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Essential Computational Fluid Dynamics.

Essential Computational Fluid Dynamics.
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10022819 Access this eBook online Ebook for Engineering   GUtech Library . . Available .  
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ISBN 9781118174777
-- 9780470423295
Author Zikanov, Oleg
Title Essential Computational Fluid Dynamics.
1st ed.
Description 1 online resource (320 pages)
Contents Essential Computational Fluid Dynamics -- Contents -- Preface -- 1 What Is CFD? -- 1.1. Introduction -- 1.2. Brief History of CFD -- 1.3. Outline of the Book -- References and Suggested Reading -- I Fundamentals -- 2 Governing Equations of Fluid Dynamics and Heat Transfer -- 2.1. Preliminary Concepts -- 2.2. Mass Conservation -- 2.3. Conservation of Chemical Species -- 2.4. Conservation of Momentum -- 2.5. Conservation of Energy -- 2.6. Equation of State -- 2.7. Equations in Integral Form -- 2.8. Equations in Conservation Form -- 2.9. Equations in Vector Form -- 2.10. Boundary Conditions -- 2.10.1. Rigid Wall Boundary Conditions -- 2.10.2. Inlet and Exit Boundary Conditions -- 2.10.3. Other Boundary Conditions -- References and Suggested Reading -- Problems -- 3 Partial Differential Equations -- 3.1. Model Equations -- Formulation of a PDE Problem -- 3.1.1. Model Equations -- 3.1.2. Domain, Boundary, and Initial Conditions -- 3.1.3. Equilibrium and Marching Problems -- 3.1.4. Examples -- 3.2. Mathematical Classification of PDE of Second Order -- 3.2.1. Classification -- 3.2.2. Hyperbolic Equations -- 3.2.3. Parabolic Equations -- 3.2.4. Elliptic Equations -- 3.3. Numerical Discretization: Different Kinds of CFD -- 3.3.1. Spectral Methods -- 3.3.2. Finite Element Methods -- 3.3.3. Finite Difference and Finite Volume Methods -- References and Suggested Reading -- Problems -- 4 Basics of Finite Difference Approximation -- 4.1. Computational Grid -- 4.1.1. Time Discretization -- 4.1.2. Space Discretization -- 4.2. Finite Differences and Interpolation -- 4.2.1. Approximation of ∂u/∂x -- 4.2.2. Truncation Error, Consistency, Order of Approximation -- 4.2.3. Other Formulas for ∂u/∂x: Evaluation of the Order of Approximation -- 4.2.4. Schemes of Higher Order for First Derivative -- 4.2.5. Higher-Order Derivatives -- 4.2.6. Mixed Derivatives.
4.2.7. Truncation Error of Linear Interpolation -- 4.3. Approximation of Partial Differential Equations -- 4.3.1. Approach and Examples -- 4.3.2. Interpretation of Truncation Error: Numerical Dissipation and Dispersion -- 4.3.3. Boundary and Initial Conditions -- 4.3.4. Consistency of Numerical Approximation -- 4.3.5. System of Difference Equations -- 4.3.6. Implicit and Explicit Methods -- 4.4. Development of Finite Difference Schemes -- 4.4.1. Taylor Series Expansions -- 4.4.2. Polynomial Fitting -- References and Suggested Reading -- Problems -- 5 Finite Volume Method -- 5.1. Introduction and Integral Formulation -- 5.1.1. Finite Volume Grid -- 5.1.2. Global Conservation Property -- 5.2. Approximation of Integrals -- 5.2.1. Volume Integrals -- 5.2.2. Surface Integrals -- 5.3. Methods of Interpolation -- 5.3.1. Upwind Interpolation -- 5.3.2. Linear Interpolation -- 5.3.3. Upwind Interpolation of Higher Order -- 5.3.4. Interpolation on Nonorthogonal Grids -- 5.4. Boundary Conditions -- References and Suggested Reading -- Problems -- 6 Stability of Transient Solutions -- 6.1. Introduction and Definition of Stability -- 6.1.1. Discretization and Round-off Error -- 6.1.2. Definition -- 6.2. Stability Analysis -- 6.2.1. Neumann Method -- 6.2.2. Matrix Method -- 6.3. Implicit versus Explicit Schemes-Stability and Efficiency Considerations -- References and Suggested Reading -- Problems -- 7 Application to Model Equations -- 7.1. Linear Convection Equation -- 7.1.1. Simple Explicit Schemes -- 7.1.2. Other Schemes -- 7.2. One-Dimensional Heat Equation -- 7.2.1. Simple Explicit Scheme -- 7.2.2. Simple Implicit Scheme -- 7.2.3. Crank-Nicolson Scheme -- 7.3. Burgers and Generic Transport Equations -- 7.4. Method of Lines Approach -- 7.4.1. Adams Methods -- 7.4.2. Runge-Kutta Methods -- 7.5. Implicit Schemes: Solution of Tridiagonal Systems by Thomas Algorithm.
