Verfügbarkeit: Computational fluid dynamics for incompressible flows

Computational fluid dynamics for incompressible flows:

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Bibliographische Detailangaben
1. Verfasser:	Roychowdhury, D. G. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Boca Raton ; London ; New York CRC Press 2021
Ausgabe:	First edition
Schlagworte:	Computational fluid dynamics-Textbooks Inkompressible Strömung Fluiddynamik
Beschreibung:	Description based on publisher supplied metadata and other sources
Beschreibung:	xxiii, 391 Seiten Illustrationen
ISBN:	9780367524326

Internformat

MARC


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245	1	0	\|a Computational fluid dynamics for incompressible flows \|c D. G. Roychowdhury
250			\|a First edition
264		1	\|a Boca Raton ; London ; New York \|b CRC Press \|c 2021
264		4	\|c ©2021
300			\|a xxiii, 391 Seiten \|b Illustrationen
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505	8		\|a Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- Acknowledgements -- Chapter 1. Overview of CFD -- 1.1 Introduction -- 1.2 Basic Principles of CFD -- 1.3 What Does a CFD Algorithm Do? -- 1.4 Stages of a CFD Analysis -- 1.4.1 Pre-Processor -- 1.4.2 Solver -- 1.4.3 Post-Processor -- 1.5 Governing Equations -- 1.6 Discretization -- 1.6.1 Finite Difference Method -- 1.6.2 Finite Volume Method -- 1.6.3 Finite Element Method -- 1.7 Discretization Properties -- Questions: -- Chapter 2. Governing Equations and Classification of PDE -- Governing Equations -- 2.1 Introduction -- 2.1.1 Integral Form -- 2.1.2 Differential Form -- 2.2 Conservative Form of the Flow Equations -- 2.2.1 Mass (Continuity) -- 2.2.1.1 Derivation of Continuity Equation -- 2.2.2 Momentum Equations -- 2.2.2.1 Derivation of X-Momentum Equation -- 2.2.3 Energy Equation -- 2.2.3.1 Derivation of Energy Equation -- 2.2.4 General Scalar -- 2.3 Some Comments -- 2.3.1 Conservative and Non-Conservative Forms of Equations -- 2.3.2 Compressible and Incompressible Flow -- Physical and Mathematical Classification of Partial Differential Equations -- 2.4 Equilibrium Problems -- 2.5 Marching Problems -- 2.6 Mathematical Classification -- 2.7 Important Equations -- 2.8 Boundary Conditions (BCs) -- 2.8.1 Inlet Boundary -- 2.8.1.1 Inflow -- 2.8.1.2 Stagnation (Reservoir) -- 2.8.2 Outlet Boundary -- 2.8.2.1 Outflow -- 2.8.2.2 Pressure -- 2.8.2.3 Radiation (Convection) -- 2.8.3 Wall Boundaries -- 2.8.3.1 No-Slip Wall -- 2.8.3.2 Slip Wall -- 2.8.4 Other Boundary Conditions -- 2.8.4.1 Symmetry Plane and Axis Boundary -- 2.8.4.2 Periodic -- 2.9 Summary -- Questions -- Chapter 3. Finite Difference Method: Fundamentals -- 3.1 Introduction -- 3.2 Taylor Series Expansion -- 3.3 Unequal Grid Spacing -- 3.4 Difference Representation of PDE -- 3.4.1 Errors
505	8		\|a 3.4.1.1 Truncation Error -- 3.4.1.2 Round-off Error -- 3.4.2 Consistency -- 3.4.3 Stability -- 3.4.3.1 Von Neumann's Method -- 3.4.4 Convergence -- 3.4.5 Lax's Equivalence Theorem -- 3.4.6 Courant Number -- 3.5 Examples -- 3.6 Summary -- Questions: -- Chapter 4. Finite Difference Method: Application -- 4.1 Introduction -- 4.2 One-Dimensional Diffusion Equations -- 4.2.1 Explicit Methods -- 4.2.1.1 The Forward Time, Central Space -- 4.2.1.2 The Richardson's Method -- 4.2.1.3 The DuFort-Frankel Method (D-F Leap-Frog Method) -- 4.2.2 Implicit Methods -- 4.2.2.1 The Classical Implicit Method -- 4.2.2.2 The Crank-Nicolson Method -- 4.2.2.3 The Method of Weighted Averages -- 4.3 One-Dimensional Transport Equations -- 4.3.1 The Wave Equation -- 4.3.1.1 The FTCS Method -- 4.3.1.2 Upwind Differencing -- 4.3.1.3 The LaxMethod (Lax-Friedrichs Method) -- 4.3.1.4 The Lax-Wendroff Method -- 4.3.1.5 The Two-Step Lax-Wendroff Method -- 4.3.1.6 The MacCormack Method -- 4.3.1.7 The Beam-Warming Method -- 4.3.1.8 The Implicit Method -- 4.3.2 The Complete Transport Equation -- 4.3.2.1 Central Difference -- 4.3.2.2 The Richardson Method -- 4.3.2.3 The DuFort-Frankel Method -- 4.3.2.4 The Upwind Method -- 4.4 Two-Dimensional Diffusion Equation -- 4.4.1 The Explicit Method -- 4.4.2 Implicit Methods -- 4.4.2.1 The Fully Implicit Method -- 4.4.2.2 The Crank-Nicolson Method -- 4.4.2.3 The Alternate Direction Implicit (ADI) Method -- 4.4.2.4 Comments on Diffusion Equations -- 4.4.2.5 Further Comments on Conservative vs. Non-Conservative Variables -- 4.4.2.6 The Grid (Mesh) Independence Study -- 4.5 Burgers' Equation -- 4.5.1 The Inviscid Burgers' Equation -- 4.5.1.1 Upwind Differencing -- 4.5.1.2 The Lax (Lax-Friedrichs) Method -- 4.5.1.3 The Lax-Wendroff Method -- 4.5.1.4 The MacCormack Method -- 4.5.1.5 Implicit Methods -- 4.5.1.6 The Godunov Method -- 4.5.1.7 The Roe Method
505	8		\|a 4.5.2 The Viscid Burgers' Equation -- 4.5.2.1 The FTCS Method -- 4.5.2.2 The DuFort-Frankel Method -- 4.5.2.3 The Lax-Wendroff Method -- 4.5.2.4 The MacCormack Method -- 4.6 The Laplace Equation -- 4.7 Examples -- 4.8 Summary -- Questions -- Chapter 5. Finite Volume Method -- 5.1 Introduction -- 5.2 The Diffusion Equation -- 5.2.1 The Steady-State One-Dimensional Diffusion Equation -- 5.2.2 Discretization of the Source Term -- 5.2.3 Discretized Equation at Boundaries -- 5.2.3.1 For Given Value at the Boundaries (Dirichlet Boundary Conditions) -- 5.2.3.2 Insulated Boundary -- 5.2.3.3 Mixed Boundary Conditions -- 5.2.4 Assembling the Algebraic Equations -- 5.2.5 Extension to Two Dimensions -- 5.2.6 Extension to Three Dimensions -- 5.2.7 Desirable Properties of a Discretization Scheme -- 5.2.8 Further Comments on Interface Diffusion Coefficients -- 5.3 The Convection-Diffusion Equation -- 5.3.1 The Steady-State One-Dimensional Advection-Diffusion Equation -- 5.3.1.1 The Central Differencing Scheme -- 5.3.1.2 The Upwind Differencing Scheme -- 5.3.1.3 Exact Solution -- 5.3.1.4 The Exponential Scheme -- 5.3.1.5 The Hybrid Differencing Scheme -- 5.3.1.6 The Second Order Upwind (SOU) Scheme -- 5.3.1.7 The Quadratic Upstream Interpolation for Convective Kinetics (QUICK) Scheme -- 5.3.1.8 The FROMM Scheme -- 5.3.1.9 Advantages and Disadvantages of Various Convective Schemes -- 5.3.2 Deferred Correction Approach -- 5.3.2.1 CDS -- 5.3.2.2 SOU -- 5.3.2.3 QUICK -- 5.3.2.4 FROMM -- 5.3.3 Extension to Two Dimension -- 5.3.3.1 UDS -- 5.3.3.2 CDS -- 5.3.3.3 SOU -- 5.3.3.4 QUICK -- 5.3.3.5 FROMM -- 5.3.4 Extension to Three Dimension -- 5.3.4.1 UDS -- 5.3.4.2 CDS -- 5.3.4.3 SOU -- 5.3.4.4 QUICK -- 5.3.4.5 FROMM -- 5.3.5 High Resolution and Bounded Convective Schemes -- 5.3.5.1 Normalized Variable Formulation -- 5.3.5.2 Convective Boundedness Criteria
505	8		\|a 5.3.5.3 High-Resolution Schemes -- 5.3.5.4 The TVD Framework -- 5.3.5.5 Implementation of Various Convective Schemes in Code -- 5.4 Time-Dependent Methods -- 5.4.1 One-Step Methods -- 5.4.1.1 Forward Differencing (Euler Method) -- 5.4.1.2 Backward Differencing (Backward Euler) -- 5.4.1.3 Central Differencing (Crank-Nicolson) -- 5.5 Time Discretization Methods Applied to the General Scalar Transport Equation -- 5.5.1 Forward Differencing - Explicit Scheme -- 5.5.2 Backward Differencing - Implicit Scheme -- 5.5.3 Crank-Nicolson - Central Difference Scheme: -- 5.6 Courant Number -- 5.7 Uses of Time-Marching in CFD -- 5.8 Implementation of Boundary Conditions in Code -- 5.8.1 Generalized Boundary Conditions -- 5.8.2 Convective Boundary Conditions -- 5.9 Examples -- 5.10 Summary -- Questions -- Chapter 6. Solution of Incompressible Navier-Stokes Equations -- 6.1 Introduction -- 6.2 Pressure-Velocity Coupling -- 6.3 The Vorticity-Stream Function Method -- 6.3.1 Boundary Conditions -- 6.4 Primitive Variable Methods -- 6.4.1 Co-located Storage of Variables -- 6.4.2 Staggered Grid -- 6.5 Solution Methods for the Primitive Variable Form of N-S Equations -- 6.5.1 The Artificial Compressibility Method -- 6.5.2 The Pressure Correction Approach -- 6.5.2.1 The MAC Method -- 6.5.2.2 The Fractional Step Pressure Projection Method -- 6.6 The SIMPLE Method -- 6.6.1 Derivation of Velocity Correction and Pressure Correction Equations -- 6.6.1.1 Pressure and Velocity Corrections -- 6.6.2 Pressure Correction Equation -- 6.6.3 The SIMPLE Algorithm -- 6.7 Variants of SIMPLE -- 6.7.1 The SIMPLER Algorithm -- 6.7.2 The SIMPLEC Algorithm -- 6.7.3 The PISO (Pressure Implicit with Split Operator) Algorithm -- 6.8 Summary -- Questions: -- Chapter 7. Finite Volume Method for Complex Geometries -- 7.1 Introduction -- 7.2 Staggered Grid Algorithm -- 7.3 The Co-located Grid Algorithm
505	8		\|a 7.4 Discretization Methods for Non-Orthogonal Structured Grids -- 7.4.1 The Continuity Equation -- 7.4.2 The Transport Equation -- 7.4.2.1 Discretization of Convective Flux -- 7.4.2.2 Discretization of Diffusive Flux -- 7.4.2.3 Discretization of Pressure Terms -- 7.4.2.4 Implementation of the QUICK Scheme -- 7.5 Solution of the Pressure Field -- 7.5.1 Derivation of Pressure Correction and Velocity Correction Equations -- 7.5.2 Implementation of Momentum Interpolation -- 7.6 Extension to Three Dimension -- 7.6.1 Discretization of Continuity Equations -- 7.6.2 Discretization of Convective Flux -- 7.6.3 Discretization of Diffusive Flux -- 7.6.4 Discretization of the Pressure Term -- 7.6.5 Implementation of the QUICK Scheme -- 7.6.6 Implementation of the SIMPLE Algorithm -- 7.7 Discretization Method for the Cartesian Structured Grid -- 7.7.1 The Continuity Equation -- 7.7.2 The Transport Equation -- 7.7.2.1 Discretization of Convective Flux -- 7.7.2.2 Discretization of Diffusive Flux -- 7.7.2.3 Discretization of the Pressure Term -- 7.7.2.4 Implementation of the QUICK Scheme -- 7.7.2.5 Derivation of Pressure Correction and Velocity Correction Equation -- 7.7.2.6 Implementation of the Momentum Interpolation -- 7.8 Discretization Method for the Non-Orthogonal Unstructured Grid -- 7.8.1 The Continuity Equation -- 7.8.2 The Transport Equation -- 7.8.2.1 Discretization of Convective Flux -- 7.8.2.2 Discretization of Diffusive Flux -- 7.8.2.3 Discretization of the Pressure Term -- 7.9 Solution of the Pressure Field -- 7.9.1 Derivation of Pressure Correction and Velocity Correction Equations -- 7.9.2 Implementation of the Momentum Interpolation -- 7.9.3 Implementation of Higher-Order Schemes -- 7.10 Summary -- Questions -- Chapter 8. Solution of Algebraic Equations -- 8.1 Introduction -- 8.2 Direct Methods -- 8.2.1 Gauss Elimination -- 8.2.2 LU Decomposition
505	8		\|a 8.2.3 Tri-Diagonal Matrix Algorithm
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author	Roychowdhury, D. G.
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contents	Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- Acknowledgements -- Chapter 1. Overview of CFD -- 1.1 Introduction -- 1.2 Basic Principles of CFD -- 1.3 What Does a CFD Algorithm Do? -- 1.4 Stages of a CFD Analysis -- 1.4.1 Pre-Processor -- 1.4.2 Solver -- 1.4.3 Post-Processor -- 1.5 Governing Equations -- 1.6 Discretization -- 1.6.1 Finite Difference Method -- 1.6.2 Finite Volume Method -- 1.6.3 Finite Element Method -- 1.7 Discretization Properties -- Questions: -- Chapter 2. Governing Equations and Classification of PDE -- Governing Equations -- 2.1 Introduction -- 2.1.1 Integral Form -- 2.1.2 Differential Form -- 2.2 Conservative Form of the Flow Equations -- 2.2.1 Mass (Continuity) -- 2.2.1.1 Derivation of Continuity Equation -- 2.2.2 Momentum Equations -- 2.2.2.1 Derivation of X-Momentum Equation -- 2.2.3 Energy Equation -- 2.2.3.1 Derivation of Energy Equation -- 2.2.4 General Scalar -- 2.3 Some Comments -- 2.3.1 Conservative and Non-Conservative Forms of Equations -- 2.3.2 Compressible and Incompressible Flow -- Physical and Mathematical Classification of Partial Differential Equations -- 2.4 Equilibrium Problems -- 2.5 Marching Problems -- 2.6 Mathematical Classification -- 2.7 Important Equations -- 2.8 Boundary Conditions (BCs) -- 2.8.1 Inlet Boundary -- 2.8.1.1 Inflow -- 2.8.1.2 Stagnation (Reservoir) -- 2.8.2 Outlet Boundary -- 2.8.2.1 Outflow -- 2.8.2.2 Pressure -- 2.8.2.3 Radiation (Convection) -- 2.8.3 Wall Boundaries -- 2.8.3.1 No-Slip Wall -- 2.8.3.2 Slip Wall -- 2.8.4 Other Boundary Conditions -- 2.8.4.1 Symmetry Plane and Axis Boundary -- 2.8.4.2 Periodic -- 2.9 Summary -- Questions -- Chapter 3. Finite Difference Method: Fundamentals -- 3.1 Introduction -- 3.2 Taylor Series Expansion -- 3.3 Unequal Grid Spacing -- 3.4 Difference Representation of PDE -- 3.4.1 Errors 3.4.1.1 Truncation Error -- 3.4.1.2 Round-off Error -- 3.4.2 Consistency -- 3.4.3 Stability -- 3.4.3.1 Von Neumann's Method -- 3.4.4 Convergence -- 3.4.5 Lax's Equivalence Theorem -- 3.4.6 Courant Number -- 3.5 Examples -- 3.6 Summary -- Questions: -- Chapter 4. Finite Difference Method: Application -- 4.1 Introduction -- 