Free-Surface Flow

Computational Methods
 
 
Elsevier (Verlag)
  • 1. Auflage
  • |
  • erschienen am 14. November 2018
  • |
  • 914 Seiten
 
E-Book | PDF mit Adobe DRM | Systemvoraussetzungen
978-0-12-815486-1 (ISBN)
 

Free-Surface Flow: Computational Methods presents a detailed analysis of numerical schemes for shallow-water waves. It includes practical applications for the numerical simulation of flow and transport in rivers and estuaries, the dam-break problem and overland flow. Closure models for turbulence, such as Reynolds-Averaged Navier-Stokes and Large Eddy Simulation are presented, coupling the aforementioned surface tracking techniques with environmental fluid dynamics. While many computer programs can solve the partial differential equations describing the dynamics of fluids, many are not capable of including free surfaces in their simulations.

  • Provides numerical solutions of the turbulent Navier-Stokes equations in three space dimensions
  • Includes closure models for turbulence, such as Reynolds-Averaged Navier-Stokes, and Large Eddy Simulation
  • Practical applications are presented for the numerical simulation of flow and transport in rivers and estuaries, the dam-break problem and overland flow


Nikolaos D. Katopodes, University Michigan Ann Arbor, Department of Civil & Environmental Engineering, Ann Arbor, United States. Dr. Katopodes has chaired or co-chaired 28 PhD student theses. His research has resulted in over 200 publications, and several software packages that are used worldwide for the analysis and control of free-surface flows.
  • Englisch
  • San Diego
  • |
  • USA
  • 52,70 MB
978-0-12-815486-1 (9780128154861)
weitere Ausgaben werden ermittelt
  • Front Cover
  • Free-Surface Flow
  • Copyright
  • Contents
  • Prologue
  • Motivation
  • Approach of This Text
  • Outline
  • Acknowledgments
  • References
  • 1 Basic Concepts
  • 1.1 Introduction
  • 1.1.1 "Newton's Rules" for Computational Modeling
  • 1.1.2 Computational Models
  • 1.2 The Taylor Series
  • 1.3 Finite-Difference Approximations
  • 1.3.1 Forward Differences
  • 1.3.2 Backward Differences
  • 1.3.3 Central Differences
  • 1.3.4 Second-Order, One-Sided Differences
  • 1.3.5 Identity and Shift Operators
  • 1.3.6 Linear Difference Equations
  • 1.4 Initial-Value Problems for ODE's
  • 1.4.1 Basic Numerical Models
  • 1.4.2 Truncation Error and Order of Accuracy
  • 1.4.3 Stability, Consistency, and Convergence
  • 1.4.4 Absolute Stability
  • 1.4.5 Runge-Kutta Methods
  • 1.4.6 Linear Multi-Step Methods
  • 1.4.7 Backward-Difference Methods
  • 1.5 Boundary-Value Problems
  • 1.5.1 Steady-State Diffusion
  • 1.5.2 Solution of a Tri-Diagonal System
  • 1.5.3 The Thomas Algorithm
  • 1.5.4 Natural Boundary Conditions
  • 1.5.5 Variable Grid Computations
  • 1.6 Error Norms
  • 1.7 Algorithmic Dissipation
  • 1.7.1 Backward Difference Model
  • 1.7.2 Damping Effect of 2nd Derivative Operator
  • 1.7.3 Order of Dissipation
  • 1.7.4 Algorithmic Dispersion
  • 1.8 von Neumann Stability Analysis
  • 1.8.1 Representation of Oscillatory Data - Wave Aliasing
  • 1.8.2 Discrete Fourier Series Representation
  • 1.8.3 The Fourier Symbol
  • 1.8.4 Temporal Evolution
  • 1.8.5 Propagation Factor
  • 1.8.6 Algorithmic Dissipation - Condition for Stability
  • 1.8.7 Algorithmic Celerity - Dispersion
  • 1.8.8 Algorithmic Portrait
  • 1.8.9 Construction of Phase and Amplitude Graphs
  • 1.8.10 PDE's With Variable Coef cients
  • 1.9 Stability, Consistency, and Convergence
