Numerical Simulation of Water Waves

✍ Scribed by Jianhua Tao

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 495
• Series: Springer Tracts in Civil Engineering
• Category: Library

✦ Synopsis

This book discusses the numerical simulation of water waves, which combines mathematical theories and modern techniques of numerical simulation to solve the problems associated with waves in coastal, ocean, and environmental engineering. Bridging the gap between practical mathematics and engineering, the book describes wave mechanics, establishment of mathematical wave models, modern numerical simulation techniques, and applications of numerical models in engineering. It also explores environmental issues related to water waves in coastal regions, such as pollutant and sediment transport, and introduces numerical wave flumes and wave basins. The material is self-contained, with numerous illustrations and tables, and most of the mathematical and engineering concepts are presented or derived in the text. The book is intended for researchers, graduate students and engineers in the fields of hydraulic, coastal, ocean and environmental engineering with a background in fluid mechanics and numerical simulation methods.

✦ Table of Contents

Preface
Contents
1 Introduction
1.1 Numerical Simulation of Fluid Flow
1.1.1 What Is Numerical Simulation of Fluid Flow
1.1.2 Contents of Numerical Simulation
1.1.3 Purpose of Numerical Simulation in Engineering
1.2 Water Waves in Engineering and Classifications of Water Waves
1.2.1 Water Waves in Engineering
1.2.2 Classification of Water Waves and Wave Theories
1.3 Numerical Methods and Techniques of Water Wave Simulation
1.3.1 Finite Difference Method
1.3.2 Finite Volume Method
1.3.3 Finite Element Method
1.3.4 Boundary Element Method
1.3.5 Numerical Techniques of Water Wave Simulation
1.4 Development of Water Wave Simulation
1.4.1 Computational Fluid Mechanics and Numerical Simulation of Water Waves
1.4.2 Development of Numerical Simulation of Water Waves
1.4.3 Relationship Among Numerical Simulation of Water Waves, Theoretical Analysis, and Experimental Study
References
2 Water Wave Theories
2.1 Mathematical Model of Water Waves
2.1.1 Governing Equations for Water Waves
2.1.2 Boundary Conditions for Water Waves
2.1.3 Initial Condition for Water Waves
2.2 Dispersive Waves
2.2.1 Governing Equations and Boundary Conditions
2.2.2 Linear Small-Amplitude Wave Theory
2.2.3 Basic Concepts of Progressive Waves
2.2.4 Stokes Finite Height Waves
2.3 Dispersive Waves in Shallow Water
2.3.1 Nonlinear Shallow Water Wave Equations
2.3.2 Boussinesq Equations
2.3.3 Unidirectional Dispersive Waves—KDV Equation
2.3.4 Permanent Wave Solutions to the KDV Equation—Solitary Waves
2.3.5 Propagating Wave Solution to the Boussinesq Equations—Cnoidal Wave
2.4 Long Waves
2.4.1 Basic Equations
2.4.2 Theory of Characteristics for 1D Long Waves in Channel
2.4.3 Influenced Zone of the Solution to Hyperbolic Equations, Requirements of Boundary, and Initial Conditions
2.4.4 Discontinuous Waves and Weak Solutions
2.5 Waves in Current
2.5.1 Waves in Steady Current
2.5.2 Vertical Structure Under the Wave–Current Interaction
2.6 Introduction of Random Wave Theory
2.6.1 Statistical Characteristics of Random Functions
2.6.2 Description of Random Waves and the Concept of Spectrum
2.6.3 Statistical Distribution of Random Wave Elements
2.6.4 Frequency Spectrum and Directional Spectrum
References
3 Numerical Simulation of Long Waves in Shallow Water
3.1 Introduction
3.2 Mathematical Model of 1D Long Waves
