Handbook of Numerical Analysis, Volume XVI, Special Volume: Numerical Methods for Non-Newtonian Fluids

826 Pages·2011·17.96 MB·English

by  R. Glowinski

Special Volume:
Numerical Methods for Non-Newtonian Fluids
Guest Editors: R. Glowinski and Jinchao Xu
Handbook of
Numerical Analysis
GeneralEditor:
P.G. Ciarlet
LaboratoireJacques-LouisLions
Universite´ PierreetMarieCurie
4PlaceJussieu
75005PARIS,France
and
DepartmentofMathematics
CityUniversityofHongKong
TatCheeAvenue
KOWLOON,HongKong
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NEWYORK•OXFORD•PARIS•SANDIEGO
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North-HollandisanimprintofElsevier
Volume XVI
Special Volume:
Numerical Methods for
Non-Newtonian Fluids
GuestEditors:
R. Glowinski
DepartmentofMathematics,
UniversityofHouston,
Houston,TXUSA
and
LaboratoireJacques-LouisLions,
Universite´ PierreetMarieCurie,
4PlaceJussieu,
75005PARIS,France
J. Xu
DepartmentofMathematics,
PennsylvaniaStateUniversity,
UniversityPark,PA16802
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SANFRANCISCO•SINGAPORE•SYDNEY•TOKYO
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General Preface
In the early eighties, when Jacques-Louis Lions and I considered the idea of a Handbook
of Numerical Analysis, we carefully laid out specific objectives, outlined in the following
excerpts from the “General Preface” which has appeared at the beginning of each of the
volumespublishedsofar:
Duringthepastdecades,giantneedsforevermoresophisticatedmathemat-
icalmodelsandincreasinglycomplexandextensivecomputersimulations
havearisen.Inthisfashion,twoindissociableactivities,mathematicalmod-
elingandcomputersimulation,havegainedamajorstatusinallaspectsof
science,technologyandindustry.
In order that these two sciences be established on the safest possible
grounds,mathematicalrigorisindispensable.Forthisreason,twocompan-
ionsciences,NumericalAnalysisandScientificSoftware,haveemergedas
essential steps for validating the mathematical models and the computer
simulationsthatarebasedonthem.
Numerical Analysis is here understood as the part of Mathematics that
describesandanalyzesallthenumericalschemesthatareusedoncomput-
ers;itsobjectiveconsistsinobtainingaclear,precise,andfaithful,represen-
tationofallthe“information”containedinamathematicalmodel;assuch,
itisthenaturalextensionofmoreclassicaltools,suchasanalyticsolutions,
special transforms, functional analysis, as well as stability and asymptotic
analysis.
The various volumes comprising the Handbook of Numerical Analy-
sis will thoroughly cover all the major aspects of Numerical Analysis, by
presentingaccessibleandin-depthsurveys,whichincludethemostrecent
trends.
Moreprecisely,theHandbookwillcoverthebasicmethodsofNumerical
Analysis,gatheredunderthefollowinggeneralheadings:
– SolutionofEquationsinRn,
– FiniteDifferenceMethods,
– FiniteElementMethods,
– TechniquesofScientificComputing.
v
vi GeneralPreface
Itwillalsocoverthenumericalsolutionofactualproblemsofcontempo-
raryinterestinAppliedMathematics,gatheredunderthefollowinggeneral
headings:
– NumericalMethodsforFluids,
– NumericalMethodsforSolids.
Inretrospect,itcanbesafelyassertedthatVolumesItoIX,whichwere
edited by both of us, fulfilled most of these objectives, thanks to the emi-
nenceoftheauthorsandthequalityoftheircontributions.
After Jacques-Louis Lions’ tragic loss in 2001, it became clear that
Volume IX would be the last one of the type published so far, i.e., edited
bybothofusanddevotedtosomeofthegeneralheadingsdefinedabove.
Itwasthendecided,inconsultationwiththepublisher,thateachfuturevol-
ume will instead be devoted to a single “specific application” and called
forthisreasonaSpecialVolume.“Specificapplications”willincludemath-
ematical finance, meteorology, celestial mechanics, computational chem-
istry, living systems, electromagnetism, computational mathematics, etc.
It is worth noting that the inclusion of such “specific applications” in the
HandbookofNumericalAnalysiswaspartofourinitialproject.
To ensure the continuity of this enterprise, I will continue to act as the
Editor of each Special Volume, whose conception will be jointly coordi-
natedandsupervisedbyaGuestEditor.
P.G.Ciarlet
July2002
Contents of Volume XVI
SpecialVolume:NumericalMethodsforNon-NewtonianFluids
GeneralPreface v
Foreword xix
NumericalMethodsforGrade-TwoFluidModels:Finite-Element
DiscretizationsandAlgorithms,V.Girault,F.Hecht 1
TheLangevinandFokker–PlanckEquationsinPolymerRheology,
AlexeiLozinski,RobertG.Owens,TimothyN.Phillips 211
ViscoelasticFlowswithComplexFreeSurfaces:NumericalAnalysisand
Simulation,AndreaBonito,PhilippeCle´ment,MarcoPicasso 305
StableFiniteElementDiscretizationsforViscoelasticFlowModels,
Young-JuLee,JinchaoXu,Chen-SongZhang 371
PositiveDefinitenessPreservingApproachesforViscoelasticFlowof
Oldroyd-BFluids:ApplicationstoaLid-DrivenCavityFlowanda
ParticulateFlow,Tsorng-WhayPan,JianHao,RolandGlowinski 433
OntheNumericalSimulationofViscoplasticFluidFlow,Roland
Glowinski,AnthonyWachs 483
Modeling,SimulationandOptimizationofElectrorheologicalFluids,
R.H.W.Hoppe,W.G.Litvinov 719
Index 795
vii
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Contents of the Handbook
VolumeI
FiniteDifferenceMethods(Part1)
Introduction,G.I.Marchuk 3
FiniteDifferenceMethodsforLinearParabolicEquations,V.Thome´e 5
SplittingandAlternatingDirectionMethods,G.I.Marchuk 197
SolutionofEquationsinRn(Part1)
LeastSquaresMethods,A˚.Bjo¨rck 465
VolumeII
FiniteElementMethods(Part1)
FiniteElements:AnIntroduction,J.T.Oden 3
BasicErrorEstimatesforEllipticProblems,P.G.Ciarlet 17
LocalBehaviorinFiniteElementMethods,L.B.Wahlbin 353
MixedandHybridMethods,J.E.Roberts,J.-M.Thomas 523
EigenvalueProblems,I.Babusˇka,J.Osborn 641
EvolutionProblems,H.Fujita,T.Suzuki 789
VolumeIII
TechniquesofScientificComputing(Part1)
HistoricalPerspectiveonInterpolation,Approximationand
Quadrature,C.Brezinski 3
Pade´Approximations,C.Brezinski,J.vanIseghem 47
ApproximationandInterpolationTheory,Bl.Sendov,A.Andreev 223
NumericalMethodsforSolids(Part1)
NumericalMethodsforNonlinearThree-DimensionalElasticity,
P.LeTallec 465
ix