4.2 One-Dimensional Diffusion Equations -- 4.2.1 Explicit Methods -- 4.2.1.1 The Forward Time, Central Space -- 4.2.1.2 The Richardson's Method -- 4.2.1.3 The DuFort-Frankel Method (D-F Leap-Frog Method) -- 4.2.2 Implicit Methods -- 4.2.2.1 The Classical Implicit Method -- 4.2.2.2 The Crank-Nicolson Method -- 4.2.2.3 The Method of Weighted Averages -- 4.3 One-Dimensional Transport Equations -- 4.3.1 The Wave Equation -- 4.3.1.1 The FTCS Method -- 4.3.1.2 Upwind Differencing -- 4.3.1.3 The LaxMethod (Lax-Friedrichs Method) -- 4.3.1.4 The Lax-Wendroff Method -- 4.3.1.5 The Two-Step Lax-Wendroff Method -- 4.3.1.6 The MacCormack Method -- 4.3.1.7 The Beam-Warming Method -- 4.3.1.8 The Implicit Method -- 4.3.2 The Complete Transport Equation -- 4.3.2.1 Central Difference -- 4.3.2.2 The Richardson Method -- 4.3.2.3 The DuFort-Frankel Method -- 4.3.2.4 The Upwind Method -- 4.4 Two-Dimensional Diffusion Equation -- 4.4.1 The Explicit Method -- 4.4.2 Implicit Methods -- 4.4.2.1 The Fully Implicit Method -- 4.4.2.2 The Crank-Nicolson Method -- 4.4.2.3 The Alternate Direction Implicit (ADI) Method -- 4.4.2.4 Comments on Diffusion Equations -- 4.4.2.5 Further Comments on Conservative vs. Non-Conservative Variables -- 4.4.2.6 The Grid (Mesh) Independence Study -- 4.5 Burgers' Equation -- 4.5.1 The Inviscid Burgers' Equation -- 4.5.1.1 Upwind Differencing -- 4.5.1.2 The Lax (Lax-Friedrichs) Method -- 4.5.1.3 The Lax-Wendroff Method -- 4.5.1.4 The MacCormack Method -- 4.5.1.5 Implicit Methods -- 4.5.1.6 The Godunov Method -- 4.5.1.7 The Roe Method 4.5.2 The Viscid Burgers' Equation -- 4.5.2.1 The FTCS Method -- 4.5.2.2 The DuFort-Frankel Method -- 4.5.2.3 The Lax-Wendroff Method -- 4.5.2.4 The MacCormack Method -- 4.6 The Laplace Equation -- 4.7 Examples -- 4.8 Summary -- Questions -- Chapter 5. Finite Volume Method -- 5.1 Introduction -- 5.2 The Diffusion Equation -- 5.2.1 The Steady-State One-Dimensional Diffusion Equation -- 5.2.2 Discretization of the Source Term -- 5.2.3 Discretized Equation at Boundaries -- 5.2.3.1 For Given Value at the Boundaries (Dirichlet Boundary Conditions) -- 5.2.3.2 Insulated Boundary -- 5.2.3.3 Mixed Boundary Conditions -- 5.2.4 Assembling the Algebraic Equations -- 5.2.5 Extension to Two Dimensions -- 5.2.6 Extension to Three Dimensions -- 5.2.7 Desirable Properties of a Discretization Scheme -- 5.2.8 Further Comments on Interface Diffusion Coefficients -- 5.3 The Convection-Diffusion Equation -- 5.3.1 The Steady-State One-Dimensional Advection-Diffusion Equation -- 5.3.1.1 The Central Differencing Scheme -- 5.3.1.2 The Upwind Differencing Scheme -- 5.3.1.3 Exact Solution -- 5.3.1.4 The Exponential Scheme -- 5.3.1.5 The Hybrid Differencing Scheme -- 5.3.1.6 The Second Order Upwind (SOU) Scheme -- 5.3.1.7 The Quadratic Upstream Interpolation for Convective Kinetics (QUICK) Scheme -- 5.3.1.8 The FROMM Scheme -- 5.3.1.9 Advantages and Disadvantages of Various Convective Schemes -- 5.3.2 Deferred Correction Approach -- 5.3.2.1 CDS -- 5.3.2.2 SOU -- 5.3.2.3 QUICK -- 5.3.2.4 FROMM -- 5.3.3 Extension to Two Dimension -- 5.3.3.1 UDS -- 5.3.3.2 CDS -- 5.3.3.3 SOU -- 5.3.3.4 QUICK -- 5.3.3.5 FROMM -- 5.3.4 Extension to Three Dimension -- 5.3.4.1 UDS -- 5.3.4.2 CDS -- 5.3.4.3 SOU -- 5.3.4.4 QUICK -- 5.3.4.5 FROMM -- 5.3.5 High Resolution and Bounded Convective Schemes -- 5.3.5.1 Normalized Variable Formulation -- 5.3.5.2 Convective Boundedness Criteria 5.3.5.3 High-Resolution Schemes -- 5.3.5.4 The TVD Framework -- 5.3.5.5 Implementation of Various Convective Schemes in Code -- 5.4 Time-Dependent Methods -- 5.4.1 One-Step Methods -- 5.4.1.1 Forward Differencing (Euler Method) -- 5.4.1.2 Backward Differencing (Backward Euler) -- 5.4.1.3 Central Differencing (Crank-Nicolson) -- 5.5 Time Discretization Methods Applied to the General Scalar Transport Equation -- 5.5.1 Forward Differencing - Explicit Scheme -- 5.5.2 Backward Differencing - Implicit Scheme -- 5.5.3 Crank-Nicolson - Central Difference Scheme: -- 5.6 Courant Number -- 5.7 Uses of Time-Marching in CFD -- 5.8 Implementation of Boundary Conditions in Code -- 5.8.1 Generalized Boundary Conditions -- 5.8.2 Convective Boundary Conditions -- 5.9 Examples -- 5.10 Summary -- Questions -- Chapter 6. Solution of Incompressible Navier-Stokes Equations -- 6.1 Introduction -- 6.2 Pressure-Velocity Coupling -- 6.3 The Vorticity-Stream Function Method -- 6.3.1 Boundary Conditions -- 6.4 Primitive Variable Methods -- 6.4.1 Co-located Storage of Variables -- 6.4.2 Staggered Grid -- 6.5 Solution Methods for the Primitive Variable Form of N-S Equations -- 6.5.1 The Artificial Compressibility Method -- 6.5.2 The Pressure Correction Approach -- 6.5.2.1 The MAC Method -- 6.5.2.2 The Fractional Step Pressure Projection Method -- 6.6 The SIMPLE Method -- 6.6.1 Derivation of Velocity Correction and Pressure Correction Equations -- 6.6.1.1 Pressure and Velocity Corrections -- 6.6.2 Pressure Correction Equation -- 6.6.3 The SIMPLE Algorithm -- 6.7 Variants of SIMPLE -- 6.7.1 The SIMPLER Algorithm -- 6.7.2 The SIMPLEC Algorithm -- 6.7.3 The PISO (Pressure Implicit with Split Operator) Algorithm -- 6.8 Summary -- Questions: -- Chapter 7. Finite Volume Method for Complex Geometries -- 7.1 Introduction -- 7.2 Staggered Grid Algorithm -- 7.3 The Co-located Grid Algorithm 7.4 Discretization Methods for Non-Orthogonal Structured Grids -- 7.4.1 The Continuity Equation -- 7.4.2 The Transport Equation -- 7.4.2.1 Discretization of Convective Flux -- 7.4.2.2 Discretization of Diffusive Flux -- 7.4.2.3 Discretization of Pressure Terms -- 7.4.2.4 Implementation of the QUICK Scheme -- 7.5 Solution of the Pressure Field -- 7.5.1 Derivation of Pressure Correction and Velocity Correction Equations -- 7.5.2 Implementation of Momentum Interpolation -- 7.6 Extension to Three Dimension -- 7.6.1 Discretization of Continuity Equations -- 7.6.2 Discretization of Convective Flux -- 7.6.3 Discretization of Diffusive Flux -- 7.6.4 Discretization of the Pressure Term -- 7.6.5 Implementation of the QUICK Scheme -- 7.6.6 Implementation of the SIMPLE Algorithm -- 7.7 Discretization Method for the Cartesian Structured Grid -- 7.7.1 The Continuity Equation -- 7.7.2 The Transport Equation -- 7.7.2.1 Discretization of Convective Flux -- 7.7.2.2 Discretization of Diffusive Flux -- 7.7.2.3 Discretization of the Pressure Term -- 7.7.2.4 Implementation of the QUICK Scheme -- 7.7.2.5 Derivation of Pressure Correction and Velocity Correction Equation -- 7.7.2.6 Implementation of the Momentum Interpolation -- 7.8 Discretization Method for the Non-Orthogonal Unstructured Grid -- 7.8.1 The Continuity Equation -- 7.8.2 The Transport Equation -- 7.8.2.1 Discretization of Convective Flux -- 7.8.2.2 Discretization of Diffusive Flux -- 7.8.2.3 Discretization of the Pressure Term -- 7.9 Solution of the Pressure Field -- 7.9.1 Derivation of Pressure Correction and Velocity Correction Equations -- 7.9.2 Implementation of the Momentum Interpolation -- 7.9.3 Implementation of Higher-Order Schemes -- 7.10 Summary -- Questions -- Chapter 8. Solution of Algebraic Equations -- 8.1 Introduction -- 8.2 Direct Methods -- 8.2.1 Gauss Elimination -- 8.2.2 LU Decomposition 8.2.3 Tri-Diagonal Matrix Algorithm
