Skip to main content Accessibility help
×
Home
Hostname: page-component-564cf476b6-zvgck Total loading time: 0.143 Render date: 2021-06-21T02:17:52.962Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true }

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

Published online by Cambridge University Press:  20 August 2015

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
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.

Type
Research Article
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.

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), 525541.CrossRefGoogle 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), 301311.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), 568587.CrossRefGoogle Scholar
[4]Fischer, P., Projection techniques for iterative solution of Ax = b with successive right-hand sides, Comp. Meth. Appl. Mech., 163 (1998), 193204.CrossRefGoogle 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.Google 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), 394417.CrossRefGoogle 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), 284304.CrossRefGoogle Scholar
[9]Sirovich, L., Turbulence and dynamics of coherent structures: I-III, Quart. Appl. Math., 45 (1987), 561590.CrossRefGoogle 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), 539575.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), 414443.CrossRefGoogle Scholar
[13]Pavarino, L. F., Dipartimento di Matematica, Universitá degli Studi di Milano, private communication.Google Scholar
6
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

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

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

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

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

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

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *