. V. Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York,
1980.
[3] Chorin, A. J. A Numerical Method for Solving Incompressible Viscous Flow
Problems, Journal of Computational Physics, 2(1), pp. 12–26, 1967.
[4] Ferziger, J. H., and Peri´c, M. Computational Methods for Fluid Dynamics, Springer,
Berlin, 1996.
[5] Hirsch, C. Numerical Computation of Internal and External Flows, 2, John Wiley,
Chichester, 1990.
[6] Laney, C. B. Computational Gasdynamics, Cambridge University Press, Cambridge,
1998.
[7] Allgower, E. L., and Georg, K. Introduction to Numerical Continuation Methods,
SIAM, Philadelphia, 1987.
[8] Deuflhard,P.NewtonMethodsforNonlinearProblems,Springer-Verlag,Berlin,2004.
[9] Wilcox, D. C. Turbulence Modeling for CFD, DCW Industries, 2006.
[10] Brezinski, C., andZaglia,M.R.Extrapolation MethodsTheoryandPractice, Elsevier
Science Publishing,Amsterdam, 1991.
[11] Saad,Y. Iterative Methods for Sparse Linear Systems SIAM, Philadelphia, 2004.
[12] Jameson,A., Schmidt, W., andTurkel, E. Numerical Solutions of the Euler Equations
by FiniteVolume Methods Using Runge-KuttaTime Stepping,AIAA Paper 81–1259,
1981.
[13] Sidi, A., and Celestina, M. L. Convergence Acceleration for Vector Sequences and
Application to Computational Fluid Dynamics, NASA Technical Memolen, 101327
(ICOMP-88-17).
[14] Washio, T., and Oosterlee, C. W. Krylov Subspace Acceleration for Nonlinear Multi-
grid Schemes, Electronic Transactions on Numerical Analysis, 6, pp. 271–290,
December 1997, ISSN 1068-9613. Institute for Computational Mechanics in Propul-
sion, Lewis Research Center, Clevland, OH.
[15] Jaschke, L. Preconditioned Arnoldi Methods for Systems of Nonlinear Equations,
PhDThesis, Swiss Federal Institute ofTechnology, Zurich, Switzerland, 2003.
[16] Andersson,C.SolvingLinearEquationsonParallelDistributedMemoryArchitectures
by Extrapolation, Technical Report, TRITA-NA-E9746, Department of Numerical
Analysis and Computer Science, Royal Institute ofTechnology, Sweden, 1997.