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Roychowdhury</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">First edition</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boca Raton ; London ; New York</subfield><subfield code="b">CRC Press</subfield><subfield code="c">2021</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">©2021</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xxiii, 391 Seiten</subfield><subfield code="b">Illustrationen</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Description based on publisher supplied metadata and other sources</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- Acknowledgements -- Chapter 1. Overview of CFD -- 1.1 Introduction -- 1.2 Basic Principles of CFD -- 1.3 What Does a CFD Algorithm Do? -- 1.4 Stages of a CFD Analysis -- 1.4.1 Pre-Processor -- 1.4.2 Solver -- 1.4.3 Post-Processor -- 1.5 Governing Equations -- 1.6 Discretization -- 1.6.1 Finite Difference Method -- 1.6.2 Finite Volume Method -- 1.6.3 Finite Element Method -- 1.7 Discretization Properties -- Questions: -- Chapter 2. Governing Equations and Classification of PDE -- Governing Equations -- 2.1 Introduction -- 2.1.1 Integral Form -- 2.1.2 Differential Form -- 2.2 Conservative Form of the Flow Equations -- 2.2.1 Mass (Continuity) -- 2.2.1.1 Derivation of Continuity Equation -- 2.2.2 Momentum Equations -- 2.2.2.1 Derivation of X-Momentum Equation -- 2.2.3 Energy Equation -- 2.2.3.1 Derivation of Energy Equation -- 2.2.4 General Scalar -- 2.3 Some Comments -- 2.3.1 Conservative and Non-Conservative Forms of Equations -- 2.3.2 Compressible and Incompressible Flow -- Physical and Mathematical Classification of Partial Differential Equations -- 2.4 Equilibrium Problems -- 2.5 Marching Problems -- 2.6 Mathematical Classification -- 2.7 Important Equations -- 2.8 Boundary Conditions (BCs) -- 2.8.1 Inlet Boundary -- 2.8.1.1 Inflow -- 2.8.1.2 Stagnation (Reservoir) -- 2.8.2 Outlet Boundary -- 2.8.2.1 Outflow -- 2.8.2.2 Pressure -- 2.8.2.3 Radiation (Convection) -- 2.8.3 Wall Boundaries -- 2.8.3.1 No-Slip Wall -- 2.8.3.2 Slip Wall -- 2.8.4 Other Boundary Conditions -- 2.8.4.1 Symmetry Plane and Axis Boundary -- 2.8.4.2 Periodic -- 2.9 Summary -- Questions -- Chapter 3. Finite Difference Method: Fundamentals -- 3.1 Introduction -- 3.2 Taylor Series Expansion -- 3.3 Unequal Grid Spacing -- 3.4 Difference Representation of PDE -- 3.4.1 Errors</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">3.4.1.1 Truncation Error -- 3.4.1.2 Round-off Error -- 3.4.2 Consistency -- 3.4.3 Stability -- 3.4.3.1 Von Neumann's Method -- 3.4.4 Convergence -- 3.4.5 Lax's Equivalence Theorem -- 3.4.6 Courant Number -- 3.5 Examples -- 3.6 Summary -- Questions: -- Chapter 4. Finite Difference Method: Application -- 4.1 Introduction -- 4.2 One-Dimensional Diffusion Equations -- 4.2.1 Explicit Methods -- 4.2.1.1 The Forward Time, Central Space -- 4.2.1.2 The Richardson's Method -- 4.2.1.3 The DuFort-Frankel Method (D-F Leap-Frog Method) -- 4.2.2 Implicit Methods -- 4.2.2.1 The Classical Implicit Method -- 4.2.2.2 The Crank-Nicolson Method -- 4.2.2.3 The Method of Weighted Averages -- 4.3 One-Dimensional Transport Equations -- 4.3.1 The Wave Equation -- 4.3.1.1 The FTCS Method -- 4.3.1.2 Upwind Differencing -- 4.3.1.3 The LaxMethod (Lax-Friedrichs Method) -- 4.3.1.4 The Lax-Wendroff Method -- 4.3.1.5 The Two-Step Lax-Wendroff Method -- 4.3.1.6 The MacCormack Method -- 4.3.1.7 The Beam-Warming Method -- 4.3.1.8 The Implicit Method -- 4.3.2 The Complete Transport Equation -- 4.3.2.1 Central Difference -- 4.3.2.2 The Richardson Method -- 4.3.2.3 The DuFort-Frankel Method -- 4.3.2.4 The Upwind Method -- 4.4 Two-Dimensional Diffusion Equation -- 4.4.1 The Explicit Method -- 4.4.2 Implicit Methods -- 4.4.2.1 The Fully Implicit Method -- 4.4.2.2 The Crank-Nicolson Method -- 4.4.2.3 The Alternate Direction Implicit (ADI) Method -- 4.4.2.4 Comments on Diffusion Equations -- 4.4.2.5 Further Comments on Conservative vs. Non-Conservative Variables -- 4.4.2.6 The Grid (Mesh) Independence Study -- 4.5 Burgers' Equation -- 4.5.1 The Inviscid Burgers' Equation -- 4.5.1.1 Upwind Differencing -- 4.5.1.2 The Lax (Lax-Friedrichs) Method -- 4.5.1.3 The Lax-Wendroff Method -- 4.5.1.4 The MacCormack Method -- 4.5.1.5 Implicit Methods -- 4.5.1.6 The Godunov Method -- 4.5.1.7 The Roe Method</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">4.5.2 The Viscid Burgers' Equation -- 4.5.2.1 The FTCS Method -- 4.5.2.2 The DuFort-Frankel Method -- 4.5.2.3 The Lax-Wendroff Method -- 4.5.2.4 The MacCormack Method -- 4.6 The Laplace Equation -- 4.7 Examples -- 4.8 Summary -- Questions -- Chapter 5. Finite Volume Method -- 5.1 Introduction -- 5.2 The Diffusion Equation -- 5.2.1 The Steady-State One-Dimensional Diffusion Equation -- 5.2.2 Discretization of the Source Term -- 5.2.3 Discretized Equation at Boundaries -- 5.2.3.1 For Given Value at the Boundaries (Dirichlet Boundary Conditions) -- 5.2.3.2 Insulated Boundary -- 5.2.3.3 Mixed Boundary Conditions -- 5.2.4 Assembling the Algebraic Equations -- 5.2.5 Extension to Two Dimensions -- 5.2.6 Extension to Three Dimensions -- 5.2.7 Desirable Properties of a Discretization Scheme -- 5.2.8 Further Comments on Interface Diffusion Coefficients -- 5.3 The Convection-Diffusion Equation -- 5.3.1 The Steady-State One-Dimensional Advection-Diffusion Equation -- 5.3.1.1 The Central Differencing Scheme -- 5.3.1.2 The Upwind Differencing Scheme -- 5.3.1.3 