  • 1.9.1 Positivity and Monotonicity
  • 1.10 Least-Squares Approximation
  • Problems
  • References
  • 2 Finite-Difference Methods for Diffusion
  • 2.1 Introduction
  • 2.2 Explicit Scheme for Diffusion (FTCS)
  • 2.2.1 Results and Error Estimates
  • 2.2.2 Stability
  • 2.2.3 Propagation of Information
  • 2.2.4 Discretization of Discontinuous Initial Data
  • 2.2.5 Boundary Effects
  • 2.2.6 Natural Boundary Conditions
  • 2.2.7 Simulation of a Point Source
  • 2.2.8 Accuracy of FTCS Scheme
  • 2.3 Oscillatory Initial Data and Spurious Signals
  • 2.3.1 Spurious Waves
  • 2.3.2 Stability of FTCS Scheme
  • 2.4 Leapfrog Scheme
  • 2.4.1 Stability Analysis of Leapfrog Scheme
  • 2.5 du Fort-Frankel Scheme
  • 2.6 Implicit Scheme for Diffusion
  • 2.6.1 Natural Boundary Conditions
  • 2.6.2 Accuracy of BTCS Scheme
  • 2.6.3 Stability of BTCS Scheme
  • 2.7 Crank-Nicolson Implicit Scheme
  • 2.7.1 Stability of Crank-Nicolson Scheme
  • 2.7.2 Weighted Average Explicit-Implicit Scheme
  • Problems
  • References
  • 3 Finite-Difference Methods for Advection
  • 3.1 Introduction
  • 3.2 The Numerical Method of Characteristics
  • 3.2.1 Curvilinear Characteristic Network
  • 3.2.2 Characteristic Scheme on a Cartesian Grid
  • 3.2.3 The Effect of Interpolation
  • 3.3 Explicit Upwind Scheme (FTBS)
  • 3.3.1 Accuracy of Upwind Scheme
  • 3.4 The Courant-Friedrichs-Lewy (CFL) Condition
  • 3.4.1 Stability of Explicit Upwind Scheme
  • 3.5 Centered Explicit Scheme (FTCS)
  • 3.6 Implicit Upwind Scheme (BTBS)
  • 3.6.1 Stability of the BTBS Scheme
  • 3.7 Lax-Friedrichs Scheme
  • 3.7.1 Stability Analysis
  • 3.8 Leapfrog Scheme
  • 3.8.1 Propagation Properties
  • 3.8.2 Stability Analysis
  • 3.8.3 Dispersion Control
  • 3.8.3.1 Leapfrog-Trapezoidal Scheme
  • 3.8.3.2 Leapfrog-RAW Scheme
  • 3.9 The Lax-Wendroff Scheme
  • 3.9.1 Fourier Analysis of Lax-Wendroff Scheme
  • 3.9.2 Two-Step Lax-Wendroff-Richtmyer Scheme
  • 3.10 Beam and Warming Scheme
  • 3.10.1 Stability Analysis
  • 3.11 Parasitic Waves, Dissipation, and Dispersion
  • 3.11.1 Leapfrog Scheme
  • 3.11.2 Lax-Wendroff Scheme
  • 3.11.3 Frequency Analysis
  • 3.11.4 Group Velocity
  • 3.12 Advection Coupled With Diffusion
  • 3.12.1 Steady State Solution
  • 3.12.2 Generalized Upwind Method
  • 3.13 Transient Advection-Diffusion Schemes
  • 3.13.1 Centered Explicit Scheme
  • 3.13.2 Crank-Nicolson Scheme
  • 3.13.3 Stability of Crank-Nicolson Scheme
  • 3.13.4 Boundary Conditions
  • Problems
  • References
  • 4 Finite-Element and Finite-Volume Methods for Scalar Transport
  • 4.1 Introduction
  • 4.1.1 Variational Principles
  • 4.1.1.1 Functional for Steady State Diffusion
  • 4.2 The Finite-Element Method (FEM)
  • 4.2.1 Basis Functions
  • 4.2.2 FEM Approximation of the Functional
  • 4.3 Method of Weighted Residuals
  • 4.3.1 Optimal Least-Squares Distance
  • 4.3.2 Inner Product Space
  • 4.3.3 Minimization of the Finite-Element Residual
  • 4.3.4 Linear Finite Elements
  • 4.3.5 Local Coordinates
  • 4.4 Diffusion Matrix and Load Vector
  • 4.5 Finite-Element Model for Transient Diffusion
  • 4.5.1 Time Domain Discretization
  • 4.6 Finite-Element Model for Advection
  • 4.6.1 Semi-Discrete Form
  • 4.6.2 Advection of a Sharp Concentration Front
  • 4.7 Petrov-Galerkin Modi cation
  • 4.7.1 Dissipative Galerkin Model
  • 4.7.2 Fourier Stability Analysis
  • 4.7.3 Phase and Amplitude Portraits
  • 4.7.4 Anti-Dissipative Behavior
  • 4.7.5 Preserving Monotonicity
