Computational Fluid Dynamics for Mechanical Engineering
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This textbook presents the basic methods, numerical schemes, and algorithms of computational fluid dynamics (CFD). Readers will learn to compose MATLAB® programs to solve realistic fluid flow problems.
Newer research results on stability and boundedness of various numerical schemes are incorporated. The book emphasizes large eddy simulation (LES) in the chapter on turbulent flow simulation besides the two-equation models. Volume of fraction (VOF) and related methods will be the focus of the chapter on two-phase flows.
The textbook was written for a first course in computational fluid dynamics (CFD) taken by undergraduate students in a Mechanical Engineering major.
Table of Contents
Preface 1 Essence of Fluid Dynamics 1.1 Introduction 1.2 General Form of Transport Equations 1.2.1 Derivation of General Form of Transport Equations 1.2.2 Maximum Principle, Conservativeness and Boundedness 1.3 Navier-Stokes Equations 1.3.1 Continuity Equation and Momentum Equations 1.3.2 Dimensionless Form of Equations and Reynolds Number Exercises 2 Finite Difference Method 2.1 Finite Difference Method 2.1.1 Finite Differences 2.1.2 Example: Laminar Channel Flow 2.1.3 TDMA Algorithm 2.2 Finite Volume Method 2.3 Error Analysis 2.3.1 Bounded Scheme and Positive Scheme 2.3.2 Properties of Positive Scheme 2.3.3 Global Error and Truncation Error 2.3.4 Global Error Estimation 2.4 Finite Volume Method (Continued) 2.4.1 Virtual Control Volume and Virtual Node 2.4.2 Example: Channel Flow Consisting of Two Immiscible Fluids 2.5 A Glimpse of Turbulence 2.5.1 Introduction 2.5.2 Mixing Length Model 2.5.3 Example: Turbulent Channel Flow 2.6 The CFD Procedure Exercises 3 Numerical Schemes 3.1 Schemes for Time Advancing 3.1.1 Example: Start-Up of Couette Flow 3.1.2 Euler Explicit Scheme 3.1.3 Consistency, Stability, and Convergence 3.1.4 von Neumann and Matrix Stability Analysis Methods 3.1.5 Euler Implicit Scheme 3.1.6 Crank-Nicolson Scheme 3.1.7 Runge-Kutta schemes 3.1.8 Second-Order Backward Difference and Adams-Bashforth Schemes 3.2 Unsteady Convection-Diffusion Equation 3.2.1 Example: Mass Transfer in 1-D Flow 3.2.2 FTCS Scheme 3.2.3 Local Mesh Refinement 3.3 Schemes for Convection Term 3.3.1 First-order Upwind Scheme 3.3.2 Godunov Theorem 3.3.3 Second and Higher-Order Upwind Schemes 3.3.4 Deferred-Correction Approach 3.3.5 Hybrid Schemes 3.3.6 Bounded Second-Order Schemes 3.3.7 ENO and WENO Schemes 3.3.8 Harten’s Lemma 3.4 Proper Boundary Conditions Exercises 4 Numerical Algorithms 4.1 Introduction 4.2 Basic Iterative Methods 4.2.1 Jacobi and Gauss-Seidel Iteration Methods 4.2.2 Successive Over-Relaxation (SOR) Method 4.2.3 Alternating Direction Implicit (ADI) Method 4.2.4 Strongly Implicit Procedure (SIP) Method 4.3 Krylov Subspace Methods 4.3.1 Conjugate Gradient Method 4.3.2 Condition Number and Preconditioned Conjugate Gradient Method 4.3.3 GMRES, BiCGSTAB and ‘\’ 4.4 FFT Method Exercises 5 Navier-Stokes Solution Methods 5.1 Odd-Even Decoupling 5.1.1 Example: 1-D Flow Through Filter 5.1.2 Staggered Mesh 5.2 Navier-Stokes Solution methods 5.2.1 Coupled vs. Segregated Methods 5.2.2 SIMPLE Method 5.2.3 Projection Method
