Preconditioned conjugate gradient methods for the Navier-Stokes equations

dc.contributor.authorAjmani, Kumuden
dc.contributor.committeechairNg, Faien
dc.contributor.committeememberMoses, Hal L.en
dc.contributor.committeememberNelson, Douglas J.en
dc.contributor.committeememberRibbens, Calvin J.en
dc.contributor.committeememberVick, Brian L.en
dc.contributor.departmentMechanical Engineeringen
dc.date.accessioned2014-03-14T21:21:09Zen
dc.date.adate2005-10-13en
dc.date.available2014-03-14T21:21:09Zen
dc.date.issued1991-11-03en
dc.date.rdate2005-10-13en
dc.date.sdate2005-10-13en
dc.description.abstractA generalized Conjugate Gradient like method 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. Preconditioning techniques are employed with the Conjugate Gradient like method to enhance the stability and convergence rate of the overall iterative method. The superiority of the new solver is established by comparisons with a conventional Line GaussSeidel Relaxation (LGSR) solver. Comparisons are based on 'number of iterations required to converge to a steady-state solution' and 'total CPU time required for convergence'. Three test cases representing widely varying flow physics are chosen to investigate the performance of the solvers. Computational test results for very 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 (shockon- shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the 1vfach 0.1 case, speed-up factors of 30 (in terms of iterations) and 20 (in terms of CPU time) are found in favor of the new solver when compared with the LGSR solver. The corresponding speed-up factors for the transonic flow case are 20 and 18, respectively. The hypersonic case shows relatively lower speed-up factors of 5 and 4, respectively. This study reveals that preconditioning can greatly enhance the range of applicability and improve the performance of Conjugate Gradient like methods.en
dc.description.degreePh. D.en
dc.format.extentxiii, 167 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-10132005-152548en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-10132005-152548/en
dc.identifier.urihttp://hdl.handle.net/10919/39840en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1991.A452.pdfen
dc.relation.isformatofOCLC# 26248021en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1991.A452en
dc.subject.lcshConjugate gradient methodsen
dc.subject.lcshNavier-Stokes equationsen
dc.titlePreconditioned conjugate gradient methods for the Navier-Stokes equationsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMechanical Engineeringen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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