Exact Solution -- 5.3.1.4 The Exponential Scheme -- 5.3.1.5 The Hybrid Differencing Scheme -- 5.3.1.6 The Second Order Upwind (SOU) Scheme -- 5.3.1.7 The Quadratic Upstream Interpolation for Convective Kinetics (QUICK) Scheme -- 5.3.1.8 The FROMM Scheme -- 5.3.1.9 Advantages and Disadvantages of Various Convective Schemes -- 5.3.2 Deferred Correction Approach -- 5.3.2.1 CDS -- 5.3.2.2 SOU -- 5.3.2.3 QUICK -- 5.3.2.4 FROMM -- 5.3.3 Extension to Two Dimension -- 5.3.3.1 UDS -- 5.3.3.2 CDS -- 5.3.3.3 SOU -- 5.3.3.4 QUICK -- 5.3.3.5 FROMM -- 5.3.4 Extension to Three Dimension -- 5.3.4.1 UDS -- 5.3.4.2 CDS -- 5.3.4.3 SOU -- 5.3.4.4 QUICK -- 5.3.4.5 FROMM -- 5.3.5 High Resolution and Bounded Convective Schemes -- 5.3.5.1 Normalized Variable Formulation -- 5.3.5.2 Convective Boundedness Criteria</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">5.3.5.3 High-Resolution Schemes -- 5.3.5.4 The TVD Framework -- 5.3.5.5 Implementation of Various Convective Schemes in Code -- 5.4 Time-Dependent Methods -- 5.4.1 One-Step Methods -- 5.4.1.1 Forward Differencing (Euler Method) -- 5.4.1.2 Backward Differencing (Backward Euler) -- 5.4.1.3 Central Differencing (Crank-Nicolson) -- 5.5 Time Discretization Methods Applied to the General Scalar Transport Equation -- 5.5.1 Forward Differencing - Explicit Scheme -- 5.5.2 Backward Differencing - Implicit Scheme -- 5.5.3 Crank-Nicolson - Central Difference Scheme: -- 5.6 Courant Number -- 5.7 Uses of Time-Marching in CFD -- 5.8 Implementation of Boundary Conditions in Code -- 5.8.1 Generalized Boundary Conditions -- 5.8.2 Convective Boundary Conditions -- 5.9 Examples -- 5.10 Summary -- Questions -- Chapter 6. Solution of Incompressible Navier-Stokes Equations -- 6.1 Introduction -- 6.2 Pressure-Velocity Coupling -- 6.3 The Vorticity-Stream Function Method -- 6.3.1 Boundary Conditions -- 6.4 Primitive Variable Methods -- 6.4.1 Co-located Storage of Variables -- 6.4.2 Staggered Grid -- 6.5 Solution Methods for the Primitive Variable Form of N-S Equations -- 6.5.1 The Artificial Compressibility Method -- 6.5.2 The Pressure Correction Approach -- 6.5.2.1 The MAC Method -- 6.5.2.2 The Fractional Step Pressure Projection Method -- 6.6 The SIMPLE Method -- 6.6.1 Derivation of Velocity Correction and Pressure Correction Equations -- 6.6.1.1 Pressure and Velocity Corrections -- 6.6.2 Pressure Correction Equation -- 6.6.3 The SIMPLE Algorithm -- 6.7 Variants of SIMPLE -- 6.7.1 The SIMPLER Algorithm -- 6.7.2 The SIMPLEC Algorithm -- 6.7.3 The PISO (Pressure Implicit with Split Operator) Algorithm -- 6.8 Summary -- Questions: -- Chapter 7. Finite Volume Method for Complex Geometries -- 7.1 Introduction -- 7.2 Staggered Grid Algorithm -- 7.3 The Co-located Grid Algorithm</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">7.4 Discretization Methods for Non-Orthogonal Structured Grids -- 7.4.1 The Continuity Equation -- 7.4.2 The Transport Equation -- 7.4.2.1 Discretization of Convective Flux -- 7.4.2.2 Discretization of Diffusive Flux -- 7.4.2.3 Discretization of Pressure Terms -- 7.4.2.4 Implementation of the QUICK Scheme -- 7.5 Solution of the Pressure Field -- 7.5.1 Derivation of Pressure Correction and Velocity Correction Equations -- 7.5.2 Implementation of Momentum Interpolation -- 7.6 Extension to Three Dimension -- 7.6.1 Discretization of Continuity Equations -- 7.6.2 Discretization of Convective Flux -- 7.6.3 Discretization of Diffusive Flux -- 7.6.4 Discretization of the Pressure Term -- 7.6.5 Implementation of the QUICK Scheme -- 7.6.6 Implementation of the SIMPLE Algorithm -- 7.7 Discretization Method for the Cartesian Structured Grid -- 7.7.1 The Continuity Equation -- 7.7.2 The Transport Equation -- 7.7.2.1 Discretization of Convective Flux -- 7.7.2.2 Discretization of Diffusive Flux -- 7.7.2.3 Discretization of the Pressure Term -- 7.7.2.4 Implementation of the QUICK Scheme -- 7.7.2.5 Derivation of Pressure Correction and Velocity Correction Equation -- 7.7.2.6 Implementation of the Momentum Interpolation -- 7.8 Discretization Method for the Non-Orthogonal Unstructured Grid -- 7.8.1 The Continuity Equation -- 7.8.2 The Transport Equation -- 7.8.2.1 Discretization of Convective Flux -- 7.8.2.2 Discretization of Diffusive Flux -- 7.8.2.3 Discretization of the Pressure Term -- 7.9 Solution of the Pressure Field -- 7.9.1 Derivation of Pressure Correction and Velocity Correction Equations -- 7.9.2 Implementation of the Momentum Interpolation -- 7.9.3 Implementation of Higher-Order Schemes -- 7.10 Summary -- Questions -- Chapter 8. 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physical	xxiii, 391 Seiten Illustrationen
publishDate	2021
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spelling	Roychowdhury, D. G. Verfasser (DE-588)1256041793 aut Computational fluid dynamics for incompressible flows D. G. Roychowdhury First edition Boca Raton ; London ; New York CRC Press 2021 ©2021 xxiii, 391 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Description based on publisher supplied metadata and other sources Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- Acknowledgements -- Chapter 1. Overview of CFD -- 1.1 Introduction -- 1.2 Basic Principles of CFD -- 1.3 What Does a CFD Algorithm Do? -- 1.4 Stages of a CFD Analysis -- 1.4.1 Pre-Processor -- 1.4.2 Solver -- 1.4.3 Post-Processor -- 1.5 Governing Equations -- 1.6 Discretization -- 1.6.1 Finite Difference Method -- 1.6.2 Finite Volume Method -- 1.6.3 Finite Element Method -- 1.7 Discretization Properties -- Questions: -- Chapter 2. Governing Equations and Classification of PDE -- Governing Equations -- 2.1 Introduction -- 2.1.1 Integral Form -- 2.1.2 Differential Form -- 2.2 Conservative Form of the Flow Equations -- 2.2.1 Mass (Continuity) -- 2.2.1.1 Derivation of Continuity Equation -- 2.2.2 Momentum Equations -- 2.2.2.1 Derivation of X-Momentum Equation -- 2.2.3 Energy Equation -- 2.2.3.1 Derivation of Energy Equation -- 2.2.4 General Scalar -- 2.3 Some Comments -- 2.3.1 Conservative and Non-Conservative Forms of Equations -- 2.3.2 Compressible and Incompressible Flow -- Physical and Mathematical Classification of Partial Differential Equations -- 2.4 Equilibrium Problems -- 2.5 Marching Problems -- 2.6 Mathematical Classification -- 2.7 Important Equations -- 2.8 Boundary Conditions (BCs) -- 2.8.1 Inlet Boundary -- 2.8.1.1 Inflow -- 2.8.1.2 Stagnation (Reservoir) -- 2.8.2 Outlet Boundary -- 2.8.2.1 Outflow -- 2.8.2.2 Pressure -- 2.8.2.3 Radiation (Convection) -- 2.8.3 Wall Boundaries -- 2.8.3.1 No-Slip Wall -- 2.8.3.2 Slip Wall -- 2.8.4 Other Boundary Conditions -- 2.8.4.1 Symmetry Plane and Axis Boundary -- 2.8.4.2 Periodic -- 2.9 Summary -- Questions -- Chapter 3. Finite Difference Method: Fundamentals -- 3.1 Introduction -- 3.2 Taylor Series Expansion -- 3.3 Unequal Grid Spacing -- 3.4 Difference Representation of PDE -- 3.4.1 Errors 3.4.1.1 Truncation Error -- 3.4.1.2 Round-off Error -- 3.4.2 Consistency -- 3.4.3 Stability -- 3.4.3.1 Von Neumann's Method -- 3.4.4 Convergence -- 3.4.5 Lax's Equivalence Theorem -- 3.4.6 Courant Number -- 3.5 Examples -- 3.6 Summary -- Questions: -- Chapter 4. Finite Difference Method: Application -- 4.1 Introduction -- 4.2 One-Dimensional Diffusion Equations -- 4.2.1 Explicit Methods -- 4.2.1.1 The Forward Time, Central Space -- 4.2.1.2 The Richardson's Method -- 4.2.1.3 The DuFort-Frankel Method (D-F Leap-Frog Method) -- 4.2.2 Implicit Methods -- 4.2.2.1 The Classical Implicit Method -- 4.2.2.2 The Crank-Nicolson Method -- 4.2.2.3 The Method of Weighted Averages -- 4.3 One-Dimensional Transport Equations -- 4.3.1 The Wave Equation -- 4.3.1.1 The FTCS Method -- 4.3.1.2 Upwind Differencing -- 4.3.1.3 The LaxMethod (Lax-Friedrichs Method) -- 4.3.1.4 The Lax-Wendroff Method -- 4.3.1.5 The Two-Step Lax-Wendroff Method -- 4.3.1.6 The MacCormack Method -- 4.3.1.7 The Beam-Warming Method -- 4.3.1.8 The Implicit Method -- 4.3.2 The Complete Transport Equation -- 4.3.2.1 Central Difference -- 4.3.2.2 The Richardson Method -- 4.3.2.3 The DuFort-Frankel Method -- 4.3.2.4 The Upwind Method -- 4.4 Two-Dimensional Diffusion Equation -- 4.4.1 The Explicit Method -- 4.4.2 Implicit Methods -- 4.4.2.1 The Fully Implicit Method -- 4.4.2.2 The Crank-Nicolson Method -- 4.4.2.3 The Alternate Direction Implicit (ADI) Method -- 4.4.2.4 Comments on Diffusion Equations -- 4.4.2.5 Further Comments on Conservative vs. Non-Conservative Variables -- 4.4.2.6 The Grid (Mesh) Independence Study -- 4.5 Burgers' Equation -- 4.5.1 The Inviscid Burgers' Equation -- 4.5.1.1 Upwind Differencing -- 4.5.1.2 The Lax (Lax-Friedrichs) Method -- 4.5.1.3 The Lax-Wendroff Method -- 4.5.1.4 The MacCormack Method -- 4.5.1.5 Implicit Methods -- 4.5.1.6 The Godunov Method -- 4.5.1.7 The Roe Method 4.5.2 The Viscid Burgers' Equation -- 4.5.2.1 The FTCS Method -- 4.5.2.2 The DuFort-Frankel Method -- 4.5.2.3 The Lax-Wendroff Method -- 4.5.2.4 The MacCormack Method -- 4.6 The Laplace Equation -- 4.7 Examples -- 4.8 Summary -- Questions -- Chapter 5. Finite Volume Method -- 5.1 Introduction -- 5.2 The Diffusion Equation -- 5.2.1 The Steady-State One-Dimensional Diffusion Equation -- 5.2.2 Discretization of the Source Term -- 5.2.3 Discretized Equation at Boundaries -- 5.2.3.1 For Given Value at the Boundaries (Dirichlet Boundary Conditions) -- 5.2.3.2 Insulated Boundary -- 5.2.3.3 Mixed Boundary Conditions -- 5.2.4 Assembling the Algebraic Equations -- 5.2.5 Extension to Two Dimensions -- 5.2.6 Extension to Three Dimensions -- 5.2.7 Desirable Properties of a Discretization Scheme -- 5.2.8 Further Comments on Interface Diffusion Coefficients -- 5.3 The Convection-Diffusion Equation -- 5.3.1 The Steady-State One-Dimensional Advection-Diffusion Equation -- 5.3.1.1 The Central Differencing Scheme -- 5.3.1.2 The Upwind Differencing Scheme -- 5.3.1.3 Exact Solution -- 5.3.1.4 The Exponential Scheme -- 5.3.1.5 The Hybrid Differencing Scheme -- 5.3.1.6 The Second Order Upwind (SOU) Scheme -- 5.3.1.7 The Quadratic Upstream Interpolation for Convective Kinetics (QUICK) Scheme -- 5.3.1.8 The FROMM Scheme -- 5.3.1.9 Advantages and Disadvantages of Various Convective Schemes -- 5.3.2 Deferred Correction Approach -- 5.3.2.1 CDS -- 5.3.2.2 SOU -- 5.3.2.3 QUICK -- 5.3.2.4 FROMM -- 5.3.3 Extension to Two Dimension -- 5.3.3.1 UDS -- 5.3.3.2 CDS -- 5.3.3.3 SOU -- 5.3.3.4 QUICK -- 5.3.3.5 FROMM -- 5.3.4 Extension to Three Dimension -- 5.3.4.1 UDS -- 5.3.4.2 CDS -- 5.3.4.3 SOU -- 5.3.4.4 QUICK -- 5.3.4.5 FROMM -- 5.3.5 High Resolution and Bounded Convective Schemes -- 5.3.5.1 Normalized Variable Formulation -- 5.3.5.2 Convective Boundedness Criteria 5.3.5.3 High-Resolution Schemes -- 5.3.5.4 The TVD Framework -- 5.3.5.5 Implementation of Various Convective Schemes in Code -- 5.4 Time-Dependent Methods -- 5.4.1 One-Step Methods -- 5.4.1.1 Forward Differencing (Euler Method) -- 5.4.1.2 Backward Differencing (Backward Euler) -- 5.4.1.3 Central Differencing (Crank-Nicolson) -- 5.5 Time Discretization Methods Applied to the General Scalar Transport Equation -- 5.5.1 Forward Differencing - Explicit Scheme -- 5.5.2 Backward Differencing - Implicit Scheme -- 5.5.3 Crank-Nicolson - Central Difference Scheme: -- 5.6 Courant Number -- 5.7 Uses of Time-Marching in CFD -- 5.8 Implementation of Boundary Conditions in Code -- 5.8.1 Generalized Boundary Conditions -- 5.8.2 Convective Boundary Conditions -- 5.9 Examples -- 5.10 Summary -- Questions -- Chapter 6. Solution of Incompressible Navier-Stokes Equations -- 6.1 Introduction -- 6.2 Pressure-Velocity Coupling -- 6.3 The Vorticity-Stream Function Method -- 6.3.1 Boundary Conditions -- 6.4 Primitive Variable Methods -- 6.4.1 Co-located Storage of Variables -- 6.4.2 Staggered Grid -- 6.5 Solution Methods for the Primitive Variable Form of N-S Equations -- 6.5.1 The Artificial Compressibility Method -- 6.5.2 The Pressure Correction Approach -- 6.5.2.1 The MAC Method -- 6.5.2.2 The Fractional Step Pressure Projection Method -- 6.6 The SIMPLE Method -- 6.6.1 Derivation of Velocity Correction and Pressure Correction Equations -- 6.6.1.1 Pressure and Velocity Corrections -- 6.6.2 Pressure Correction Equation -- 6.6.3 The SIMPLE Algorithm -- 6.7 Variants of SIMPLE -- 6.7.1 The SIMPLER Algorithm -- 6.7.2 The SIMPLEC Algorithm -- 6.7.3 The PISO (Pressure Implicit with Split Operator) Algorithm -- 6.8 Summary -- Questions: -- Chapter 7. Finite Volume Method for Complex Geometries -- 7.1 Introduction -- 7.2 Staggered Grid Algorithm -- 7.3 The Co-located Grid Algorithm 7.4 Discretization Methods for Non-Orthogonal Structured Grids -- 7.4.1 The Continuity Equation -- 7.4.2 The Transport Equation -- 7.4.2.1 Discretization of Convective Flux -- 7.4.2.2 Discretization of