3.2.1 Governing Equations
3.2.2 Difference Equations
3.2.3 Solving Method
3.2.4 Boundary Conditions
3.2.5 Flood Waves in Tidal Rivers
3.3 Mathematical Model of 2D Long Waves
3.3.1 2D Depth-Integrated Long Wave Equations
3.3.2 Definite Conditions and Boundary Treatments
3.3.3 Difference Equations
3.3.4 Numerical Simulation of Circulation
3.3.5 Tidal Current Field in Bohai Sea and Its Validation
3.4 Mathematical Model of 3D Shallow Water Long Waves
3.4.1 Governing Equations
3.4.2 Quasi-3D Long Wave Model by Stratified Integral
3.4.3 Full 3D Long Wave Model in the Sigma Coordinate System
3.5 Mathematical Model of Dam-Break Waves in Channel
3.5.1 Calculation of Dam-Break Waves by a Level Set Method
3.5.2 Calculation of Dam-Break Waves by a TVD Method
References
4 Numerical Simulation of Shallow Water Waves in Coastal Regions
4.1 Introduction
4.2 Mathematical Models of Wave Shoaling and Wave Refraction
4.2.1 Wave Shoaling
4.2.2 Wave Refraction
4.3 Mathematical Model of Wave Diffraction
4.3.1 Linear Wave Diffraction Theory
4.3.2 Mathematical Model of Wave Diffraction by Breakwaters
4.3.3 Diffraction of Random Waves
4.4 Mathematical Models of Mild Slope Equations for Wave Refraction and Diffraction
4.4.1 Elliptic Mild Slope Equation Model
4.4.2 Time-Dependent Mild Slope Equation
4.4.3 Parabolic Mild Slope Equation Model
4.5 Mathematical Model of Boussinesq Equations for Dispersive Shallow Water Waves
4.5.1 Governing Equations
4.5.2 Boussinesq-Type Equations
4.5.3 Difference Scheme with Higher Accuracy for the Boussinesq Equations
References
5 Numerical Simulation of Wave Run-up and Breaking on Beach
5.1 A Treatment of Moving Boundary on Beach—The Slot Method
5.1.1 Basic Idea of the Slot Method
5.1.2 Selection of the Slot Parameters
5.1.3 Numerical Simulation of Wave Run-up on a Beach
5.2 Wave Breaking Criteria
5.2.1 Classical Wave Breaking Criterion
5.2.2 Criterion of Ultimate Wave Height
5.3 Turbulence Model for Breaking Waves
5.3.1 Constant Viscosity Coefficient
5.3.2 k-Equation Model
5.4 Surface Roller Model for Breaking Waves
5.4.1 Roller Model for Breaking Waves in the Boussinesq Equations
5.4.2 Roller Model for Breaking Waves in the Parabolic Mild Slope Equation
5.4.3 Calculated Irregular Breaking Waves on a Circular Shoal Compared with Experimental Data
5.5 Energy Dissipation Model for Breaking Waves
5.5.1 Multiple-Breaking Model for Regular Waves
5.5.2 Energy Dissipation Model of Irregular Breaking Waves
5.6 Wave-Induced Radiation Stress
5.6.1 Concept of Radiation Stress
5.6.2 Radiation Stress Tensor
5.6.3 Calculation of Radiation Stress—An Example
References
6 Numerical Simulation of Wave Forces on Structures
6.1 Introduction
6.2 Wave Forces on a Small-Scale Structure
6.2.1 Flow Around a Cylinder in Steady Current and the Forces
6.2.2 Flow Around a Cylinder in Oscillatory Flow and the KC Number
6.2.3 Forces on a Small-Scale Cylinder in Regular Waves—The Morison Equation
6.3 Wave Forces on a Large-Scale Circular Cylinder
6.3.1 Problem of Linear Wave Diffraction
6.3.2 Wave Forces on a Large-Scale Cylinder
6.4 Wave Forces on Large-Scale Circular Multiple Cylinders
6.4.1 Coordinate System and Basic Equations
6.4.2 Wave Forces on Multiple Circular Cylinders
6.4.3 Random Wave Forces on Large-Scale Multiple Cylinders
6.4.4 Diagrams of Cylinder Group Effect Coefficients for Irregular Wave Forces on Multiple Cylinders
6.5 Wave Forces on 2D Large-Scale Structures
6.5.1 Calculation of Wave Forces on a 2D Large-Scale Structure Using Boundary Element Method