  • 4.7.6 Selective Dissipation and Shock Capturing
  • 4.7.7 Fully Discrete Monotone DG Model
  • 4.8 Finite-Volume Method for Diffusion
  • 4.9 Finite Volume Method for Advection
  • 4.9.1 Conservative Fluxes
  • 4.9.2 Upwind Finite Volume Scheme
  • 4.9.3 QUICK Scheme for Advection
  • 4.10 Total Variation Diminishing
  • 4.11 Superbee Limiter for Advection
  • 4.11.1 Comparison With the Petrov-Galerkin Finite-Element Model
  • 4.12 Discontinuous Galerkin Method
  • 4.12.1 Linear Advection Equation
  • 4.12.2 Stability Analysis
  • Problems
  • References
  • 5 Finite-Difference Methods for Equilibrium Problems
  • 5.1 Introduction
  • 5.2 Domain Discretization
  • 5.2.1 Choice of Computational Nodes
  • 5.3 Equilibrium Problems
  • 5.3.1 Finite-Difference Solution of Laplace's Equation
  • 5.3.2 Sources and Anisotropic Media
  • 5.3.3 Natural Node Ordering
  • 5.3.4 The Right Hand Side Vector
  • 5.3.5 The Coef cient Matrix of the Discrete Laplacian
  • 5.3.6 Fast Poisson Solvers
  • 5.3.7 The Residual Equation
  • 5.4 Iterative Solution of Sparse Systems
  • 5.4.1 Relaxation Methods
  • 5.4.2 Over Relaxation
  • 5.4.3 Application of SOR to a Square Domain
  • 5.4.4 Convergence of the Iterations
  • 5.4.5 The Spectral Radius
  • 5.4.6 Optimum Relaxation Factor
  • 5.4.7 Comparison of Relaxation Methods
  • 5.4.8 Impact of Problem Size
  • 5.5 Optimization Methods for Solving Sparse Systems of Linear Equations
  • 5.5.1 Conjugate Gradient Method
  • 5.6 Matrix Preconditioning
  • 5.6.1 Preconditioned Conjugate Gradient Method
  • 5.6.1.1 Incomplete Factorization
  • 5.6.1.2 LDU Factorization
  • 5.6.2 Incomplete Factorization
  • 5.6.3 Incomplete Cholesky Factorization Algorithm
  • 5.6.4 Preconditioned Conjugate Gradient Method
  • 5.6.5 Modi ed Incomplete Cholesky Factorization
  • 5.6.6 Convergence Tests
  • 5.7 Multigrid Methods
  • 5.7.1 Diffusion of Iteration Error
  • 5.7.2 Eigenvalues of the Iteration Matrix
  • 5.7.2.1 Higher Dimensions
  • 5.7.3 Modes of the Jacobi Iteration
  • 5.7.4 Behavior on Coarse Grid
  • 5.7.5 Elements of Multigrid Method
  • 5.7.6 Inter-Grid Operations
  • 5.7.6.1 Prolongation
  • 5.7.7 Restriction
  • 5.7.8 Cycling Schemes
  • 5.7.9 Multigrid Solution of Laplace Equation
  • 5.8 Multi-Domain Methods
  • 5.8.1 Schwarz Alternating Method
  • 5.8.1.1 General Boundary Conditions
  • 5.8.2 Steklov-Poincaré Method
  • 5.8.3 Schur Complement and Iterative Substructuring
  • 5.9 Irregular Boundaries
  • 5.9.1 Dirichlet Boundaries
  • 5.9.2 Neumann Boundaries
  • Problems
  • References
  • 6 Methods for Two-Dimensional Scalar Transport
  • 6.1 Introduction
  • 6.2 Finite-Difference Models for Diffusion
  • 6.2.1 Explicit Method (FTCS) for Diffusion
  • 6.2.2 Stability of 2D-FTCS
  • 6.2.2.1 The Relaxation Analogy
  • 6.2.3 Alternating Direction Implicit (ADI) Scheme
  • 6.2.4 Stability of ADI Scheme
  • 6.3 Finite-Difference Models for Advection
  • 6.3.1 The Method of Characteristics for 2D Advection
  • 6.3.2 Stability of 2D Method of Characteristics
  • 6.3.3 Upwind Method (FTBS) for Advection
  • 6.3.4 Stability of 2D-Upwind Scheme for Advection
  • 6.3.5 Modi ed Equation of the Upwind Scheme
  • 6.3.6 2D Lax-Friedrichs Scheme
  • 6.3.7 Stability Analysis of Lax-Friedrichs Scheme
  • 6.3.8 2D Lax-Wendroff Scheme
  • 6.3.9 Stability Analysis of 2D Lax-Wendroff Scheme
  • 6.4 Advection Coupled With Diffusion
  • 6.4.1 Stability of Crank-Nicolson Scheme
  • 6.4.2 Cross-Wind Diffusion
  • 6.5 Finite-Element Analysis
