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The finite volume method in computational fluid dynamics : an advanced introduction with OpenFOAM and Matlab
Moukalled, Fadl Hassan,
- ISBN:3319168746
- ISBN:9783319168746
- ISBN:9783319168739
- Call Number : QA 911 .M69 2016
- Main Entry: Moukalled, Fadl Hassan, 1961-
- Title:The finite volume method in computational fluid dynamics : an advanced introduction with OpenFOAM and Matlab [electronic resource] / F. Moukalled, L. Mangani, M. Darwish.
- Publisher:New York : Springer, 2016.
- Physical Description:xxiii, 791 p.: ill (some color)
- Series:Fluid mechanics and its applications, 0926-5112; v.113
- Notes:Includes bibliographical references
- Subject:Finite volume method.
- Subject:Computational Science and Engineering.
- Subject:Engineering Fluid Dynamics.
- Subject:Fluid- and Aerodynamics.
- Added Entry:Darwish, M.
- Added Entry:Mangani, L.
محتواي کتاب
- Preface
- Acknowledgments
- Contents
- About the Authors
- Part I Foundation
- 1 Introduction
- 2 Review of Vector Calculus
- 3 Mathematical Description of Physical Phenomena
- Abstract
- 3.1 Introduction
- 3.2 Classification of Fluid Flows
- 3.3 Eulerian and Lagrangian Description of Conservation Laws
- 3.4 Conservation of Mass (Continuity Equation)
- 3.5 Conservation of Linear Momentum
- 3.6 Conservation of Energy
- 3.7 General Conservation Equation
- 3.8 Non-dimensionalization Procedure
- 3.9 Dimensionless Numbers
- 3.10 Closure
- 3.11 Exercises
- References
- 4 The Discretization Process
- 5 The Finite Volume Method
- Abstract
- 5.1 Introduction
- 5.2 The Semi-Discretized Equation
- 5.3 Boundary Conditions
- 5.4 Order of Accuracy
- 5.5 Transient Semi-Discretized Equation
- 5.6 Properties of the Discretized Equations
- 5.7 Variable Arrangement
- 5.8 Implicit Versus Explicit Numerical Methods
- 5.9 The Mesh Support
- 5.10 Computational Pointers
- 5.11 Closure
- 5.12 Exercises
- References
- 6 The Finite Volume Mesh
- 7 The Finite Volume Mesh in OpenFOAM and uFVM
- Part II Discretization
- 8 Spatial Discretization: The Diffusion Term
- Abstract
- 8.1 Two-Dimensional Diffusion in a Rectangular Domain
- 8.2 Comments on the Discretized Equation
- 8.3 Boundary Conditions
- 8.4 The Interface Diffusivity
- 8.5 Non-Cartesian Orthogonal Grids
- 8.6 Non-orthogonal Unstructured Grid
- 8.7 Skewness
- 8.8 Anisotropic Diffusion
- 8.9 Under-Relaxation of the Iterative Solution Process
- 8.10 Computational Pointers
- 8.11 Closure
- 8.12 Exercises
- References
- 9 Gradient Computation
- 10 Solving the System of Algebraic Equations
- Abstract
- 10.1 Introduction
- 10.2 Direct or Gauss Elimination Method
- 10.2.1 Gauss Elimination
- 10.2.2 Forward Elimination
- 10.2.3 Forward Elimination Algorithm
- 10.2.4 Backward Substitution
- 10.2.5 Back Substitution Algorithm
- 10.2.6 LU Decomposition
- 10.2.7 The Decomposition Step
- 10.2.8 LU Decomposition Algorithm
- 10.2.9 The Substitution Step
- 10.2.10 LU Decomposition and Gauss Elimination
- 10.2.11 LU Decomposition Algorithm by Gauss Elimination
- 10.2.12 Direct Methods for Banded Sparse Matrices
- 10.2.13 TriDiagonal Matrix Algorithm (TDMA)
- 10.2.14 PentaDiagonal Matrix Algorithm (PDMA)
- 10.3 Iterative Methods
- 10.3.1 Jacobi Method
- 10.3.2 Gauss-Seidel Method
- 10.3.3 Preconditioning and Iterative Methods
- 10.3.4 Matrix Decomposition Techniques
- 10.3.5 Incomplete LU (ILU) Decomposition
- 10.3.6 Incomplete LU Factorization with no Fill-in ILU(0)
- 10.3.7 ILU(0) Factorization Algorithm
- 10.3.8 ILU Factorization Preconditioners
- 10.3.9 Algorithm for the Calculation of {{\bf D}}^{*} in the DILU Method
- 10.3.10 Forward and Backward Solution Algorithm with the DILU Method
- 10.3.11 Gradient Methods for Solving Algebraic Systems
- 10.3.12 The Method of Steepest Descent
- 10.3.13 The Conjugate Gradient Method
- 10.3.14 The Bi-conjugate Gradient Method (BiCG) and Preconditioned BICG
- 10.4 The Multigrid Approach
- 10.5 Computational Pointers
- 10.6 Closure
- 10.7 Exercises
- References
- 11 Discretization of the Convection Term
- Abstract
- 11.1 Introduction
- 11.2 Steady One Dimensional Convection and Diffusion
- 11.3 Truncation Error: Numerical Diffusion and Anti-Diffusion
- 11.4 Numerical Stability
- 11.5 Higher Order Upwind Schemes
- 11.5.1 Second Order Upwind Scheme
- 11.5.2 The Interpolation Profile
- 11.5.3 The Discretized Equation
- 11.5.4 Truncation Error
- 11.5.5 Stability Analysis
- 11.5.6 The QUICK Scheme
