1st Edition

# Computational River Dynamics

508 Pages
by CRC Press

508 Pages
by CRC Press

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 of numerical methods for open-channel flows, such as the SIMPLE(C) algorithms on staggered and non-staggered grids, the projection method, and the stream function and vorticity method. The state-of-the-art in sediment transport modeling approaches is described, such as non-equilibrium transport models, non-uniform total-load transport models, and semi-coupled and coupled procedures for flow and sediment calculations. Sediment transport theory is discussed and many newly-developed, non-uniform sediment transport formulae are presented. The many worked examples illustrate various conditions, such as reservoir sedimentation; channel erosion due to dam construction; channel widening and meandering; local scour around in-stream hydraulic structures; vegetation effects on channel morphodynamic processes; cohesive sediment transport; dam-break fluvial processes and contaminant transport. Recommended as a reference guide for river and hydraulic engineers and as a course text for teaching sediment transport modeling, computational free-surface flow, and computational river dynamics to senior students.

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

2.1.3 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

§2.7 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

3.4.1 Total Transport Rate of Bed Load

3.4.2 Fractional Transport Rate of Bed Load

3.5.1 Vertical Distribution of Suspended-Load Concentration

3.5.2 Near-Bed Concentration of Suspended Load

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

4.5.4 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 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 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

6.3.4 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

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

### Biography

Weiming Wu has more than twenty years of experience with 1D-, 2D-, and 3D-numerical modeling of turbulent flow, sediment transport, and pollutant transport in surface water systems. He participated in the study of the navigation and sediment problems of the Three Gorges Project in the Yangtze River. He is one of the developers of the FAST3D model, used to simulate sedimentation processes, and the main developer of the CCHE1D model, a channel-network model that is integrated with landscape and watershed models. He has also developed the FVM-based CCHE2D model, a depth-averaged 2D model for unsteady flow and non-uniform sediment transport in open channels.

‘This book is a brand new addition to the sparse literature on computational river dynamics. It covers a very important subject: the numerical modeling of fluvial processes including turbulent flows in rivers, sediment transport, and the deformation of alluvial channels. This book is very welcome as it provides a worthy synthesis of knowledge in one of the fast growing fields of hydraulic engineering.’

‘With his background from China, studies in Europe, and practice in the United States, the author presents this subject from a unique international perspective.’

Pierre Y. Julien in JOURNAL OF HYDRAULIC ENGINEERING © ASCE. October 2008

‘… the present book is to my knowledge a unique resource for engineers and scientists interested in numerical modeling of flow and sediment transport in alluvial channels.’ George S. Constantinescu in JOURNAL OF HYDRAULIC RESEARCH vol. 46, no. 6 (2008)

'This book is one of the first to present a complete picture of the physical principles and numerical methods used in computational river dynamics.' W. Czernuszenko in ARCHIVES OF HYDRO-ENGINEERING AND ENVIRONMENTAL MECHANICS. vol. 54 no. 4 (2007)