  • 6.5.1 Two-Dimensional Shape Functions
  • 6.6 Galerkin Formulation
  • 6.6.1 Transformation of Shape Function Derivatives
  • 6.6.2 Transformation of Integrals to Local Coordinates
  • 6.6.3 Finite Element Equations
  • 6.6.4 Gaussian Quadrature
  • 6.6.4.1 Transient Advection-Diffusion Problems
  • 6.6.5 Petrov-Galerkin Approximation
  • 6.6.6 Large-Scale Applications
  • Problems
  • References
  • 7 Methods for Open-Channel Flow
  • 7.1 The Method of Characteristics
  • 7.1.1 Kinematic Waves
  • 7.1.2 Kinematic Shock Model
  • 7.1.3 Dynamic Waves
  • 7.1.4 Massau's Method
  • 7.1.5 Moving Boundaries
  • 7.1.6 Hartree's Method
  • 7.1.6.1 Moving Boundaries
  • 7.1.6.2 Shock Fitting
  • 7.2 Finite-Difference Methods
  • 7.2.1 Naive FTCS Scheme
  • 7.2.1.1 Boundary Conditions
  • 7.2.1.2 Stability Analysis
  • 7.2.2 Lax-Friedrichs Scheme
  • 7.2.3 Lax-Wendroff Scheme
  • 7.2.3.1 Two Step Version of LW Scheme
  • 7.2.3.2 Boundary Conditions
  • 7.2.3.3 Stability Analysis
  • 7.2.4 The Preissmann Implicit Scheme
  • 7.2.4.1 Double Sweep Method
  • 7.2.4.2 Stability Analysis
  • 7.2.5 Implicit ENO Method
  • 7.2.5.1 Computational Results
  • 7.3 FEM for Open-Channel Flow
  • 7.3.1 Bubnov-Galerkin Method (BG)
  • 7.3.1.1 Computational Results
  • 7.3.1.2 Stability Analysis
  • 7.3.2 Taylor-Galerkin Method
  • 7.3.2.1 Stability Analysis
  • 7.3.3 Petrov-Galerkin Method
  • 7.3.4 Dissipative Galerkin Scheme (DG)
  • 7.3.4.1 Stability Analysis
  • 7.3.5 Characteristic Galerkin Scheme (CG)
  • 7.3.5.1 Stability Analysis
  • 7.3.6 Comparative Analysis of Petrov-Galerkin Schemes
  • 7.4 Finite-Volume Methods for Open-Channel Flow
  • 7.4.1 The Riemann Problem
  • 7.4.2 Numerical Flux Functions
  • 7.4.3 Transcritical Depression Waves
  • 7.4.4 Source Term Discretization
  • 7.4.5 Extension to Second Order Accuracy
  • 7.4.6 Flux Limiting
  • 7.4.7 Stability Analysis
  • 7.4.8 Computational Results
  • 7.4.9 Zero-Inertia Deforming-Cell Model
  • 7.4.9.1 In ow Boundary
  • 7.4.9.2 Surge Front
  • 7.5 Dispersive Waves
  • 7.5.1 Stability Analysis
  • 7.5.2 Computational Results
  • 7.5.3 Serre Equations
  • 7.5.4 Finite-Volume Methods
  • Problems
  • References
  • 8 Methods for Two-Dimensional Shallow-Water Flow
  • 8.1 Introduction
  • 8.2 The Numerical Method of Bicharacteristics
  • 8.2.1 Parametric Form of Characteristic Relations
  • 8.2.2 Direct Tetrahedral Network
  • 8.2.3 Inverse Tetrahedral Network
  • 8.2.4 Inverse Pentahedral Network
  • 8.2.4.1 Discrete Compatibility Equations
  • 8.2.4.2 Predictor Step
  • 8.2.4.3 Corrector Step
  • 8.2.4.4 Bicharacteristic Tangency Condition
  • 8.2.4.5 Bivariate Interpolation of Initial Data
  • 8.2.4.6 Stability Analysis
  • 8.2.4.7 Moving Grid Algorithm
  • 8.2.4.8 Boundary Conditions
  • 8.2.4.9 Computational Results
  • 8.3 Finite-Difference Models
  • 8.3.1 Leendertse Scheme
  • 8.3.1.1 Stability Analysis
  • 8.3.2 Computational Results
  • 8.3.3 MacCormack Scheme
  • 8.3.3.1 Boundary Conditions
  • 8.3.3.2 Stability Analysis
  • 8.3.3.3 Computational Results
  • 8.4 Finite-Element Models
  • 8.4.1 Deforming Element Formulation
  • 8.4.2 The Dissipative Interface
  • 8.4.3 Deforming Flow Domain
  • 8.4.4 Computational Results
  • 8.5 Finite-Volume Models
  • 8.5.1 Structured Grid Model
  • 8.5.2 The MUSCL Scheme for Two-Dimensional Flow
  • 8.5.3 Boundary Conditions
  • 8.5.4 Source Term Discretization
  • 8.5.4.1 Hydrostatic Imbalance
  • 8.5.5 Critical Flow Sections
  • 8.5.6 Stability Analysis
