Computational River Dynamics

Comprehensive text on the fundamentals of modeling flow and sediment transport in rivers treating both physical principles and numerical methods for various degrees of complexity. Includes 1-D, 2-D (both depth- and width-averaged) and 3-D models, as well as the integration and coupling of these models. Contains a broad selection

Table of Contents:
Preface Notations CHAPTER 1. Introduction 1.1 Overview of River Engineering 1.2 Role of Computational Simulation in River Engineering Analysis 1.3 Scope, Problems and Strategies of Computational River Dynamics 1.4 Classification of Flow and Sediment Transport Models 1.5 Coverage and Features of This Book CHAPTER 2. Mathematical Description of Flow and Sediment Transport 2.1 Properties of Water and Sediment 2.1.1 Properties of Water 2.1.2 Properties of Sediment 2.1.2.1 Physical Properties of Single Particles 2.1.2.2 Bulk Properties of Sediment Mixtures 2.1.2.3 Definition of Sediment Loads 2.1.3 Properties of the Water and Sediment Mixture 2.2 Governing Equations of Water and Sediment Two-Phase Flow 2.2.1 Hydrodynamic Equations 2.2.2 Sediment Transport Equation 2.2.3 Simplification in the case of Low Sediment Concentration 2.3 Time-Averaged Models of Turbulent Flow and Sediment Transport 2.3.1 Mean Movement Equations 2.3.2 Zero-Equation Turbulence Models 2.3.3 One-Equation Turbulence Models 2.3.4 Two-Equation Turbulence Models 2.3.5 Other Turbulence Models and Simulations 2.4 Derivation of 1-D and 2-D Flow and Sediment Transport Equations 2.4.1 Depth-Averaged 2-D Model Equations 2.4.2 Width-Averaged 2-D Model Equations 2.4.3 Section-Averaged 1-D Model Equations 2.4.4 Effects of Sediment Transport and Bed Change on Flow 2.5 Net Exchange Flux of Suspended Load near Bed 2.5.1 Exchange Model Using Near-Bed Capacity Formula 2.5.2 Exchange Model Using Average Capacity Formula 2.5.3 Complexity of Adaptation Coefficient of Sediment 2.6 Equilibrium and Non-equilibrium Sediment Transport Models 2.6.1 Formulation of Equilibrium Transport Model 2.6.2 Formulation of Non-equilibrium Transport Model 2.6.3 Adaptation Length of Sediment 2.7 Transport and Sorting of Non-uniform Sediment Mixtures 2.7.1 Non-uniform Sediment Transport 2.7.2 Bed Material Sorting 2.7.3 Mixing Layer Thickness CHAPTER 3. Fundamentals of Sediment Transport 3.1 Settling of Sediment Particles 3.1.1 General Considerations 3.1.2 Settling Velocity of Spherical Particles 3.1.3 Settling Velocity of Sediment Particles 3.1.4 Influence of Sediment Concentration on Settling Velocity 3.2 Incipient Motion of Sediment 3.2.1 Equilibrium of a Single Sediment Particle at Incipient Motion 3.2.2 Incipient Motion Criteria for a Group of Sediment Particles 3.2.3 Incipient Motion of Uniform Sediment Particles 3.2.4 Incipient Motion of Non-uniform Sediment Particles 3.2.5 Incipient Motion of Sediment Particles on Slopes 3.3 Movable Bed Roughness in Alluvial Rivers 3.3.1 Bed Forms in Alluvial Rivers 3.3.2 Division of Grain and Form Resistances 3.3.3 Movable Bed Roughness Formulas 3.3.4 Comparison of Movable Bed Roughness Formulas 3.4 Bed-Load Transport 3.4.1 Total Transport Rate of Bed Load 3.4.2 Fractional Transport Rate of Bed Load 3.4.3 