6.5.2 A Case Study of Numerical Solution of Wave Forces on Multiple Cylinders by Using Boundary Element Method [8]
6.6 Nonlinear Wave Forces on a Semicircular Breakwater
6.6.1 Physical Phenomena of the Interaction of Nonlinear Waves and a Semicircular Breakwater
6.6.2 Mathematical Model
6.6.3 Numerical Nonlinear Wave Generation and Boundary Treatments
6.6.4 Establishment, Discritization, and Numerical Solution of the Boundary Integral Equation
6.6.5 Procedure of Solving the Equations and the Pressure Formula
6.6.6 Verification of Numerical Model
6.7 Wave Forces on 3D Large-Scale Structures
6.7.1 Solutions of Wave Forces by Linear Diffraction Theory
6.7.2 Numerical Calculation of Wave Forces on an Offshore Gravity Platform [19]
6.8 Second-Order Wave Forces on a Large-Scale Cylinder Using Green’s Function Method
6.8.1 Basic Equations
6.8.2 The Fixed Solution Problem of Second-Order Scattered Waves
6.8.3 Solving the Particular Solution and the General Solution Φ2 by Using Green’s Function Method
6.8.4 Second-Order Wave Forces and Moment on a Large-Scale Cylinder
6.8.5 Calculation Cases
6.9 Mathematical Model of Wave–Current Forces on a Submerged Structure Near the Free Surface
6.9.1 Wave-Making Problem in Steady Current
6.9.2 Mathematical Model of Diffraction by a Submerged Body Near Water Surface Under Wave–Current Interaction
6.9.3 Numerical Solution
6.10 Mathematical Model of Wave–Current Forces on a Large-Scale Cylinder
6.10.1 Diffraction of a Large-Scale Vertical Cylinder Under the Wave–Current Interaction
6.10.2 Numerical Solution of Wave–Current Forces on a Large-Scale Circular Cylinder
References
7 Numerical Simulation of Pollutant Transport Under Waves and Tidal Currents in Coastal Regions
7.1 Introduction
7.2 Wave Model
7.2.1 Regular Waves
7.2.2 Irregular Waves
7.3 Model of Nearshore Currents Under Waves
7.3.1 Mathematical Model of Nearshore Currents
7.3.2 Nearshore Currents in Coastal Regions: Case Studies
7.3.3 Characteristics of the Longshore Current Induced by Waves Over Bathymetry with a Uniform Slope
7.4 Mathematical Model of Pollutant Transport Under Interaction of Waves and Tidal Currents
7.4.1 Governing Equation for Pollutant Transport
7.4.2 Simulations of Pollutant Transport Under Interaction of Waves and Tidal Currents in Coastal Regions
7.5 Nearshore Currents and Pollutant Transport in Shallow Water with Mild Slope Under Wave Action and Interaction of Waves and Tidal Currents
7.5.1 Nearshore Currents Under Wave Action and Interaction of Waves and Tidal Currents
7.5.2 Pollutant Transport Under Interaction of Waves and Tidal Currents
References
8 Numerical Simulation of Coastal Morphological Evolution
8.1 Introduction
8.1.1 Relations Among the Coastal Morphological Evolution, Coastal Dynamic Factors, and Sediment Transport
8.1.2 Basics of Simulating Coastal Morphological Evolution
8.1.3 Classification of Mathematical Models of Coastal Morphological Evolution
8.2 Mathematical Model of Shoreline Evolution
8.2.1 Mathematical Shoreline Model
8.2.2 Study on Shoreline Evolution and Protection Works in the Downstream of the Breakwater at Friendship Port in Mauritania
8.3 Region Model of Sandy Beach Evolution Under Wave Action
8.3.1 Sub-models of the Region Model of Sandy Beach Evolution
8.3.2 Calculation Case of Bathymetry Evolution Around a Breakwater
8.3.3 Bathymetry Evolution Around a Sunken Ship Near Shore
8.3.4 Comparison of Sub-models in Several Coastal Region Models
8.4 Mathematical Model of Estuarine Morphological Evolution
8.4.1 2D Hydrodynamic Equations
8.4.2 2D Mathematical Model of Sediment Transport
