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High-Resolution Methods for Incompressible and Low-Speed Flows

High-Resolution Methods for Incompressible and Low-Speed Flows
Author: D. Drikakis
Publisher: Springer Science & Business Media
Total Pages: 623
Release: 2005-08-02
Genre: Science
ISBN: 354026454X
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The study of incompressible ?ows is vital to many areas of science and te- nology. This includes most of the ?uid dynamics that one ?nds in everyday life from the ?ow of air in a room to most weather phenomena. Inundertakingthesimulationofincompressible?uid?ows,oneoftentakes many issues for granted. As these ?ows become more realistic, the problems encountered become more vexing from a computational point-of-view. These range from the benign to the profound. At once, one must contend with the basic character of incompressible ?ows where sound waves have been analytically removed from the ?ow. As a consequence vortical ?ows have been analytically “preconditioned,” but the ?ow has a certain non-physical character (sound waves of in?nite velocity). At low speeds the ?ow will be deterministic and ordered, i.e., laminar. Laminar ?ows are governed by a balance between the inertial and viscous forces in the ?ow that provides the stability. Flows are often characterized by a dimensionless number known as the Reynolds number, which is the ratio of inertial to viscous forces in a ?ow. Laminar ?ows correspond to smaller Reynolds numbers. Even though laminar ?ows are organized in an orderly manner, the ?ows may exhibit instabilities and bifurcation phenomena which may eventually lead to transition and turbulence. Numerical modelling of suchphenomenarequireshighaccuracyandmostimportantlytogaingreater insight into the relationship of the numerical methods with the ?ow physics.

Computational Fluid Dynamics 2006

Computational Fluid Dynamics 2006
Author: Herman Deconinck
Publisher: Springer
Total Pages: 916
Release: 2016-04-01
Genre:
ISBN: 9783662500903
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ThisbookcontainstheproceedingsoftheFourthInternationalConference onComputationalFluidDynamics(ICCFD4), heldinGent, Belgiumfrom July10through16,2006. TheICCFDconferenceseriesisanoutcomeofthe mergeroftwoimportantstreamsofconferencesinComputationalFluid- namics: InternationalConferenceonNumericalMethodsinFluidDynamics, ICNMFD(since1996)andInternationalSymposiumonComputationalFluid Dynamics, ISCFD(since1985). In1998itwasdecidedtojointhetwoand ICCFD emerged as a biannual meeting, held in Kyoto in 2000, Sydney in 2002, Toronto in 2004 and Gent in 2006. Thus, the ICCFD series became theleadinginternationalconferenceseriesforscientists, mathematiciansand engineersinterestedinthecomputationof?uid?ow. The4theditionoftheconferencehasattracted200participantsfromall overtheworld;270abstractswerereceived, ofwhich135wereselectedina carefulpeerreviewprocessbytheexecutivecommittee(C. H. Bruneau, J. -J. Chattot, D. Kwak, N. Satofuka, D. W. Zingg, E. DickandH. Deconinck)for oralpresentationandafurther21forposterpresentation. Thepaperscontainedintheseproceedingsprovideanexcellentsnapshot of the ?eld of Computational Fluid Dynamics as of 2006. Invited keynote lecturesbyrenownedresearchersareincluded, withcontributionsinthe?eld ofdiscretizationschemes, high-endcomputingandengineeringchallenges, and two-phase?ow. Thesekeynotecontributionsarecomplementedby137regular papersonthemostdiverseaspectsofCFD: -Innovativealgorithmdevelopmentfor?owsimulation, optimisationandc- trol: higher-ordermethods(DG, FV, FEandRDmethods), iterativemethods andmultigrid, solutionadaptivemeshtechniques, errorestimationandc- trol, parallelalgorithms. -Innovativemodelingof?owphysicsintheareaofcompressibleandinc- pressible ?ows: hypersonic and reacting ?ows, two-phase ?ows, turbulence (LES, DES, DNS, andtransition), vortexdynamics, boundarylayerstability, multi-scalephysics, magnetohydrodynamics. Preface VII -advancedapplicationsusingtheabovementionedinnovativetechnology, and multidisciplinaryapplicationsincludingaero-elasticityandaero-acoustics. ThanksareduetooursponsorsNASA, theFWOResearchFoundation FlandersandtheEuropeanUnionthroughtheEUA4XMarieCurieproject. Inparticular, thegenerousgrantfromNASAisakeyfactorinthesuccessof thisconferenceseriesandthepublicationoftheseProceedings. Wealsowouldliketothankthesta?andPhDstudentsofthevonKarman InstituteandtheDepartmentof?ow, heatandcombustionmechanicsofthe University of Gent, for the help they provided toward the success of this conference. Sint-Genesius-Rode, Belgium HermanDeconinck vonKarmanInstituteforFluidDynamics Ghent, Belgium ErikDick GhentUniversity September2006 ConferenceChair Contents PartIInvitedSpeakers Twonewtechniquesforgeneratingexactlyincompressible approximatevelocities BernardoCockburn. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 RoleofHigh-EndComputinginMeetingNASA'sScience andEngineeringChallenges RupakBiswas, EugeneL. Tu, WilliamR. VanDalsem. . . . . . . . . . . . . . . . 14 RecentAdvancesofMulti-phaseFlowComputationwiththe AdaptiveSoroban-gridCubicInterpolatedPropagation(CIP) Method TakashiYabe, YouichiOgata, KenjiTakizawa. . . . . . . . . . . . . . . . . . . . . . . 29 PartIISchemes OntheComputationofSteady-StateCompressibleFlows UsingaDGMethod HongLuo, JosephD. Baum, RainaldL]ohner. . . . . . . . . . . . . . . . . . . . . . . . 47 Space-TimeDiscontinuousGalerkinMethodforLarge AmplitudeNonlinearWaterWaves YanXu, JaapJ. W. vanderVegt. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 AdiscontinuousGalerkinmethodwi