Comparison of Bed-Load Formulas 3.5 Suspended-Load Transport 3.5.1 Vertical Distribution of Suspended-Load Concentration 3.5.2 Near-Bed Concentration of Suspended Load 3.5.3 Suspended-Load Transport Rate 3.6 Bed-Material Load Transport 3.6.1 Total Transport Rate of Bed-Material Load 3.6.2 Fractional Transport Rate of Bed-Material Load 3.6.3 Comparison of Bed-Material Load Formulas 3.7 Sediment Transport over Steep Slopes 3.8 Temporal Lags between Flow and Sediment Transport CHAPTER 4. Numerical Methods 4.1 Concepts of Numerical Solution 4.1.1 General Procedure of Numerical Solution 4.1.2 Properties of Numerical Solution 4.1.3 Discretization Methods 4.2 Finite Difference Method 4.2.1 Finite Difference Method for 1-D Problems 4.2.1.1 Taylor-Series Formulation of Finite Difference Schemes 4.2.1.2 Discretization of 1-D Steady Problems 4.2.1.3 Discretization of 1-D Unsteady Problems 4.2.1.4 High-Order Difference Schemes 4.2.2 Finite Difference Method for Multidimensional Problems on Regular Grids 4.2.2.1 Discretization of Multidimensional Steady Problems 4.2.2.2 Discretization of Multidimensional Unsteady Problems 4.2.3 Finite Difference Method for Multidimensional Problems on Curvilinear Grids 4.2.3.1 Governing Equations in Generalized Coordinate System 4.2.3.2 Typical Coordinate Transformations 4.2.3.3 Discretization of the Transformed Equations 4.2.4 Interpolation Method 4.2.4.1 Isoparametric Interpolation Method on Fixed Grids 4.2.4.2 Upwind Interpolation Method on Fixed Grids 4.2.4.3 Interpolation Method on Moving Grids 4.3 Finite Volume Method 4.3.1 Finite Volume Method for 1-D Problems 4.3.1.1 Discretization of 1-D Steady Problems 4.3.1.2 Discretization of 1-D Unsteady Problems 4.3.2 Finite Volume Method for Multidimensional Problems on Fixed Grids 4.3.3 Finite Volume Method for Multidimensional Problems on Moving Grids 4.4 Numerical Solution of Navier-Stokes Equations 4.4.1 Primitive Variables: MAC Formulation on Staggered Grid 4.4.2 Primitive Variables: Projection Formulation on Staggered Grid 4.4.3 Primitive Variables: SIMPLE(C) Formulation on Staggered Grid 4.4.4 Primitive Variables: SIMPLE(C) Formulation on Non-Staggered Grid 4.4.5 Stream Function and Vorticity Formulation 4.5 Solution of Algebraic Equations 4.5.1 Thomas Algorithm 4.5.2 Jacobi and Gauss-Seidel Iteration Methods 4.5.3 ADI Iteration Method 4.5.4 SIP Iteration Method 4.5.5 Over-Relaxation and Under-Relaxation CHAPTER 5. 1-D Numerical Models 5.1 Formulation of 1-D Decoupled Flow and Sediment Transport Model 5.1.1 Formulation of 1-D Clear Water Flow Model 5.1.1.1 1-D Hydrodynamic Equations 5.1.1.2 Imposition of Boundary and Initial Conditions of Flow 5.1.1.3 Manning Roughness Coefficient 5.1.1.4 Composite Hydraulic Properties 5.1.1.5 Momentum Correction Factor 5.1.2 Formulation of 1-D Sediment Transport Model 5.1.2.1 1-D Non-equilibrium Sediment Transport Equations 5.1.2.2 1-D Equilibrium Sediment Transport Equations 5.1.2.3 Characteristics of Equilibrium and Non-equilibrium Transport Models 5.1.2.4 Boundary and Initial Conditions of Sediment 5.2 1-D Calculation of Open-Channel Flow 5.2.1 1-D Steady Flow Calculation 5.2.1.1 Discretization of Steady Flow Equations 5.2.1.2 