Applied computational hydraulics for engineers / Necati Agiralioglu and Mehmet Ozger.

Format:

Book

Author/Creator:

Ağıralioğlu, Necati, author.

Ozger, Mehmet, author.

Series:

Theoretical and applied mathematics.

Theoretical and applied mathematics

Language:

English

Subjects (All):

Hydraulic engineering--Data processing.

Hydraulic engineering.

Physical Description:

1 online resource (334 pages)

Edition:

First edition.

Place of Publication:

New York : Nova Science Publishers, Inc., [2024]

Summary:

"This book delves into the increasing role of computers, particularly personal computers, in solving hydraulic problems across various engineering disciplines, with a specific focus on civil engineering's hydraulics and water resources aspects. By leveraging Microsoft Excel, readers can easily grasp hydraulic principles and apply them to numerous problems without the need for complex software codes. The content has been refined through years of teaching Computational Hydraulics at the master's level and based on the theses of numerous doctoral and graduate students. It is designed for undergraduate and graduate students who have completed prerequisite courses in fluid mechanics, hydraulics, and differential equations. The book can be studied over two semesters and is also valuable for engineers seeking insights into this subject. Throughout the book, theoretical concepts are reinforced with a wealth of examples solved at the end of each chapter. These examples comprehensively address practical complexities, enhancing the reader's understanding. Moreover, the book covers not only "computer hydraulics" but also touches on "computational fluid dynamics" to provide a broader perspective on the subject, incorporating examples from environmental and structural engineering. The book introduces the finite differences method, a valuable tool for solving common partial differential equations used in fluid mechanics and hydraulics. It also presents alternative solution methods for three types of partial differential equations: elliptic, parabolic, and hyperbolic, supplemented with real-world applications and thorough solutions. Recommended primarily for third and fourth-year undergraduate and graduate students, the book caters to those interested in numerical modeling, including software developers working on finite difference numerical methods. In summary, the book is a comprehensive resource for those in the fields of civil and environmental engineering, offering practical problem-solving skills for real-world applications and serving as a guide for software developers creating programs related to finite difference numerical methods"-- Provided by publisher.

Contents:

Intro

Chapter 1

Introduction to Computational Hydraulics

1.1. Definition of Computational Hydraulics

1.2. Basic Principles of Computational Hydraulics

1.3. Forms of the Governing Water-Flow Equations

1.4. Integral Equations

1.5. Differential Equations

1.6. Numerical Methods of Ordinary Differential Equations

1.6.1. The Euler Method

1.6.2. The Modified Euler Method

1.7. Numerical Methods of Partial Differential Equations

1.8. Terms of Hydraulic Modeling

1.8.1. Terms Referring to Numerical Modeling

Chapter 2

Review of Governing Equations

2.1. Introduction

2.2. Continuity Equation

2.2.1. General Remarks

2.2.2. Continuity Equation in Cartesian Coordinates

2.2.3. Continuity Equation in Cylindrical Coordinates

2.3. Momentum Equation

2.3.1. General Remarks

2.3.2. Momentum Equation in Cartesian Coordinates

2.3.3. Momentum Equation in Cylindrical Coordinates

2.3.4. Bernoulli Equation

2.3.5. Momentum and Forces in Fluid Flow

2.4. Energy Equation

2.4.1. General Remarks

2.4.2. Energy Equation in Cartesian Coordinates

2.4.3. Energy Equation in Cylindrical Coordinates

2.5. Transport Equation

2.5.1. General Remarks

2.5.2. Convection-Diffusion Equation

2.5.3. Convection Equation

2.5.4. Diffusion Equation

2.5.5. Diffusion Equation in Cylindrical Coordinates

2.5.6. The Advection-Diffusion-Reaction Equation

2.6. Navier-Stokes Equations in Stream Function-Vorticity Form

2.6.1. General Remarks

2.6.2. Vorticity - Stream Function in Cartesian Coordinates

2.6.3. Stream Function for Plane Two-Dimensional Flow in Cartesian Coordinates

2.6.4. Vorticity - Stream Function in Cylindrical Coordinates

2.6.5. Stream Function for Plane Two-Dimensional Flow in Cylindrical Coordinates

2.7. Saint-Venant Equations

2.7.1. General Remarks.

2.7.2. Continuity Equation

2.7.3. Momentum Equation

2.7.4. Saint-Venant Equations for Steady State Flow

2.8. Vorticity

2.9. Potential Flow

2.9.1. Velocity Potential Function

2.9.2. Stream Function

2.9.3. Laplace Equation in Cartesian Coordinates

2.9.4. Laplace Equation in Cylindrical Coordinates

2.9.5. Potential Lines and Streamlines

2.10. Hydrostatic Balance and Earth's Rotation

2.10.1. Hydrostatic Balance

2.10.2. Earth's Rotation

2.11. Scales and Dimensionless Numbers

2.11.1. Definition of Scales

2.11.2. The Froude Number

2.11.3. The Richardson Number

2.11.4. The Reynolds Number

2.11.5. The Peclet Number

2.11.6. The Rossby Number

Chapter 3

Some Analytical Solutions

3.1. Introduction

3.2. Sample Equations

3.2.1. Some Differential Equations in Hydraulics

3.2.2. Order and Degree of a Differential Equation

3.2.3. Linear and Non-Linear Differential Equations

3.2.4. Classification of a Second-Order Partial Differential Equation

3.3. Solution of Emptying Time of a Dam Reservoir

3.4. Solution of an Ordinary Linear Differential Equation

3.5. Example for a Simple Lake Purification Model

Chapter 4

Applications of Numerical Analysis

4.1. Introduction

4.2. Newton-Raphson Method

4.3. Least Squares Method

4.4. Polynomial Curve Fitting

4.5. Numerical Integration

4.5.1. Numerical Integration Using Trapezoidal Rule

4.5.2. Numerical Integration by Simpson's Rule

4.6. Applications by Numerical Analysis

4.6.1. Calculation of Flow Velocity at Downstream of a Spillway Using Newton-Raphson Method

4.6.2. Finding a Relationship between Temperature and Liquid Volume Using Least Squares Method

4.6.3. Application of Polynomial Fitting

4.6.4. Determining a Relationship between Water Depth and Reservoir Volume Using Curve Fitting.

4.6.5. Applications of Numerical Integration Using Simpson's Rule

4.6.6. Determination of Emptying Time of a Reservoir with Constant Inflow

4.6.7. Determination of Emptying Time for a Small Reservoir

4.6.8. Determination of Emptying Time of a Reservoir with No Inflow

Chapter 5

Finite Difference Methods

5.1. Introduction

5.2. Difference Equation

5.3. Partial Differential Equations

5.4. Derivation of Some Basic Finite Difference Forms

5.4.1. Taylor Series Expansions

5.4.2. Polynomial Fitting

5.5. Types of Finite Difference Schemes

5.5.1. Basic Forms

5.5.2. Geometric Interpretation of Basic Finite Difference Forms

5.5.3. Explicit and Implicit Finite Difference Schemes

5.5.4. Comparison of Explicit and Implicit Schemes

5.6. Finite Difference Schemes

5.6.1. Finite Difference Formulas for First Derivatives

5.6.2. Finite Difference Formulas for Second Derivatives

5.6.3. Finite Difference Formulas for Third Derivatives

5.6.4. Finite Difference Formulas for Fourth Derivatives

5.7. Finite Difference Formulations for Some Equations

