双曲问题用的有限元方法：英文版

定　价：¥99.00

作　者：	（）R.J.Leveque著
出版社：	世界图书出版公司北京公司
丛编项：
标　签：	有限元方法

购买这本书可以去

ISBN：	9787506266352	出版时间：	2004-11-01	包装：	简裝本
开本：	23cm	页数：	558	字数：

内容简介

　　This book contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution， including both Iinear problems and nonlinear conservation laws. These equations describe a wide range of wavepropagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner， along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed， in which Riemann problems are solved to determine the local wavestructure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately， but are also useful tools for studying linear wave-propagation problems， particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package. Source code for all the examples presented can be found on the web， along with animations of many timedependent solutions. This provides an excellent leaning environment for understanding wave-propagation phenomena and finite volume methods.Randall LeVeque is the Boeing Professor of Applied Mathematics at the University of Washington.

作者简介

暂缺《双曲问题用的有限元方法：英文版》作者简介

图书目录

Preface
1Introduction
1.1ConservationLaws
1.2FiniteVolumeMethods
1.3MultidimensionalProblems
1.4LinearWavesandDiscontinuousMedia
1.5CLAWPACKSoftware
1.6References
1.7Notation
PartILinearEquations
2ConservationLawsandDifferentialEquations
2.1TheAdvectionEquation
2.2DiffusionandtheAdvection-DiffusionEquation
2.3TheHeatEquation
2.4CapacityFunctions
2.5SourceTerms
2.6NonlinearEquationsinFluidDynamics
2.7LinearAcoustics
2.8SoundWaves
2.9HyperbolicityofLinearSystems
2.10Variable-CoefficientHyperbolicSystems
2.11HyperbolicityofQuasilinearandNonlinearSystems
2.12SolidMechanicsandElasticWaves
2.13LagrangianGasDynamicsandthep-System
2.14ElectromagneticWaves
Exercises
3CharacteristicsandRiemannProblemsforLinearHyperbolicEquations
3.1SolutiontotheCauchyProblem
3.2SuperpositionofWavesandCharacteristicVariables
3.3LeftEigenvectors
3.4SimpleWaves
3.5Acoustics
3.6DomainofDependenceandRangeofInfluence
3.7DiscontinuousSolutions
3.8TheRiemannProblemforaLinearSystem
3.9ThePhasePlaneforSystemsofTwoEquations
3.10CoupledAcousticsandAdvection
3.11Initial-Boundary-ValueProblems
Exercises
4FiniteVolumeMethods
4.1GeneralFormulationforConservationLaws
4.2ANumericalFluxfortheDiffusionEquation
4.3NecessaryComponentsforConvergence
4.4TheCFLCondition
4.5AnUnstableFlux
4.6TheLax-FriedrichsMethod
4.7TheRichtmyerTwo-StepLax-WendroffMethod
4.8UpwindMethods
4.9TheUpwindMethodforAdvection
4.10Godunov'sMethodforLinearSystems
4.11TheNumericalFluxFunctionforGodunov'sMethod
4.12TheWave-PropagationFormofGodunov'sMethod
4.13Flux-Differencevs.Flux-VectorSplitting
4.14Roe'sMethod
Exercises
5IntroductiontotheCLAWPACKSoftware
5.1BasicFramework
5.2ObtainingCLAWPACK
5.3GettingStarted
5.4UsingCLAWPACK-aGuidethroughexamplel
5.5OtherUser-SuppliedRoutinesandFiles
5.6AuxiliaryArraysandsetaux.f
5.7AnAcousticsExample
Exercises
6High-ResolutionMethods
6.1TheLax-WendroffMethod
6.2TheBeam-WarmingMethod
6.3PreviewofLimiters
6.4TheREAAlgorithmwithPiecewiseLinearReconstruction
6.5ChoiceofSlopes
6.6Oscillations
6.7TotalVariation