Diffusive Flux -- 7.4.2.3 Discretization of Pressure Terms -- 7.4.2.4 Implementation of the QUICK Scheme -- 7.5 Solution of the Pressure Field -- 7.5.1 Derivation of Pressure Correction and Velocity Correction Equations -- 7.5.2 Implementation of Momentum Interpolation -- 7.6 Extension to Three Dimension -- 7.6.1 Discretization of Continuity Equations -- 7.6.2 Discretization of Convective Flux -- 7.6.3 Discretization of Diffusive Flux -- 7.6.4 Discretization of the Pressure Term -- 7.6.5 Implementation of the QUICK Scheme -- 7.6.6 Implementation of the SIMPLE Algorithm -- 7.7 Discretization Method for the Cartesian Structured Grid -- 7.7.1 The Continuity Equation -- 7.7.2 The Transport Equation -- 7.7.2.1 Discretization of Convective Flux -- 7.7.2.2 Discretization of Diffusive Flux -- 7.7.2.3 Discretization of the Pressure Term -- 7.7.2.4 Implementation of the QUICK Scheme -- 7.7.2.5 Derivation of Pressure Correction and Velocity Correction Equation -- 7.7.2.6 Implementation of the Momentum Interpolation -- 7.8 Discretization Method for the Non-Orthogonal Unstructured Grid -- 7.8.1 The Continuity Equation -- 7.8.2 The Transport Equation -- 7.8.2.1 Discretization of Convective Flux -- 7.8.2.2 Discretization of Diffusive Flux -- 7.8.2.3 Discretization of the Pressure Term -- 7.9 Solution of the Pressure Field -- 7.9.1 Derivation of Pressure Correction and Velocity Correction Equations -- 7.9.2 Implementation of the Momentum Interpolation -- 7.9.3 Implementation of Higher-Order Schemes -- 7.10 Summary -- Questions -- Chapter 8. Solution of Algebraic Equations -- 8.1 Introduction -- 8.2 Direct Methods -- 8.2.1 Gauss Elimination -- 8.2.2 LU Decomposition 8.2.3 Tri-Diagonal Matrix Algorithm Computational fluid dynamics-Textbooks Inkompressible Strömung (DE-588)4129759-3 gnd rswk-swf Fluiddynamik (DE-588)1172567794 gnd rswk-swf Fluiddynamik (DE-588)1172567794 s Inkompressible Strömung (DE-588)4129759-3 s DE-604 Äquivalent Druck-Ausgabe, Hardcover 978-0-367-40806-0 Erscheint auch als Online-Ausgabe 978-0-367-80917-1
spellingShingle	Roychowdhury, D. G. Computational fluid dynamics for incompressible flows Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- Acknowledgements -- Chapter 1. Overview of CFD -- 1.1 Introduction -- 1.2 Basic Principles of CFD -- 1.3 What Does a CFD Algorithm Do? -- 1.4 Stages of a CFD Analysis -- 1.4.1 Pre-Processor -- 1.4.2 Solver -- 1.4.3 Post-Processor -- 1.5 Governing Equations -- 1.6 Discretization -- 1.6.1 Finite Difference Method -- 1.6.2 Finite Volume Method -- 1.6.3 Finite Element Method -- 1.7 Discretization Properties -- Questions: -- Chapter 2. Governing Equations and Classification of PDE -- Governing Equations -- 2.1 Introduction -- 2.1.1 Integral Form -- 2.1.2 Differential Form -- 2.2 Conservative Form of the Flow Equations -- 2.2.1 Mass (Continuity) -- 2.2.1.1 Derivation of Continuity Equation -- 2.2.2 Momentum Equations -- 2.2.2.1 Derivation of X-Momentum Equation -- 2.2.3 Energy Equation -- 2.2.3.1 Derivation of Energy Equation -- 2.2.4 General Scalar -- 2.3 Some Comments -- 2.3.1 Conservative and Non-Conservative Forms of Equations -- 2.3.2 Compressible and Incompressible Flow -- Physical and Mathematical Classification of Partial Differential Equations -- 2.4 Equilibrium Problems -- 2.5 Marching Problems -- 2.6 Mathematical Classification -- 2.7 Important Equations -- 2.8 Boundary Conditions (BCs) -- 2.8.1 Inlet Boundary -- 2.8.1.1 Inflow -- 2.8.1.2 Stagnation (Reservoir) -- 2.8.2 Outlet Boundary -- 2.8.2.1 Outflow -- 2.8.2.2 Pressure -- 2.8.2.3 Radiation (Convection) -- 2.8.3 Wall Boundaries -- 2.8.3.1 No-Slip Wall -- 2.8.3.2 Slip Wall -- 2.8.4 Other Boundary Conditions -- 2.8.4.1 Symmetry Plane and Axis Boundary -- 2.8.4.2 Periodic -- 2.9 Summary -- Questions -- Chapter 3. Finite Difference Method: Fundamentals -- 3.1 Introduction -- 3.2 Taylor Series Expansion -- 3.3 Unequal Grid Spacing -- 3.4 Difference Representation of PDE -- 3.4.1 Errors 3.4.1.1 Truncation Error -- 3.4.1.2 Round-off Error -- 3.4.2 Consistency -- 3.4.3 Stability -- 3.4.3.1 Von Neumann's Method -- 3.4.4 Convergence -- 3.4.5 Lax's Equivalence Theorem -- 3.4.6 Courant Number -- 3.5 Examples -- 3.6 Summary -- Questions: -- Chapter 4. Finite Difference Method: Application -- 4.1 Introduction -- 4.2 One-Dimensional Diffusion Equations -- 4.2.1 Explicit Methods -- 4.2.1.1 The Forward Time, Central Space -- 4.2.1.2 The Richardson's Method -- 4.2.1.3 The DuFort-Frankel Method (D-F Leap-Frog Method) -- 4.2.2 Implicit Methods -- 4.2.2.1 The Classical Implicit Method -- 4.2.2.2 The Crank-Nicolson Method -- 4.2.2.3 The Method of Weighted Averages -- 4.3 One-Dimensional Transport Equations -- 4.3.1 The Wave Equation -- 4.3.1.1 The FTCS Method -- 4.3.1.2 Upwind Differencing -- 4.3.1.3 The LaxMethod (Lax-Friedrichs Method) -- 4.3.1.4 The Lax-Wendroff Method -- 4.3.1.5 The Two-Step Lax-Wendroff Method -- 4.3.1.6 The MacCormack Method -- 4.3.1.7 The Beam-Warming Method -- 4.3.1.8 The Implicit Method -- 4.3.2 The Complete Transport Equation -- 4.3.2.1 Central Difference -- 4.3.2.2 The Richardson Method -- 4.3.2.3 The DuFort-Frankel Method -- 4.3.2.4 The Upwind Method -- 4.4 Two-Dimensional Diffusion Equation -- 4.4.1 The Explicit Method -- 4.4.2 Implicit Methods -- 4.4.2.1 The Fully Implicit Method -- 4.4.2.2 The Crank-Nicolson Method -- 4.4.2.3 The Alternate Direction Implicit (ADI) Method -- 4.4.2.4 Comments on Diffusion Equations -- 4.4.2.5 Further Comments on Conservative vs. Non-Conservative Variables -- 4.4.2.6 The Grid (Mesh) Independence Study -- 4.5 Burgers' Equation -- 4.5.1 The Inviscid Burgers' Equation -- 4.5.1.1 Upwind Differencing -- 4.5.1.2 The Lax (Lax-Friedrichs) Method -- 4.5.1.3 The Lax-Wendroff Method -- 4.5.1.4 The MacCormack Method -- 4.5.1.5 Implicit Methods -- 4.5.1.6 The Godunov Method -- 4.5.1.7 The Roe Method 4.5.2 The Viscid Burgers' Equation -- 4.5.2.1 The FTCS Method -- 4.5.2.2 The DuFort-Frankel Method -- 4.5.2.3 The Lax-Wendroff Method -- 4.5.2.4 The MacCormack Method -- 4.6 The Laplace Equation -- 4.7 Examples -- 4.8 Summary -- Questions -- Chapter 5. Finite Volume Method -- 5.1 Introduction -- 5.2 The Diffusion Equation -- 5.2.1 The Steady-State One-Dimensional Diffusion Equation -- 5.2.2 Discretization of the Source Term -- 5.2.3 Discretized Equation at Boundaries -- 5.2.3.1 For Given Value at the