5.7.1. Pure Diffusion Equation

5.7.2. Pure Advection Equation

5.7.3. Numerical vs Physical diffusion

5.7.4. Truncation Error and Round-off Error

5.8. A Numerical Scheme Analysis

5.8.1. Taylor Series Analysis

5.8.2. Fourier Analysis

5.9. Steps for Finite Difference Solutions

5.10. Numerical Solutions of Differential Equations

5.10.1. Example of Finite Difference Approximation

Chapter 6

Boundary and Initial Conditions

6.1. Introduction

6.2. Governing Equations

6.3. Definition of Stream Function and Velocity Potential Function

6.4. Boundary Conditions for the Primitive Equations

6.5. Determination of Velocity Components from Nondimensional Stream Function

6.6. Boundary Conditions for the Stream Function Equations.

6.7. Boundary Conditions for the Vorticity and Stream Function Equations

6.7.1. General

6.7.2. Walls in the First Mesh System

6.7.3. Sloping Wall Boundary

6.7.4. Symmetry Boundaries

6.7.5. Upper Boundary

6.7.6. Upstream Boundary

6.7.7. Outflow Boundary

6.8. Irregular Boundaries

6.9. Boundary Conditions for Sharp Corners

6.10. Initial Conditions

6.11. Number of Boundary Conditions

6.12. Applications of Boundary and Initial Conditions

6.12.1. Determination of Velocity Components from Non-Dimensional Stream Function

6.12.2. Example for Irregular Boundary Conditions

6.12.3. Determination of Boundary Conditions for Navier-Stokes Equations in Vorticity/Stream Function Form

Chapter 7

Solutions of Elliptic Equations

7.1. Introduction

7.2. Governing Equations

7.3. Finite Difference Formulation of Laplace Equation

7.4. Solution Methods for Elliptic Partial Differential Equations

7.4.1. Direct Method

7.4.2. Jacobi Iteration

7.4.3. Gauss-Seidel Iteration

7.4.4. Successive Over Relaxation Method

7.5. Applications of Elliptic Partial Differential Equations

7.5.1. Numerical Solution to the Groundwater Flow Equation

7.5.2. Numerical Solution of Stream Function Values, Velocities, Flow Rate for Flow, Potential Function Values and Pressures under Sheet Piles

7.5.3. Numerical Solution for Deflection of a Thin Plate

7.5.4. Numerical Solution for Flow under a Dam

7.5.5. Calculating Stream Function for a Potential Flow

7.5.6. Calculation of Velocity Components of Flow from Stream Function Values in a Potential Flow

Chapter 8

Solutions of Parabolic Equations

8.1. Introduction

8.2. Classification of Parabolic Partial Differential Equations

8.3. Schemes for Parabolic Partial Differential Equations

8.3.1. Forward in Time and Centered Space (FTCS) Scheme.

8.3.2. Backward-Time Centered Space (BTCS) Scheme

8.3.3. Dufort-Frankel Scheme

8.3.4. Crank-Nicolson Scheme

8.3.5. Leapfrog Scheme

8.3.6. ADI Method

8.4. Comparison of Schemes for Numerical Solution of Parabolic Equations

8.5. Stability for Parabolic Partial Differential Equations

8.6. Applications of Parabolic Partial Differential Equations

8.6.1. Solution of Parabolic Partial Differential Equation Using Explicit Finite Differences

8.6.2. Determination of the Stability Criterion for Flow Between Two Parallel Plates

8.6.3. Numerical Solution of Heat Flow Equation

Chapter 9

Solutions of Hyperbolic Equations

9.1. Introduction

9.2. Hyperbolic Partial Differential Equations

9.3. Boundary and Initial Conditions

9.4. Review of Some Hyperbolic Equations

9.4.1. General

9.4.2. The Advection Equation in One Dimension

9.4.3. The Advection Equation in One Dimension Using a Finite Difference Method

9.4.4. The Wave Equation in Two Spatial Dimensions

9.5. Finite Difference Schemes in Hyperbolic Differential Equation

9.5.1. Finite Difference Formulation for Schemes

9.5.2. The Courant-Friedrichs-Levy Stability Condition

9.6. Applications of Hyperbolic Equations

9.6.1. Solution of a Linear Kinematic Wave Model

9.6.2. Example for Flood Routing Using Kinematic Wave Model

9.6.3. Determination of Stability Criterion

9.6.4. Example for Numerical Solution of an Overland Flow

9.6.5. Numerical Solution of Shoreline Change

Chapter 10

Applications of Unsteady Open Channel Flows

10.1. Introduction

10.2. The Saint-Venant Equations

10.3. Open Channel Flow Models

10.3.1. Steady Flow

10.3.2. Quasi-Steady Approximation

10.3.3. Kinematic and Diffusion Wave Models

10.3.4. Inertial and Dynamic Wave Models

10.4. Applicability of Kinematic and Diffusion Wave Models.

10.5. Unsteady Flow Models in Open Channel Flow.

Notes:

Includes bibliographical references and index.

Description based on print version record.

Other Format:

Print version: Agiralioglu, Necati Applied Computational Hydraulics for Engineers

ISBN:

979-88-911-3506-2