Solution of Discretized Steady Flow Equations 5.2.1.3 Treatments for Flow at Channel Confluences and Splits 5.2.2 1-D Unsteady Flow Calculation 5.2.2.1 Discretization of Unsteady Flow Equations 5.2.2.2 Local Linearization of Discretized Unsteady Flow Equations 5.2.2.3 Solution of Discretized Unsteady Flow Equations 5.2.2.4 Treatment of Hydraulic Structures as Internal Boundaries 5.2.2.5 Stability of Preissmann Scheme for Unsteady Flow Equations 5.2.2.6 Auxiliary Treatments for Unsteady Flow Calculation 5.3 1-D Calculation of Sediment Transport 5.3.1 1-D Equilibrium Sediment Transport Model 5.3.2 1-D Quasi-Steady Non-equilibrium Sediment Transport Model 5.3.2.1 Representation of Hydrographs 5.3.2.2 Discretization of Quasi-Steady Sediment Transport Equations 5.3.3 1-D Unsteady Non-equilibrium Sediment Transport Model 5.3.3.1 Discretization of Unsteady Sediment Transport Equations 5.3.3.2 Solution of Discretized Unsteady Sediment Transport Equations 5.3.3.3 Stability of Preissmann Scheme for Sediment Transport Equation 5.3.3.4 Advantages of the Coupled Sediment Calculation Procedure 5.3.4 Treatments for Sediment Transport in Channel Networks 5.3.5 Lateral Allocation of Bed Change in 1-D Model 5.3.6 1-D Simulation of Bank Erosion and Channel Meandering 5.3.7 Overall Procedure for 1-D Decoupled Flow and Sediment Calculations 5.4 1-D Coupled Calculation of Flow and Sediment Transport 5.4.1 1-D Coupled Flow and Sediment Transport Equations 5.4.2 Discretization of Coupled Flow and Sediment Transport Equations 5.4.3 Solution of Discretized Coupled Flow and Sediment Transport Equations 5.4.4 Justification of Decoupled and Coupled Models 5.5 Data Requirements of 1-D Model 5.6 Model Sensitivity to Input Parameters CHAPTER 6. 2-D Numerical Models 6.1 Depth-Averaged 2-D Simulation of Flow in Nearly Straight Channels 6.1.1 Governing Equations 6.1.2 Boundary Conditions 6.1.3 Numerical Solutions 6.1.3.1 SIMPLE(C) Algorithm 6.1.3.2 Projection Method 6.1.3.3 Stream Function and Vorticity Method 6.1.4 Wetting and Drying Techniques 6.2 Depth-Averaged 2-D Simulation of Sediment Transport in Nearly Straight Channels 6.2.1 Governing Equations 6.2.2 Boundary and Initial Conditions 6.2.3 Numerical Solutions 6.2.3.1 Discretization of Sediment Transport Equations 6.2.3.2 Solution of Discretized Sediment Transport Equations 6.2.3.3 Implementation of Sediment Boundary Conditions 6.2.4 Examples 6.3 Depth-Averaged 2-D Simulation of Flow and Sediment Transport in Curved and Meandering Channels 6.3.1 Flow Properties in Curved Channels 6.3.2 Dispersion of Flow Momentum 6.3.3 Dispersion of Suspended Load 6.3.4 Bed-Load Transport in Curved Channels 6.3.5 Channel Meandering Process 6.4 Width-Averaged 2-D Model of Flow and Sediment Transport 6.4.1 Width-Averaged 2-D Hydrodynamic Model 6.4.1.1 Governing Equations 6.4.1.2 Boundary Conditions 6.4.1.3 Numerical Solutions 6.4.2 Width-Averaged 2-D Sediment Transport Model CHAPTER 7. 