  • 8.5.7 Wave Propagation on Dry Terrain
  • 8.5.7.1 Steep Slopes With Low Runoff
  • 8.5.8 Computational Results
  • Problems
  • References
  • 9 Methods for Incompressible Viscous Flow
  • 9.1 Introduction
  • 9.2 Projection Method
  • 9.2.1 2D Staggered Grid Discretization
  • 9.2.2 Time Integration
  • 9.2.2.1 Stability Condition
  • 9.2.2.2 Semi-Implicit Formulation
  • 9.2.3 Spatial Discretization
  • 9.2.3.1 Averaging Errors
  • 9.2.4 Upwinding of Advective Terms
  • 9.2.5 Boundary Conditions
  • 9.2.6 Computational Results
  • 9.2.7 Higher-Order Projection methods
  • 9.2.7.1 Block LU Factorization
  • 9.2.7.2 Strong-Stability-Preserving Methods
  • 9.3 Finite-Element Methods
  • 9.3.1 Mixed Element Formulation
  • 9.3.2 Lagrange Multiplier Approach
  • 9.3.3 Penalty Methods
  • 9.3.4 Arti cial Compressibility
  • 9.4 Finite-Volume Methods
  • 9.4.1 Semi-Implicit Method for Pressure-Linked Equations (SIMPLE)
  • 9.4.1.1 SIMPLE Algorithm
  • 9.4.2 FVM on Collocated Grids
  • 9.4.3 Pressure-Implicit With Splitting of Operator (PISO)
  • 9.4.3.1 PISO Algorithm
  • 9.4.3.2 Stability Analysis
  • Problems
  • References
  • 10 Deforming Grid Methods
  • 10.1 Introduction
  • 10.2 Finite-Difference Projection Method
  • 10.2.1 Flow With Small Density Gradients
  • 10.2.2 Staggered Spatial Discretization
  • 10.2.3 Computational Results
  • 10.3 FEM for Ideal Fluid Flow
  • 10.3.1 Finite-Element Solution
  • 10.3.1.1 Backwater Subdomain
  • 10.3.1.2 Tailwater Subdomain
  • 10.4 FEM for Viscous Flow
  • 10.4.1 Boundary Conditions
  • 10.4.2 Steady, Two-Dimensional Flow
  • 10.4.2.1 Domain Discretization
  • 10.4.2.2 Method of Weighted Residuals
  • 10.4.2.3 Local Coordinates
  • 10.4.2.4 Formulation of Global Matrices
  • 10.4.2.5 Computation of Free-Surface
  • 10.4.2.6 Computational Results
  • 10.4.3 Unsteady Viscous Flow
  • 10.4.3.1 Formulation of Residuals
  • 10.4.3.2 Time Integration Scheme
  • 10.4.3.3 Unsteady Flow Simulations
  • 10.4.4 Extended Finite Element Method
  • 10.4.5 Three-Dimensional Deforming FEM
  • 10.4.5.1 Upstream Weighting
  • 10.4.5.2 Deforming Element Formulation
  • 10.4.5.3 Evaluation of Element Matrices
  • 10.4.5.4 Nonlinear System Solver
  • 10.4.5.5 Computational Results
  • 10.4.6 ALE FEM in Three Dimensions
  • 10.5 Structured Finite-Volume Method
  • 10.5.1 Conservation Form of Equations
  • 10.5.2 Velocity of Nodal Motion
  • 10.5.3 Finite Volume Equations
  • 10.5.4 Time Integration
  • 10.5.4.1 Free Surface Elevation
  • 10.5.4.2 The Dynamic Pressure Solver
  • 10.5.5 Scalar Transport
  • 10.5.6 Spatial Discretization
  • 10.5.7 Computational Results
  • 10.6 Unstructured Large-Scale Models
  • 10.6.1 Vertical Coordinates
  • 10.6.2 Governing Equations
  • 10.6.3 z-Level Unstructured Grid
  • 10.6.4 Numerical Algorithm
  • 10.6.4.1 Drag Boundary Conditions
  • 10.6.5 Discrete Continuity Equation
  • 10.6.6 Advection of Momentum
  • 10.6.6.1 Horizontal Diffusion of Momentum
  • 10.6.6.2 Non-Hydrostatic Pressure
  • 10.6.6.3 Discretized Transport Equations
  • 10.6.6.4 Stability Conditions
  • 10.6.7 Computational Results
  • Problems
  • References
  • 11 Marker and Cell Method
  • 11.1 Introduction
  • 11.2 Particle-In-Cell Method
  • 11.2.1 Computational Results
  • 11.3 Marker-And-Cell Method
  • 11.3.1 2D MAC Method
  • 11.3.2 Initial and Boundary Conditions
  • 11.3.2.1 In ow Boundary
  • 11.3.2.2 Out ow Boundary
  • 11.3.2.3 Free-Slip Wall Boundary
  • 11.3.2.4 No-Slip Wall Boundary