Boundaries (Dirichlet Boundary Conditions) -- 5.2.3.2 Insulated Boundary -- 5.2.3.3 Mixed Boundary Conditions -- 5.2.4 Assembling the Algebraic Equations -- 5.2.5 Extension to Two Dimensions -- 5.2.6 Extension to Three Dimensions -- 5.2.7 Desirable Properties of a Discretization Scheme -- 5.2.8 Further Comments on Interface Diffusion Coefficients -- 5.3 The Convection-Diffusion Equation -- 5.3.1 The Steady-State One-Dimensional Advection-Diffusion Equation -- 5.3.1.1 The Central Differencing Scheme -- 5.3.1.2 The Upwind Differencing Scheme -- 5.3.1.3 Exact Solution -- 5.3.1.4 The Exponential Scheme -- 5.3.1.5 The Hybrid Differencing Scheme -- 5.3.1.6 The Second Order Upwind (SOU) Scheme -- 5.3.1.7 The Quadratic Upstream Interpolation for Convective Kinetics (QUICK) Scheme -- 5.3.1.8 The FROMM Scheme -- 5.3.1.9 Advantages and Disadvantages of Various Convective Schemes -- 5.3.2 Deferred Correction Approach -- 5.3.2.1 CDS -- 5.3.2.2 SOU -- 5.3.2.3 QUICK -- 5.3.2.4 FROMM -- 5.3.3 Extension to Two Dimension -- 5.3.3.1 UDS -- 5.3.3.2 CDS -- 5.3.3.3 SOU -- 5.3.3.4 QUICK -- 5.3.3.5 FROMM -- 5.3.4 Extension to Three Dimension -- 5.3.4.1 UDS -- 5.3.4.2 CDS -- 5.3.4.3 SOU -- 5.3.4.4 QUICK -- 5.3.4.5 FROMM -- 5.3.5 High Resolution and Bounded Convective Schemes -- 5.3.5.1 Normalized Variable Formulation -- 5.3.5.2 Convective Boundedness Criteria 5.3.5.3 High-Resolution Schemes -- 5.3.5.4 The TVD Framework -- 5.3.5.5 Implementation of Various Convective Schemes in Code -- 5.4 Time-Dependent Methods -- 5.4.1 One-Step Methods -- 5.4.1.1 Forward Differencing (Euler Method) -- 5.4.1.2 Backward Differencing (Backward Euler) -- 5.4.1.3 Central Differencing (Crank-Nicolson) -- 5.5 Time Discretization Methods Applied to the General Scalar Transport Equation -- 5.5.1 Forward Differencing - Explicit Scheme -- 5.5.2 Backward Differencing - Implicit Scheme -- 5.5.3 Crank-Nicolson - Central Difference Scheme: -- 5.6 Courant Number -- 5.7 Uses of Time-Marching in CFD -- 5.8 Implementation of Boundary Conditions in Code -- 5.8.1 Generalized Boundary Conditions -- 5.8.2 Convective Boundary Conditions -- 5.9 Examples -- 5.10 Summary -- Questions -- Chapter 6. Solution of Incompressible Navier-Stokes Equations -- 6.1 Introduction -- 6.2 Pressure-Velocity Coupling -- 6.3 The Vorticity-Stream Function Method -- 6.3.1 Boundary Conditions -- 6.4 Primitive Variable Methods -- 6.4.1 Co-located Storage of Variables -- 6.4.2 Staggered Grid -- 6.5 Solution Methods for the Primitive Variable Form of N-S Equations -- 6.5.1 The Artificial Compressibility Method -- 6.5.2 The Pressure Correction Approach -- 6.5.2.1 The MAC Method -- 6.5.2.2 The Fractional Step Pressure Projection Method -- 6.6 The SIMPLE Method -- 6.6.1 Derivation of Velocity Correction and Pressure Correction Equations -- 6.6.1.1 Pressure and Velocity Corrections -- 6.6.2 Pressure Correction Equation -- 6.6.3 The SIMPLE Algorithm -- 6.7 Variants of SIMPLE -- 6.7.1 The SIMPLER Algorithm -- 6.7.2 The SIMPLEC Algorithm -- 6.7.3 The PISO (Pressure Implicit with Split Operator) Algorithm -- 6.8 Summary -- Questions: -- Chapter 7. Finite Volume Method for Complex Geometries -- 7.1 Introduction -- 7.2 Staggered Grid Algorithm -- 7.3 The Co-located Grid Algorithm 7.4 Discretization Methods for Non-Orthogonal Structured Grids -- 7.4.1 The Continuity Equation -- 7.4.2 The Transport Equation -- 7.4.2.1 Discretization of Convective Flux -- 7.4.2.2 Discretization of Diffusive Flux -- 7.4.2.3 Discretization of Pressure Terms -- 7.4.2.4 Implementation of the QUICK Scheme -- 7.5 Solution of the Pressure Field -- 7.5.1 Derivation of Pressure Correction and Velocity Correction Equations -- 7.5.2 Implementation of Momentum Interpolation -- 7.6 Extension to Three Dimension -- 7.6.1 Discretization of Continuity Equations -- 7.6.2 Discretization of Convective Flux -- 7.6.3 Discretization of Diffusive Flux -- 7.6.4 Discretization of the Pressure Term -- 7.6.5 Implementation of the QUICK Scheme -- 7.6.6 Implementation of the SIMPLE Algorithm -- 7.7 Discretization Method for the Cartesian Structured Grid -- 7.7.1 The Continuity Equation -- 7.7.2 The Transport Equation -- 7.7.2.1 Discretization of Convective Flux -- 7.7.2.2 Discretization of Diffusive Flux -- 7.7.2.3 Discretization of the Pressure Term -- 7.7.2.4 Implementation of the QUICK Scheme -- 7.7.2.5 Derivation of Pressure Correction and Velocity Correction Equation -- 7.7.2.6 Implementation of the Momentum Interpolation -- 7.8 Discretization Method for the Non-Orthogonal Unstructured Grid -- 7.8.1 The Continuity Equation -- 7.8.2 The Transport Equation -- 7.8.2.1 Discretization of Convective Flux -- 7.8.2.2 Discretization of Diffusive Flux -- 7.8.2.3 Discretization of the Pressure Term -- 7.9 Solution of the Pressure Field -- 7.9.1 Derivation of Pressure Correction and Velocity Correction Equations -- 7.9.2 Implementation of the Momentum Interpolation -- 7.9.3 Implementation of Higher-Order Schemes -- 7.10 Summary -- Questions -- Chapter 8. Solution of Algebraic Equations -- 8.1 Introduction -- 8.2 Direct Methods -- 8.2.1 Gauss Elimination -- 8.2.2 LU Decomposition 8.2.3 Tri-Diagonal Matrix Algorithm Computational fluid dynamics-Textbooks Inkompressible Strömung (DE-588)4129759-3 gnd Fluiddynamik (DE-588)1172567794 gnd
subject_GND	(DE-588)4129759-3 (DE-588)1172567794
title	Computational fluid dynamics for incompressible flows
title_auth	Computational fluid dynamics for incompressible flows
title_exact_search	Computational fluid dynamics for incompressible flows
title_exact_search_txtP	Computational fluid dynamics for incompressible flows
title_full	Computational fluid dynamics for incompressible flows D. G. Roychowdhury
title_fullStr	Computational fluid dynamics for incompressible flows D. G. Roychowdhury
title_full_unstemmed	Computational fluid dynamics for incompressible flows D. G. Roychowdhury
title_short	Computational fluid dynamics for incompressible flows
title_sort	computational fluid dynamics for incompressible flows
topic	Computational fluid dynamics-Textbooks Inkompressible Strömung (DE-588)4129759-3 gnd Fluiddynamik (DE-588)1172567794 gnd
topic_facet	Computational fluid dynamics-Textbooks Inkompressible Strömung Fluiddynamik
work_keys_str_mv	AT roychowdhurydg computationalfluiddynamicsforincompressibleflows

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