- 11.5.7 The Interpolation Profile
- 11.5.8 Truncation Error
- 11.5.9 Stability Analysis
- 11.5.10 The FROMM Scheme
- 11.5.11 The Interpolation Profile
- 11.5.12 The Discretized Equation
- 11.5.13 Truncation Error
- 11.5.14 Stability Analysis
- 11.5.15 Comparison of the Various Schemes
- 11.5.16 Functional Relationships for Uniform and Non-uniform Grids
- 11.6 Steady Two Dimensional Advection
- 11.7 High Order Schemes on Unstructured Grids
- 11.8 The Deferred Correction Approach
- 11.9 Computational Pointers
- 11.10 Closure
- 11.11 Exercises
- References
- 12 High Resolution Schemes
- Abstract
- 12.1 The Normalized Variable Formulation (NVF)
- 12.2 The Convection Boundedness Criterion (CBC)
- 12.3 High Resolution (HR) Schemes
- 12.4 The TVD Framework
- 12.5 The NVF-TVD Relation
- 12.6 HR Schemes in Unstructured Grid Systems
- 12.7 Deferred Correction for HR Schemes
- 12.8 The DWF and NWF Methods
- 12.9 Boundary Conditions
- 12.10 Computational Pointers
- 12.11 Closure
- 12.12 Exercises
- References
- 13 Temporal Discretization: The Transient Term
- Abstract
- 13.1 Introduction
- 13.2 The Finite Difference Approach
- 13.3 The Finite Volume Approach
- 13.3.1 First Order Transient Schemes
- 13.3.2 First Order Implicit Euler Scheme
- 13.3.3 First Order Explicit Euler Scheme
- 13.3.4 Second Order Transient Euler Schemes
- 13.3.5 Crank-Nicholson (Central Difference Profile)
- 13.3.6 Second Order Upwind Euler (SOUE) Scheme
- 13.3.7 Initial Condition for the FV Approach
- 13.4 Non-Uniform Time Steps
- 13.5 Computational Pointers
- 13.6 Closure
- 13.7 Exercises
- References
- 14 Discretization of the Source Term, Relaxation, and Other Details
- Part III Algorithms
- 15 Fluid Flow Computation: Incompressible Flows
- Abstract
- 15.1 The Main Difficulty
- 15.2 A Preliminary Derivation
- 15.2.1 Discretization of the Momentum Equation
- 15.2.2 Discretization of the Continuity Equation
- 15.2.3 The Checkerboard Problem
- 15.2.4 The Staggered Grid
- 15.2.5 The Pressure Correction Equation
- 15.2.6 The SIMPLE Algorithm on Staggered Grid
- 15.2.7 Pressure Correction Equation in Two Dimensional Staggered Cartesian Grids
- 15.2.8 Pressure Correction Equation in Three Dimensional Staggered Cartesian Grid
- 15.3 Disadvantages of the Staggered Grid
- 15.4 The Rhie-Chow Interpolation
- 15.5 General Derivation
- 15.6 Boundary Conditions
- 15.6.1 Boundary Conditions for the Momentum Equation
- 15.6.2 Boundary Conditions for the Pressure Correction Equation
- 15.6.2.1 Wall Boundary Condition
- 15.6.2.2 Inlet Boundary Conditions
- Specified Velocity \left( {p_{b} = ?;\dot{m}_{b} \;specified;{{\bf v}}_{b} \,specified} \right)
- Specified Pressure and Velocity Direction \scale90%{\left( {p_{b}} = p_{specified} ;\right. \scale90%{ \left.{\dot{m}_{b} ?;\,{{\bf e}}_{{{\bf v}}} \,specified;{{\bf v}}_{b} ?} \right)
- Specified Total Pressure and Velocity Direction \left( {p_{o,b}} = p_{o,specified} ;\right. \;\left.{\dot{m}_{b} ?; {{\bf e}}_{{{\bf v}}} \;specified;{{\bf v}}_{b} ?} \right)
- 15.6.2.3 Outlet Boundary Conditions
- 15.6.2.4 Symmetry Boundary Condition
- 15.6.2.5 The Relative Nature of Pressure
- 15.7 The SIMPLE Family of Algorithms
- 15.8 Optimum Under-Relaxation Factor Values for v and p^{\prime}
- 15.9 Treatment of Various Terms with the Rhie-Chow Interpolation
- 15.10 Computational Pointers
- 15.11 Closure
- 15.12 Exercises
- References
- 16 Fluid Flow Computation: Compressible Flows
- Abstract
- 16.1 Historical
- 16.2 Introduction
- 16.3 The Conservation Equations
- 16.4 Discretization of the Momentum Equation
- 16.5 The Pressure Correction Equation
- 16.6 Discretization of The Energy Equation
- 16.7 The Compressible SIMPLE Algorithm
- 16.8 Boundary Conditions
- 16.9 Computational Pointers
- 16.10 Closure
- 16.11 Exercises
- References
- Part IV Applications
- 17 Turbulence Modeling
- Abstract
- 17.1 Turbulence Modeling
- 17.2 Reynolds Averaging
- 17.3 Boussinesq Hypothesis
- 17.4 Turbulence Models
- 17.5 Two-Equation Turbulence Models
- 17.6 Summary of Incompressible Turbulent Flow Equations
- 17.7 Discretization of the Turbulent Flow Equations
- 17.8 Boundary Conditions
- 17.9 Calculating Normal Distance to the Wall
- 17.10 Computational Pointers
- 17.11 Closure
- 17.12 Exercises
- References
- 18 Boundary Conditions in OpenFOAM and uFVM
- 19 An OpenFOAM Turbulent Flow Application
- 20 Closing Remarks
- Erratum to: The Finite Volume Methodin Computational Fluid Dynamics
- Appendix uFVM