  • 11.3.2.5 Permeable Wall Boundary
  • 11.3.2.6 Corner Boundary
  • 11.3.2.7 Free-Surface Boundary
  • 11.3.3 Modi ed Free-Surface Condition
  • 11.3.4 Particle Movement
  • 11.3.5 The Overall Algorithm
  • 11.3.6 Stability Conditions
  • 11.3.7 Laminar Flow Applications
  • 11.4 Turbulent Flow Simulation
  • 11.4.1 The Donor Cell Upwind Scheme
  • 11.4.1.1 Boundary Conditions for Turbulent Flow
  • 11.4.2 Turbulent Flow Applications
  • 11.5 Semi-Implicit MAC Method
  • 11.5.1 Streamwise Momentum Equation
  • 11.5.2 Vertical Momentum Equation
  • 11.5.3 Enforcement of Incompressibility
  • 11.6 Extension to Inclined Channels
  • 11.6.1 Particle Movement
  • 11.6.2 Computational Results
  • 11.7 Recent Developments
  • Problems
  • References
  • 12 Volume of Fluid Method
  • 12.1 Introduction
  • 12.2 Simple Line Interface Calculation
  • 12.3 Fractional Volume of Fluid
  • 12.3.1 Pressure De nition in a Surface Cell
  • 12.3.2 Advection of Fractional Volume of Fluid
  • 12.3.3 Subgrid Computations
  • 12.3.3.1 Computational Results
  • 12.3.4 Piece-Wise Linear Interface Calculation
  • 12.3.4.1 The Interface Normal
  • 12.3.5 Intersection With Cell Edges
  • 12.4 Analytical Reconstruction Methods
  • 12.4.1 Interface Position
  • 12.4.2 Lagrangian Advection of the Interface
  • 12.4.3 Extension to Three Dimensions
  • 12.4.4 Computational Results
  • 12.4.5 Eulerian Advection of the Interface
  • 12.4.5.1 Sudden Closing of Sluice Gate
  • 12.4.5.2 Fluid-Structure Interaction
  • 12.4.5.3 Two-Phase Flow: Breaking Waves
  • 12.4.5.4 Two-Phase Flow: Bubble Formation
  • Problems
  • References
  • 13 Level Set Method
  • 13.1 Introduction
  • 13.2 Implicit Surfaces
  • 13.3 Level Set Method
  • 13.3.1 The Level Set Function
  • 13.3.2 Evolution of the Level Set Function
  • 13.3.3 Free-Surface Thickness
  • 13.3.4 The Signed Distance Function
  • 13.3.5 Re-Initialization of the Level Set Function
  • 13.3.5.1 Smoothing the Signed Distance Function
  • 13.4 WENO Scheme for Interface Advection
  • 13.5 Computational Results
  • 13.5.1 Multi-Marker, Level Set Method
  • 13.5.2 Iso-Geometric Analysis Model
  • 13.5.3 Immersed Boundary - Level Set Method
  • 13.5.4 Comparison of Volume of Fluid and Level Set Methods
  • Problems
  • References
  • 14 Smoothed Particle Hydrodynamics
  • 14.1 Introduction
  • 14.2 Integral Representation of Fluid Properties
  • 14.2.1 Selection of SPH Kernel
  • 14.2.2 Approximate Kernel Functions
  • 14.2.3 Accuracy of SPH Approximation
  • 14.2.4 Evaluation of Derivatives
  • 14.3 Summation Representation of Fluid Properties
  • 14.3.1 Summation Representation of Derivatives
  • 14.4 SPH for Viscous Flow
  • 14.4.1 Conservation of Mass
  • 14.4.2 Conservation of Momentum
  • 14.4.2.1 Viscosity Models
  • 14.4.2.2 Arti cial Viscosity
  • 14.4.2.3 Equation of State
  • 14.4.3 Adaptive Smoothing Length
  • 14.5 Boundary Conditions
  • 14.5.1 No-Slip Wall Boundary
  • 14.5.2 Free-Slip Wall Boundary
  • 14.5.3 Free Surface Boundary
  • 14.6 Propagation of Particles
  • 14.6.1 Stability Conditions
  • 14.6.2 Enhanced SPH Methods
  • 14.7 Practical Implementation
  • 14.8 Computational Results
  • 14.8.1 Two-Dimensional Dam-Break Wave
  • 14.8.2 Impact and Ricochet of Plunging Jet
  • 14.8.3 Ice-Shelf Dynamics
  • 14.8.4 Three-Dimensional Dam-Break Model
  • 14.8.5 Simulation of Spillway Flow
  • 14.8.6 Combined SPH and Level Set Method
  • Problems
  • References
  • Epilogue
  • Note
  • Bibliography
  • Index
  • Back Cover

