Hostname: page-component-74656f9884-npj9w Total loading time: 0 Render date: 2026-11-09T19:54:48.896Z Has data issue: false hasContentIssue false
  • English
  • Français

Extrapolation-Based Acceleration of Iterative Solvers: Application to Simulation of 3D Flows

Published online by Cambridge University Press:  20 August 2015

Leopold Grinberg  and
George Em Karniadakis
Leopold Grinberg*
Affiliation:
Division of Applied Mathematics, Brown University, Providence 02912, USA
George Em Karniadakis*
Affiliation:
Division of Applied Mathematics, Brown University, Providence 02912, USA
*
Corresponding author.Email:lgrinb@dam.brown.edu
Email:gk@dam.brown.edu
Get access

Abstract

We investigate the effectiveness of two extrapolation-based methods aiming to approximate the initial state required by an iterative solver in simulations of unsteady flow problems. The methods lead to about a ten-fold reduction in the iteration count while requiring only negligible computational overhead. They are particularly suitable for parallel computing since they are based almost exclusively on data stored locally on each processor. Performance has been evaluated in simulations of turbulent flow in a stenosed carotid artery and also in laminar flow in a very large domain containing the human intracranial arterial tree.

Keywords

52B1065D1868U0568U07High-order methodsPODCFDlow-energy preconditioner

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 3 , March 2011 , pp. 607 - 626
Copyright
Copyright © Global Science Press Limited 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1]Markovinović, R. and Jansen, J. D., Accelerating iterative solution methods using reduced-order models as solution predictors, Int. J. Numer. Meth. Engng., 68 (2006), 525–541.Google Scholar
[2]Tromeur-Dervout, D. and Vassilevski, Y., POD acceleration of fully implicit solver for unsteady nonlinear flows and its application on grid architecture, Adv. Eng. Software., 38 (2007), 301–311.CrossRefGoogle Scholar
[3]Sirisup, S., Karniadakis, G. E., Xiu, D. and Kevrekidis, I. G., Equation-free/Galerkin-free POD-assisted computation of incompressible flows, J. Comput. Phys., 2007 (2005), 568–587.Google Scholar
[4]Fischer, P., Projection techniques for iterative solution of Ax = b with successive right-hand sides, Comp. Meth. Appl. Mech., 163 (1998), 193–204.Google Scholar
[5]Karniadakis, G. E. and Sherwin, S. J., Spectral/hp Element Methods for CFD, Second Edition, Oxford University Press, Oxford, 2005.Google Scholar
[6]Canuto, C. G., Hussaini, M. Y., Quarteroni, A. M. and Zang, T. A., Spectral Methods Evolution to Complex Geometries and Applications to Fluid Dynamics, Springer-Verlag, Berlin, Heidelberg, 2007.CrossRefGoogle Scholar
[7]Sherwin, S. and Casarin, M., Low-energy basis preconditioning for elliptic substructured solvers based on unstructured spectral/hp element discretization, J. Comput. Phys., 171 (2001), 394–417.Google Scholar
[8]Grinberg, L., Pekurovsky, D., Sherwin, S. J. and Karniadakis, G. E., Parallel performance of a low energy basis preconditioner for spectral/hp elements, Parallel. Comput., 35 (2009), 284–304.Google Scholar
[9]Sirovich, L., Turbulence and dynamics of coherent structures: I-III, Quart. Appl. Math., 45 (1987), 561–590.Google Scholar
[10]Lumley, J. L., The structure of inhomogeneous turbulent flow, in Atmospheric Turbulence and Radio Wave Propagation, (ed. Yaglom, A. M. and Tatarski, V. I.), Nauka, Moscow, 160–178, 1967.Google Scholar
[11]Berkooz, G., Holmes, P. and Lumley, J. L., The proper orthogonal decomposition in the analysis of turbulent flows, Ann. Rev. Fluid. Mech., 25 (1993), 539–575.CrossRefGoogle Scholar
[12]Karniadakis, G. E., Israeli, M. and Orszag, S. A., High-order splitting methods for the incompressible Navier-Stokes equations, J. Comput. Phys., 97 (1991), 414–443.Google Scholar
[13]Pavarino, L. F., Dipartimento di Matematica, Universitá degli Studi di Milano, private communication.Google Scholar