8.4.3 Procedure of Calculating Estuarial Morphological Evolution
8.5 Long-Term Model of Coastal Morphological Evolution
References
9 Incompressible Viscous Fluid Model for Simulating Water Waves
9.1 Introduction
9.2 Mathematical Model of Incompressible Viscous Fluid Flow
9.2.1 Navier–Stokes Equations
9.2.2 Reynolds Equations
9.2.3 Turbulence Model
9.2.4 Boundary and Initial Conditions
9.3 Free Surface Treatments for Simulating Water Waves by Reynolds Equation Model
9.3.1 Level-Set Method
9.3.2 Volume of Fluid (VOF) Method
9.4 Discretization and Solution of the Incompressible Reynolds Equations
9.4.1 Solution of the Incompressible Reynolds Equations
9.4.2 Discretization of the Computational Domain
9.4.3 Discretization of the Equations
9.4.4 Procedure of Solving the Discretized Equations
9.5 Verification and Application of the Reynolds Equation Model for Water Waves
9.5.1 Transformation of Wave Passing Over a Step
9.5.2 Simulation and Verification of Velocity Field Around a Submerged Rectangular Breakwater
9.5.3 Simulation and Verification of Wave Uplift Forces on the Wharf Upper-Structure
9.6 Numerical Simulation of Wave-Structure Interaction Using a 3D Reynolds Equation Model
9.6.1 Surface Elevation of a Solitary Wave Passing Through a Gate Between Two Piles
9.6.2 Pressure and Velocity on a Horizontal Section
9.6.3 Velocity Variation on Vertical Transects
References
10 Numerical Wave Flume and Numerical Wave Basin
10.1 Introduction
10.1.1 Numerical Experiments of Water Waves on Computer
10.1.2 Key Components of a Numerical Wave Flume/Basin
10.2 Numerical Wave Flume Based on the Reynolds Equations
10.2.1 Governing Equations of the Mathematical Model
10.2.2 Treatment of Free Surface
10.2.3 Numerical Wave Generation
10.2.4 Non-reflective Open Boundary
10.2.5 Verification of the Numerical Wave Flume
10.2.6 Numerical Experiments on the Interaction of a Solitary Wave and a Semicircle Breakwater in the Numerical Wave Flume
10.3 Numerical Wave Basin Based on the Boussinesq Equations
10.3.1 Core Computing Module
10.3.2 Pre-processing System
10.3.3 Post-processing System
10.3.4 Application of the Numerical Wave Basin
References
11 Applications of Numerical Simulation of Water Waves in Coastal Waters and Coastal Engineering
11.1 Study on Water Exchange Characteristics of Bohai Sea
11.1.1 Validation of the 2D Long Wave Model of Bohai Sea
11.1.2 Convection–Diffusion Model and Age Model
11.1.3 Water Exchange Characteristics in Bohai Sea
11.2 Numerical Simulation of Water Quality for Pearl River Estuary and Adjacent Coastal Areas in South China Sea
11.2.1 Introduction
11.2.2 Water Quality Model
11.2.3 Verifications of Hydrodynamic Model and Water Quality Model
11.2.4 Distribution of Pollutant Response Concentration
11.2.5 Improving Water Quality in Pearl River Estuary
11.2.6 Conclusions
11.3 Numerical Simulations of Tidal Flow and Sediment Transport for Design of a Deepwater Port in East China Sea
11.3.1 Models for Two-Dimensional Sediment Transport and Quasi-Three-Dimensional Tidal Flow
11.3.2 Determinations of Calculation Domain and Boundary Conditions
11.3.3 Validation of Tidal Flow Model in the Local Project Area
11.3.4 Analyses on Tidal Current in Design Layouts
11.3.5 Analyses of Sediment Transport in Design Layouts
11.4 Comparisons of Numerical Predictions of Shoreline Evolutions Against Satellite Images of Friendship Port (Port of Nouakchott) in Mauritania
11.4.1 Introduction
11.4.2 Comparisons Between Numerical Predictions of Shoreline Evolution and the Satellite Images
References