ISBN-13: 9781119474623 / Angielski / Twarda / 2019 / 384 str.
ISBN-13: 9781119474623 / Angielski / Twarda / 2019 / 384 str.
Preface xviiAbout the Companion Website xxi1 What is CFD? 11.1. Introduction 11.2. Brief History of CFD 41.3. Outline of the Book 5Bibliography 7I Fundamentals 92 Governing Equations of Fluid Dynamics and Heat Transfer 112.1. Preliminary Concepts 112.2. Conservation Laws 142.2.1. Conservation of Mass 152.2.2. Conservation of Chemical Species 152.2.3. Conservation of Momentum 162.2.4. Conservation of Energy 202.3. Equation of State 212.4. Equations of Integral Form 222.5. Equations in Conservation Form 252.6. Equations in Vector Form 262.7. Boundary Conditions 272.7.1. Rigid Wall Boundary Conditions 282.7.2. Inlet and Exit Boundary Conditions 292.7.3. Other Boundary Conditions 302.8. Dimensionality and Time Dependence 312.8.1. Two- and One-Dimensional Problems 322.8.2. Equilibrium and Marching Problems 33Bibliography 34Problems 343 Partial Different Equations 373.1. Model Equations: Formulation of a PDE Problem 383.1.1. Model Equations 383.1.2. Domain, Boundary and Initial Conditions, and Well-Posed PDE Problem 403.1.3. Examples 423.2. Mathematical Classification of PDEs of Second Order 453.2.1. Classification 453.2.2. Hyperbolic Equations 483.2.3. Parabolic Equations 503.2.4. Elliptic Equations 523.2.5. Classification of Full Fluid Flow and Heat Transfer Equations 523.3. Numerical Discretization: Different Kinds of CFD 533.3.1. Spectral Methods 543.3.2. Finite Element Methods 563.3.3. Finite Difference and Finite Volume Methods 56Bibliography 59Problems 594 Finite Difference Method 634.1. Computational Grid 634.1.1. Time Discretization 634.1.2. Space Discretization 644.2. Finite Difference Approximation 654.2.1. Approximation of au/ax 654.2.2. Truncation Error, Consistency, and Order of Approximation 664.2.3. Other Formulas for au/ax: Evaluation of the Order of Approximation 694.2.4. Schemes of Higher Order for First Derivative 714.2.5. Higher-Order Derivatives 714.2.6. Mixed Derivatives 734.2.7. Finite Difference Approximation on Nonuniform Grids 744.3. Development of Finite Difference Schemes 774.3.1. Taylor Series Expansions 774.3.2. Polynomial Fitting 794.3.3. Development on Nonuniform Grids 804.4. Finite Difference Approximation of Partial Differential Equations 814.4.1. Approach and Examples 814.4.2. Boundary and Initial Conditions 854.4.3. Difference Molecule and Difference Equation 874.4.4. System of Difference Equations 884.4.5. Implicit and Explicit Methods 894.4.6. Consistency of Numerical Approximation 914.4.7. Interpretation of Truncation Error: Numerical Dissipation and Dispersion 924.4.8. Methods of Interpolation for Finite Difference Schemes 95Bibliography 98Problems 985 Finite Volume Schemes 1035.1. Introduction and General Formulation 1035.1.1. Introduction 1035.1.2. Finite Volume Grid 1055.1.3. Consistency, Local, and Global Conservation Property 1075.2. Approximation of Integrals 1095.2.1. Volume Integrals 1095.2.2. Surface Integrals 1105.3. Methods of Interpolation 1125.3.1. Upwind Interpolation 1125.3.2. Linear Interpolation of Convective Fluxes 1155.3.3. Central Difference (Linear Interpolation) Scheme for Diffusive Fluxes 1155.3.4. Interpolation of Diffusion Coefficients 1175.3.5. Upwind Interpolation of Higher Order 1185.4. Finite Volume Method on Unstructured Grids 1195.5. Implementation of Boundary Conditions 122Bibliography 123Problems 1236 Numerical Stability for Marching Problems 1276.1. Introduction and Definition of Stability 1276.1.1. Example 1276.1.2. Discretization and Round-Off Error 1296.1.3. Definition 1316.2. Stability Analysis 1326.2.1. Neumann Method 1326.2.2. Matrix Method 1406.3. Implicit Versus Explicit Schemes - Stability and Efficiency Considerations 142Bibliography 144Problems 144II Methods 1477 Application to Model Equations 1497.1. Linear Convection Equation 1507.1.1. Simple Explicit Schemes 1517.1.2. Simple Implicit Scheme 1547.1.3. Leapfrog Scheme 1557.1.4. Lax-Wendroff Scheme 1567.1.5. MacCormack Scheme 1577.2. One-Dimensional Heat Equation 1577.2.1. Simple Explicit Scheme 1577.2.2. Simple Implicit Scheme 1597.2.3. Crank-Nicolson Scheme 