3-D Numerical Models 7.1 Full 3-D Hydrodynamic Model 7.1.1 Governing Equations 7.1.2 Boundary Conditions 7.1.3 Numerical Solutions 7.1.3.1 MAC and VOF Methods 7.1.3.2 SIMPLE Algorithm 7.1.3.3 Projection Method 7.2 3-D Flow Model with Hydrostatic Pressure Assumption 7.2.1 Layer-Integrated Model 7.2.2 Splitting of Internal and External Modes 7.2.3 Projection Method 7.2.4 SIMPLE Algorithm 7.3 3-D Sediment Transport Model 7.3.1 Governing Equations and Boundary Conditions 7.3.2 Discretization of Sediment Transport Equations 7.3.3 Solution of Discretized Sediment Transport Equations 7.3.4 Examples 7.4 3-D Simulation of Local Scour around In-stream Structures 7.4.1 Complexity of Local Scour Processes around In-stream Structures 7.4.2 Simulation of Sediment Transport and Local Scour near In-stream Structures 7.4.3 Headcut Migration Model CHAPTER 8. Domain Decomposition and Model Integration 8.1 Multiblock Method 8.1.1 General Considerations 8.1.2 Multiblock Method for 1-D Problems 8.1.3 Multiblock Method for Multidimensional Problems 8.1.4 Efficiency of Multiblock Method 8.2 Coupling of 1-D, 2-D and 3-D Models 8.2.1 General Considerations 8.2.2 Connection Conditions 8.2.3 Calculation Procedures 8.2.4 Examples 8.3 Integration of Channel and Watershed Models 8.3.1 Modeling Components 8.3.2 Integration Approaches 8.3.3 Scale Issues 8.3.4 Application to Goodwin Creek Watershed CHAPTER 9. Simulation of Dam-Break Fluvial Processes 9.1 Simulation of Dam-Break Flow over Fixed Beds 9.1.1 Central Difference Scheme with Artificial Diffusion Flux 9.1.2 Approximate Riemann Solvers 9.1.3 TVD Schemes 9.1.4 WAF Schemes 9.1.5 Upwind Flux Schemes 9.1.6 Stability and Accuracy of Explicit and Implicit Schemes 9.2 Simulation of Dam-Break Flow over Movable Beds 9.3 Simulation of Dam Surface Erosion due to Overtopping Flow CHAPTER 10. Simulation of Flow and Sediment Transport in Vegetated Channels 10.1 Effects of Vegetation on Flow and Sediment Transport 10.1.1 Geometric Characteristics of Vegetation 10.1.2 Flow Resistance due to Vegetation 10.1.3 Sediment Transport Capacity in Vegetated Channels 10.2 Simulation of Flow in Vegetated Channels 10.3 Simulation of Sediment Transport in Vegetated Channels CHAPTER 11. Cohesive Sediment Transport Modeling 11.1 Cohesive Sediment Transport Processes 11.1.1 General Transport Patterns 11.1.2 Factors Affecting Flocculation 11.1.3 Formulas of Floc Settling Velocity 11.1.4 Deposition of Cohesive Sediments 11.1.5 Erosion of Cohesive Sediments 11.1.6 Consolidation of Cohesive Bed Materials 11.2 Multiple-Floc-Size Model of Cohesive Sediment Transport 11.3 Single-Floc-Size Model of Cohesive Sediment Transport 11.4 Simulation of Transport of Cohesive and Non-cohesive Sediment Mixtures CHAPTER 12. Contaminant Transport Modeling 12.1 Heat and Salinity Transport Model 12.1.1 Governing Equations 12.1.2 Effects of Buoyancy on Vertical Turbulent Transport 12.1.3 Effective Diffusivities 12.1.4 Heat Transfer across Water and Bed Surfaces 12.1.5 Numerical Solutions 12.2 Water Quality Model 12.2.1 Kinetics and Rate Coefficients 12.2.2 Constituent Reactions and Interrelationships 12.2.3 Other Biochemical Processes 12.3 Simulation of Sediment-Borne Contaminant Transport 12.3.1 Sorption and Desorption of Contaminants on Sediment Particles 12.3.2 Contaminant Transport in Water Column 12.3.2.1 Non-equilibrium Partition Model 12.3.2.2 Equilibrium Partition Model 12.3.3 Contaminant Transport in Sediment Bed References