Efficient Semi-Implicit Time-Stepping Schemes for Incompressible Flows

Efficient Semi-Implicit Time-Stepping Schemes for Incompressible Flows
Author: Kak Choon Loy
Publisher:
Total Pages:
Release: 2017
Genre:
ISBN:
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The development of numerical methods for the incompressible Navier-Stokes equations received much attention in the past 50 years. Finite element methods emerged given their robustness and reliability. In our work, we choose the P2-P1 finite element for space approximation which gives 2nd-order accuracy for velocity and 1st-order accuracy for pressure. Our research focuses on the development of several high-order semi-implicit time-stepping methods to compute unsteady flows. The methods investigated include backward difference formulae (SBDF) and defect correction strategy (DC). Using the defect correction strategy, we investigate two variants, the first one being based on high-order artificial compressibility and bootstrapping strategy proposed by Guermond and Minev (GM) and the other being a combination of GM methods with sequential regularization method (GM-SRM). Both GM and GM-SRM methods avoid solving saddle point problems as for SBDF and DC methods. This approach reduces the complexity of the linear systems at the expense that many smaller linear systems need to be solved. Next, we proposed several numerical improvements in terms of better approximations of the nonlinear advection term and high-order initialization for all methods. To further minimize the complexity of the resulting linear systems, we developed several new variants of grad-div splitting algorithms besides the one studied by Guermond and Minev. Splitting algorithm allows us to handle larger flow problems. We showed that our new methods are capable of reproducing flow characteristics (e.g., lift and drag parameters and Strouhal numbers) published in the literature for 2D lid-driven cavity and 2D flow around the cylinder. SBDF methods with grad-div stabilization terms are found to be very stable, accurate and efficient when computing flows with high Reynolds numbers. Lastly, we showcased the robustness of our methods to carry 3D computations.

Virtual Node Methods for Incompressible Flow

Virtual Node Methods for Incompressible Flow
Author: Russell Edward Howes
Publisher:
Total Pages: 94
Release: 2014
Genre:
ISBN:
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This thesis details two numerical methods for the solution of incompressible flow problems using the virtual node framework introduced in (Bedrossian, 2010). The first method is a novel discrete Hodge decomposition for velocity fields defined over irregular domains in two and three dimensions. This new decomposition leads to a sparse, 5-point stencil in 2D (7-point in 3D) at all nodes in the domain, even near the boundary. The corresponding linear system can be factored simply into a weighted product of the standard discrete divergence and gradient operators, is symmetric positive definite, and yields second order accurate pressures and first order velocities in the maximum norm (second order in the 1-norm). The second method is an extension of the work in (Assen & ccedil;o, 2013), which simulates the Stokes equations in two dimensions, to a method that models the Navier-Stokes equations in two and three spatial dimensions. The extension to three dimensions is partially accomplished by a new approach to discretizing the multiplier term corresponding to the system jump conditions. This method works either on domains with interfacial discontinuities in material quantities such as density and viscosity, or on irregularly shaped domains with Dirichlet, Neumann, or slip boundary conditions. This method leads to a discrete, KKT system solving for velocities and pressures simultaneously, and yields second order accurate velocities in both time and space, and first order pressures.