References and Suggested Reading -- Problems -- II Methods -- 8 Steady-State Problems -- 8.1. Problems Reducible to Matrix Equations -- 8.1.1. Elliptic PDE -- 8.1.2. Implicit Integration of Nonsteady Equations -- 8.2. Direct Methods -- 8.2.1. Band-Diagonal and Block-Diagonal Matrices -- 8.2.2. LU Decomposition -- 8.3. Iterative Methods -- 8.3.1. General Methodology -- 8.3.2. Jacobi Iterations -- 8.3.3. Gauss-Seidel Algorithm -- 8.3.4. Successive Over- and Underrelaxation -- 8.3.5. Convergence of Iterative Procedures -- 8.3.6. Multigrid Methods -- 8.3.7. Pseudo-transient Approach -- 8.4. Systems of Nonlinear Equations -- 8.4.1. Newton's Algorithm -- 8.4.2. Iteration Methods Using Linearization -- 8.4.3. Sequential Solution -- References and Suggested Reading -- Problems -- 9 Unsteady Problems of Fluid Flows and Heat Transfer -- 9.1. Introduction -- 9.2. Compressible Flows -- 9.2.1. Overview and General Comments -- 9.2.2. Explicit MacCormack Method -- 9.2.3. Beam-Warming Method -- 9.2.4. Upwinding -- 9.2.5. Methods for Purely Hyperbolic Systems -- 9.3. Unsteady Conduction Heat Transfer -- 9.3.1. Simple Methods for Multidimensional Heat Conduction -- 9.3.2. Approximate Factorization -- 9.3.3. ADI Method -- References and Suggested Reading -- Problems -- 10 Incompressible Flows -- 10.1. General Considerations -- 10.1.1. Introduction -- 10.1.2. Role of Pressure -- 10.2. Discretization Approach -- 10.2.1. Colocated and Staggered Grids -- 10.3. Projection Method for Unsteady Flows -- 10.3.1. Explicit Schemes -- 10.3.2. Implicit Schemes -- 10.4. Projection Methods for Steady-State Flows -- 10.4.1. SIMPLE -- 10.4.2. SIMPLEC, SIMPLER, and PISO -- 10.5. Other Methods -- 10.5.1. Vorticity-Streamfunction Formulation for Two-Dimensional Flows -- 10.5.2. Artificial Compressibility -- References and Suggested Reading -- Problems -- III Art of CFD -- 11 Turbulence.
11.1. Introduction -- 11.1.1. A Few Words About Turbulence -- 11.1.2. Why Is the Computation of Turbulent Flows Difficult? -- 11.1.3. Overview of Numerical Approaches -- 11.2. Direct Numerical Simulation (DNS) -- 11.2.1. Homogeneous Turbulence -- 11.2.2. Inhomogeneous Turbulence -- 11.3. Reynolds-Averaged Navier-Stokes (RANS) Models -- 11.3.1. Reynolds-Averaged Equations -- 11.3.2. Eddy Viscosity Hypothesis -- 11.3.3. Algebraic Models -- 11.3.4. Two-Equation Models -- 11.3.5. Numerical Implementation of RANS Models -- 11.4. Large-Eddy Simulation (LES) -- 11.4.1. Filtered Equations -- 11.4.2. Closure Models -- 11.4.3. Implementation of LES in CFD Analysis: Numerical Resolution and Near-Wall Treatment -- References and Suggested Reading -- Problems -- 12 Computational Grids -- 12.1. Introduction: Need for Irregular and Unstructured Grids -- 12.2. Irregular Structured Grids -- 12.2.1. Generation by Coordinate Transformation -- 12.2.2. Examples -- 12.2.3. Grid Quality -- 12.3. Unstructured Grids -- 12.3.1. Grid Generation -- 12.3.2. Finite Volume Discretization on Unstructured Grids -- 12.3.3. Cell Topology -- 12.3.4. Grid Quality -- References and Suggested Reading -- Problems -- 13 Conducting CFD Analysis -- 13.1. Overview: Setting and Solving a CFD Problem -- 13.2. Errors and Uncertainty -- 13.2.1. Errors in CFD Analysis -- 13.2.2. Verification and Validation -- 13.3. Adaptive Grids -- References and Suggested Reading -- INDEX.
Subject Fluid dynamics -- Mathematics
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