Dateiformat: PDF
Kopierschutz: Adobe-DRM (Digital Rights Management)

Systemvoraussetzungen:

Computer (Windows; MacOS X; Linux): Installieren Sie bereits vor dem Download die kostenlose Software Adobe Digital Editions (siehe E-Book Hilfe).

Tablet/Smartphone (Android; iOS): Installieren Sie bereits vor dem Download die kostenlose App Adobe Digital Editions (siehe E-Book Hilfe).

E-Book-Reader: Bookeen, Kobo, Pocketbook, Sony, Tolino u.v.a.m. (nicht Kindle)

Das Dateiformat PDF zeigt auf jeder Hardware eine Buchseite stets identisch an. Daher ist eine PDF auch für ein komplexes Layout geeignet, wie es bei Lehr- und Fachbüchern verwendet wird (Bilder, Tabellen, Spalten, Fußnoten). Bei kleinen Displays von E-Readern oder Smartphones sind PDF leider eher nervig, weil zu viel Scrollen notwendig ist. Mit Adobe-DRM wird hier ein "harter" Kopierschutz verwendet. Wenn die notwendigen Voraussetzungen nicht vorliegen, können Sie das E-Book leider nicht öffnen. Daher müssen Sie bereits vor dem Download Ihre Lese-Hardware vorbereiten.

Bitte beachten Sie bei der Verwendung der Lese-Software Adobe Digital Editions: wir empfehlen Ihnen unbedingt nach Installation der Lese-Software diese mit Ihrer persönlichen Adobe-ID zu autorisieren!

Weitere Informationen finden Sie in unserer E-Book Hilfe.


Download (sofort verfügbar)

261,80 €
inkl. 19% MwSt.
Download / Einzel-Lizenz
PDF mit Adobe DRM
siehe Systemvoraussetzungen
E-Book bestellen