6.8TVDMethodsBasedontheREAAlgorithm
6.9Slope-LimiterMethods
6.10FluxFormulationwithPiecewiseLinearReconstruction
6.11FluxLimiters
6.12TVDLimiters
6.13High-ResolutionMethodsforSystems
6.14Implementation
6.15ExtensiontoNonlinearSystems
6.16Capacity-FormDifferencing
6.17NonuniformGrids
Exercises
7BoundaryConditionsandGhostCells
7.1PeriodicBoundaryConditions
7.2Advection
7.3Acoustics
Exercises
8Convergence,Accuracy,andStability
8.1Convergence
8.2One-StepandLocalTruncationErrors
8.3StabilityTheory
8.4AccuracyatExtrema
8.5OrderofAccuracyIsn'tEverything
8.6ModifiedEquations
8.7AccuracyNearDiscontinuities
Exercises
9Variable-CoefficientLinearEquations
9.1AdvectioninaPipe
9.2FiniteVolumeMethods
9.3TheColorEquation
9.4TheConservativeAdvectionEquation
9.5EdgeVelocities
9.6Variable-CoefficientAcousticsEquations
9.7Constant-ImpedanceMedia
9.8VariableImpedance
9.9SolvingtheRiemannProblemforAcoustics
9.10TransmissionandReflectionCoefficients
9.11Godunov'sMethod
9.12High-ResolutionMethods
9.13WaveLimiters
9.14HomogenizationofRapidlyVaryingCoefficients
Exercises
10OtherApproachestoHighResolution
10.1Centered-in-TimeFluxes
10.2Higher-OrderHigh-ResolutionMethods
10.3LimitationsoftheLax-Wendroff(TaylorSeries)Approach
10.4SemidiscreteMethodsplusTimeStepping
10.5StaggeredGridsandCentralSchemes
Exercises
PartIINonlinearEquations
11NonlinearScalarConservationLaws
11.1TrafficFlow
11.2QuasilinearFormandCharacteristics
11.3Burgers'Equation
11.4RarefactionWaves
11.5CompressionWaves
11.6VanishingViscosity
11.7Equal-AreaRule
11.8ShockSpeed
11.9TheRankine-HugoniotConditionsforSystems
11.10SimilaritySolutionsandCenteredRarefactions
11.11WeakSolutions
11.12ManipulatingConservationLaws
11.13Nonuniqueness,Admissibility,andEntropyConditions
11.14EntropyFunctions
11.15Long-TimeBehaviorandN-WaveDecay
Exercises
12FiniteVolumeMethodsforNonlinearScalarConservationLaws
12.1Godunov'sMethod
12.2Fluctuations,Waves,andSpeeds
12.3TransonicRarefactionsandanEntropyFix
12.4NumericalViscosity
12.5TheLax-FriedrichsandLocalLax-FriedrichsMethods
12.6TheEngquist-OsherMethod
12.7E-schemes
12.8High-ResolutionTVDMethods
12.9TheImportanceofConservationForm
12.10TheLax-WendroffTheorem
12.11TheEntropyCondition
12.12NonlinearStability
Exercises
13NonlinearSystemsofConservationLaws
13.1TheShallowWaterEquations
13.2Dam-BreakandRiemannProblems
13.3CharacteristicStructure
13.4ATwo-ShockRiemannSolution
13.5WeakWavesandtheLinearizedProblem
13.6StrategyforSolvingtheRiemannProblem
13.7ShockWavesandHugoniotLoci
13.8SimpleWavesandRarefactions
13.9SolvingtheDam-BreakProblem
13.10TheGeneralRiemannSolverforShallowWaterEquations
13.11ShockCollisionProblems
13.12LinearDegeneracyandContactDiscontinuities
Exercises
14GasDynamicsandtheEulerEquations
14.1Pressure
14.2Energy
14.3TheEulerEquations
14.4PolytropicIdealGas
14.5Entropy
14.6IsothermalFlow
14.7TheEulerEquationsinPrimitiveVariables
14.8TheRiemannProblemfortheEulerEquations
14.9ContactDiscontinuities
14.10RiemannInvariants
14.11SolutiontotheRiemannProblem
14.12TheStructureofRarefactionWaves
14.13ShockTubesandRiemannProblems
14.14MultifluidProblems
14.15OtherEquationsofStateandIncompressibleFlow