5.2.4 Co-located Mesh and Momentum Interpolation Method 5.3 Example: Lid-Driven Cavity Flow 5.3.1 Problem Statement, Mesh and Formulas 5.3.2 Under-Relaxation 5.3.3 Boundary Conditions Implementation 5.3.4 Flow Field Visualization 5.3.5 Procedure of SIMPLE Method 5.3.6 Results and Discussion 5.3.7 Procedure of Projection Method 5.4 Example: Natural Convection in a Cavity 5.4.1 Problem Description 5.4.2 Governing Equations and Boussinesq Assumption 5.4.3 Discretization and Boundary Conditions 5.4.4 Results and Discussion 5.5 Example: Flow over a Backward Facing Step 5.5.1 Problem Description 5.5.2 Boundary Conditions 5.5.3 Results and Discussion 5.5.4 SIMPLEC Method 5.6 Example: Flow over a Square Cylinder 5.6.1 Problem Description 5.6.2 Mesh and Boundary Conditions 5.6.3 Results and Discussion 5.6.4 Flow over a Square Cylinder at Re = 100 5.7 Verification and Validation Exercises 6 Unstructured Mesh 6.1 Introduction 6.2 Triangular Mesh Generation 6.2.1 Delaunay Triangulation 6.2.2 Mesh Generation Algorithm of Persson and Strang 6.2.3 Connectivity and Geometry Information 6.3 Solving General Convection-Diffusion Equation with Unstructured Mesh 6.3.1 The General Convection-Diffusion Equation 6.3.2 Discretization of the General Convection-Diffusion Equation 6.3.3 Boundary Conditions 6.3.4 Example: Heat Transfer over Corner 6.4 Solving Navier-Stokes Equations with Unstructured Mesh 6.4.1 The SIMPLE Procedure 6.4.2 Example: Lid-Driven Cavity Flow 6.4.3 Example: Natural Convection in Concentric Cylindrical Annulus 6.5 Other Means to Handle Complex Boundaries Exercises 7 Multiphase Flow 7.1 Introduction 7.2 VOF Method 7.2.1 Interface Representation 7.2.2 Interface Reconstruction 7.2.3 Interface Advection 7.2.4 Example: Interface Transportation by Uniform Velocity 7.2.5 Flow Field Calculation 7.2.6 Example: Dam-Break Problem 7.2.7 Surface Tension 7.2.8 Example: Excess Pressure in Water Drop 7.3 Level-set Method 7.3.1 Interface Representation 7.3.2 Interface Advection 7.3.3 Reinitialization of Level-set Function 7.3.4 Flow Field Calculation 7.3.5 Example: Gas Bubble Rising Problem 7.4 Multiphase Flow with Phase Change 7.4.1 Introduction 7.4.2 Temperature Field Computation 7.4.3 Flow Field Computation 7.4.4 Example: 1-D Stefan Problem Exercises 8 Turbulent Flow 8.1 Introduction 8.2 Two-Equation Models 8.2.1 k-ϵ Model 8.2.2 k-ϵ Model with Wall Models 8.2.3 k-ω Model 8.2.4 SST Model 8.2.5 V2F Model 8.2.6 Turbulent Flow with Heat Transfer 8.3 Large Eddy Simulation 8.3.1 Filtering 8.3.2 Subgrid Scale Models Exercises Appendix A MATLAB Functions A.1 Assemble Diagonal Vectors to Form Coefficient Matrix A.2 TDMA Algorithm (Thomas Algorithm) A.3 Stone’s Strongly Implicit Procedure (SIP) A.4 Assemble Diagonal Matrices to Form Coefficient Matrix A.5 Incomplete Cholesky Conjugate Gradient (ICCG) Method A.6 2-D Poisson Solver A.7 Triangular Mesh Generation Program of Persson and Strang A.8 Useful Accessory Functions to Triangular Mesh Generation Program of Persson and Strang B von Neumann Analysis of FTCS Scheme References Index
Dr. George (Zhaohui) Qin is currently an associate professor in the School of Engineering and Computer Science of Cedarville University at Cedarville, Ohio. George obtained his B.S. and M.S. degrees in Mechanical Engineering from Shanghai Jiaotong University of China. He carried out research on large eddy simulation (LES) of turbulent flows in rotating ducts under supervision of Dr. Richard Pletcher of Iowa State University for his Ph.D. degree. Upon receiving his degree in 2007, George began to work as a lecturer and post-doc research fellow in Iowa State University. He moved to Cedarville University in 2012. George teaches and researches in the general thermal-fluids area including Thermodynamics, Fluid Mechanics, Heat Transfer, Computational Fluid Dynamics, and Turbulent Flows.