1597.3. Burgers and Generic Transport Equations 1617.4. Method of Lines 1627.4.1. Adams Methods 1637.4.2. Runge-Kutta Methods 1647.5. Solution of Tridiagonal Systems by Thomas Algorithm 165Bibliography 169Problems 1698 Steady-State Problems 1738.1. Problems Reducible to Matrix Equations 1738.1.1. Elliptic PDE 1748.1.2. Marching Problems Solved by Implicit Schemes 1778.1.3. Structure of Matrices 1798.2. Direct Methods 1808.2.1. Cyclic Reduction Algorithm 1818.2.2. Thomas Algorithm for Block-Tridiagonal Matrices 1848.2.3. LU Decomposition 1858.3. Iterative Methods 1868.3.1. General Methodology 1878.3.2. Jacobi Iterations 1888.3.3. Gauss-Seidel Algorithm 1898.3.4. Successive Over- and Underrelaxation 1908.3.5. Convergence of Iterative Procedures 1918.3.6. Multigrid Methods 1948.3.7. Pseudo-transient Approach 1978.4. Systems of Nonlinear Equations 1978.4.1. Newton's Algorithm 1988.4.2. Iteration Methods Using Linearization 1998.4.3. Sequential Solution 2018.5. Computational Performance 202Bibliography 203Problems 2039 Unsteady Compressible Fluid Flows and Conduction Heat Transfer 2079.1. Introduction 2079.2. Compressible Flows 2089.2.1. Equations, Mathematical Classification, and General Comments 2089.2.2. MacCormack Scheme 2129.2.3. Beam-Warming Scheme 2149.2.4. Upwinding 2189.2.5. Methods for Purely Hyperbolic Systems: TVD Schemes 2209.3. Unsteady Conduction Heat Transfer 2239.3.1. Overview 2239.3.2. Simple Methods for Multidimensional Heat Conduction 2239.3.3. Approximate Factorization 2259.3.4. ADI Method 227Bibliography 228Problems 22910 Incompressible Flows 23310.1. General Considerations 23310.1.1. Introduction 23310.1.2. Role of Pressure 23410.2. Discretization Approach 23610.2.1. Conditions for Conservation of Mass by Numerical Solution 23710.2.2. Colocated and Staggered Grids 23810.3. Projection Method for Unsteady Flows 24310.3.1. Explicit Schemes 24410.3.2. Implicit Schemes 24710.4. Projection Methods for Steady-State Flows 25010.4.1. SIMPLE 25210.4.2. SIMPLEC and SIMPLER 25410.4.3. PISO 25610.5. Other Methods 25710.5.1. Vorticity-Streamfunction Formulation for Two-Dimensional Flows 25710.5.2. Artificial Compressibility 261Bibliography 261Problems 262III Art of CFD 26511 Turbulence 26711.1. Introduction 26711.1.1. A Few Words About Turbulence 26811.1.2. Why is the Computation of Turbulent Flows Difficult? 27111.1.3. Overview of Numerical Approaches 27311.2. Direct Numerical Simulation (DNS) 27511.2.1. Homogeneous Turbulence 27511.2.2. Inhomogeneous Turbulence 27811.3. Reynolds-Averaged Navier-Stokes (RANS) Models 27911.3.1. Mean Flow and Fluctuations 28011.3.2. Reynolds-Averaged Equations 28111.3.3. Reynolds Stresses and Turbulent Kinetic Energy 28211.3.4. Eddy Viscosity Hypothesis 28411.3.5. Closure Models 28511.3.6. Algebraic Models 28611.3.7. One-Equation Models 28711.3.8. Two-Equation Models 28911.3.9. RANS and URANS 29111.3.10. Models of Turbulent Scalar Transport 29211.3.11. Numerical Implementation of RANS Models 29411.4. Large Eddy Simulation (LES) 29711.4.1. Filtered Equations 29811.4.2. Closure Models 30111.4.3. Implementation of LES in CFD Analysis: Numerical Resolution and Near-Wall Treatment 304Bibliography 307Problems 30912 Computational Grids 31312.1. Introduction: Need for Irregular and Unstructured Grids 31312.2. Irregular Structured Grids 31612.2.1. Generation by Coordinate Transformation 31612.2.2. Examples 31912.2.3. Grid Quality 32112.3. Unstructured Grids 32212.3.1. Grid Generation 32512.3.2. Cell Topology 32512.3.3. Grid Quality 32612.4. Adaptive Grids 329Bibliography 331Problems 33213 Conducting CFD Analysis 33513.1. Overview: Setting and Solving a CFD Problem 33513.2. Errors and Uncertainty 33913.2.1. Errors in CFD Analysis 33913.2.2. Verification and Validation 346Bibliography 349Problems 349Index 351
OLEG ZIKANOV, PHD, is a Professor of Mechanical Engineering at the University of Michigan-Dearborn, MI, USA. His teaching activities are in the area of thermal-fluid sciences with focus on CFD, fluid dynamics, and energy technologies. He is an active researcher in the field of computational analysis of fluid flow phenomena.
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