15FiniteVolumeMethodsforNonlinearSystems
15.1Godunov'sMethod
15.2ConvergenceofGodunov'sMethod
15.3ApproximateRiemannSolvers
15.4High-ResolutionMethodsforNonlinearSystems
15.5AnAlternativeWave-PropagationImplementationofApproximateRiemannSolvers
15.6Second-OrderAccuracy
15.7Flux-VectorSplitting
15.8TotalVariationforSystemsofEquations
Exercises
16SomeNonclassicalHyperbolicProblems
16.1NonconvexFluxFunctions
16.2NonstrictlyHyperbolicProblems
16.3LossofHyperbolicity
16.4SpatiallyVaryingFluxFunctions
16.5NonconservativeNonlinearHyperbolicEquations
16.6NonconservativeTransportEquations
Exercises
17SourceTermsandBalanceLaws
17.1Fractional-StepMethods
17.2AnAdvection-ReactionEquation
17.3GeneralFormulationofFractional-StepMethodsforLinearProblems
17.4StrangSplitting
17.5AccuracyofGodunovandStrangSplittings
17.6ChoiceofODESolver
17.7ImplicitMethods,ViscousTerms,andHigher-OrderDerivatives
17.8Steady-StateSolutions
17.9BoundaryConditionsforFractional-StepMethods
17.10StiffandSingularSourceTerms
17.11LinearTrafficFlowwithOn-RampsorExits
17.12Rankine-HugoniotJumpConditionsataSingularSource
17.13NonlinearTrafficFlowwithOn-RampsorExits
17.14AccurateSolutionofQuasisteadyProblems
17.15BurgersEquationwithaStiffSourceTerm
17.16NumericalDifficultieswithStiffSourceTerms
17.17RelaxationSystems
17.18RelaxationSchemes
Exercises
PartIIIMultidimensionalProblems
18MultidimensionalHyperbolicProblems
18.1DerivationofConservationLaws
18.2Advection
18.3CompressibleFlow
18.4Acoustics
18.5Hyperbolicity
18.6Three-DimensionalSystems
18.7ShallowWaterEquations
18.8EulerEquations
18.9SymmetryandReductionofDimension
Exercises
19MultidimensionalNumericalMethods
19.1FiniteDifferenceMethods
19.2FiniteVolumeMethodsandApproachestoDiscretization
19.3FullyDiscreteFlux-DifferencingMethods
19.4SemidiscreteMethodswithRunge-KuttaTimeStepping
19.5DimensionalSplitting
Exercise
20MultidimensionalScalarEquations
20.1TheDonor-CellUpwindMethodforAdvection
20.2TheComer-TransportUpwindMethodforAdvection
20.3Wave-PropagationImplementationoftheCTUMethod
20.4yonNeumannStabilityAnalysis
20.5TheCTUMethodforVariable-CoefficientAdvection
20.6High-ResolutionCorrectionTerms
20.7RelationtotheLax-WendroffMethod
20.8Divergence-FreeVelocityFields
20.9NonlinearScalarConservationLaws
20.10Convergence
Exercises
21MultidimensionalSystems
21.1Constant-CoefficientLinearSystems
21.2TheWave-PropagationApproachtoAccumulatingFluxes
21.3CLAWPACKImplementation
21.4Acoustics
21.5AcousticsinHeterogeneousMedia
21.6TransverseRiemannSolversforNonlinearSystems
21.7ShallowWaterEquations
21.8BoundaryConditions
22ElasticWaves
22.1DerivationoftheElasticityEquations
22.2ThePlane-StrainEquationsofTwo-DimensionalElasticity
22.3One-DimensionalSlices
22.4BoundaryConditions
22.5ThePlane-StressEquationsandTwo-DimensionalPlates
22.6AOne-DimensionalRod
22.7Two-DimensionalElasticityinHeterogeneousMedia
23FiniteVolumeMethodsonQuadrilateralGrids
23.1CellAveragesandInterfaceFluxes
23.2LogicallyRectangularGrids
23.3Godunov'sMethod
23.4FluctuationForm
23.5AdvectionEquations
23.6Acoustics
23.7ShallowWaterandEulerEquations
23.8UsingCLAWPACKonQuadrilateralGrids
23.9BoundaryConditions
Bibliography
Index