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Computational Fluid
Dynamics
Fourth Edition
Volume 2
2000, 469 PP
Hoffmann, Chiang
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Table of Contents
The fundamental concepts of computational
schemes established in the first volume are extended to the solution of
Euler equations, Parabolized Navier-Stokes equations, and Navier-Stokes
equations, along with treatment of boundary conditions. In
addition, chemically reacting flows, unstructured grids, finite volume
schemes, and finite element method at the introductory level are
included.
This volume begins with a review of the
basic concepts which is presented in Chapter 10. Subsequently, the
transformation of the equations of fluid motion from physical space to
computational space is provided in Chapter 11. This chapter also
includes the linearization of the equations as well as the derivation of
the Jacobian matrices. Chapter 12 presents numerical schemes for
the solution of the Euler equations for inviscid flow fields.
Specifications of the boundary conditions, along with illustrated
examples, are provided in this chapter. Chapter 13 presents
Parabolized Navier-Stokes (PNS) equations and a numerical algorithm for
solution. The shock fitting procedure is discussed in this chapter
as well. The Navier-Stokes equations and various numerical schemes
for solutions are discussed in Chapter 14. Specification of
boundary conditions, derivation of governing equations, and comparison
of several types of boundary conditions are provided in Chapter 15.
An extension of the governing equations to include the effect of
chemistry for hypersonic flowfield computations is included in Chapter
16. To familiarize the reader with unstructured grids which are
used in conjunction with finite volume and finite element schemes, they
are introduced in Chapter 17. It develops some fundamental
concepts and explores two techniques for generation of unstructured
grids in two dimensions. Finally, finite volume schemes and finite
element method are developed at the introductory level in Chapters 18
and 19, respectively.
Several computer
codes are developed based on the materials presented in this text.
These codes, manuals, and additional examples are presented in the test,
Student Guide to CFD- Volume II.
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Table
of Contents |
Chapter: |
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10 |
A
Review
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11 |
Transformation of the Equations of Fluid Motion from Physical Space to Computational Space
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12
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Euler
Equations |
13
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Parabolized
Navier-Stokes Equations |
14
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Navier-Stokes
Equations |
15
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Boundary
Conditions |
16
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An
Introduction to High Temperature Gases |
17
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Grid
Generation - Unstructured Grids |
18
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Finite
Volume Method |
19
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Finite
Element Method |
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Appendices
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| G |
An
Introduction to Theory of Characteristics:
Euler Equations
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| H |
Computation
of Pressure at the Body Surface
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| I |
Rate
of Formation of Species |
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References
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Index
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Preface
Introduction
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Chapter
Ten:
A Review |
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Introductory Remarks, Classification of Partial Differential Equations,
Linear and Nonlinear PDEs, Classification Based on Characteristics, Boundary Conditions, Finite
Difference Equations, Parabolic
Equations, One-Space
Dimension, Multi-Space
Dimensions Elliptic
Equations, Hyperbolic
Equations, Linear
Equations,
Nonlinear Equations, Stability
Analysis, Error
Analysis, Grid
Generation – Structured Grids,
Transformation of the Equations from the Physical Space to
Computational Space.
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Chapter Eleven:
Transformation of the Equations of Fluid Motion from Physical
Space to Computational Space
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Introductory Remarks,
Generalized Coordinate Transformation,
Equations for the Metrics,
Nondimensionalization of the Equations of Fluid Motion,
Navier-Stokes Equations,
Linearization, Inviscid and Viscous Jacobian Matrices, Thin-Layer Approximation,
Parabolized Navier-Stokes Equations,
Two-Dimensional Planar or Axisymmetric Formulation,
Incompressible Navier-Stokes Equations,
Inviscid and Viscous Jacobian Matrices,
Two-Dimensional Incompressible Navier-Stokes Equations,
Problems.
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Chapter Twelve:
Euler Equations |
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Introductory Remarks,
Euler Equations, Quasi
One-Dimensional Euler Equations,
Numerical Issues, Explicit
Formulations, Steger
and Warming Flux Vector Splitting,
Van Leer Flux Vector Splitting,
Modified Runge-Kutta Formulation,
Second-Order TVD Formulation,
Harten-Yee Upwind TVD,
Roe-Sweby Upwind TVD,
David-Yee Symmetric TVD,
Modified Runge-Kutta Scheme with TVD,
Implicit Formulations,
Steger and Warming Flux Vector Splitting,
Boundary Conditions, Application
1: Diverging Nozzle Configuration,
Supersonic Inflow, Supersonic Outflow,
Analytical Solution, Numerical
Solutions, Supersonic
Inflow, Subsonic Outflow, Analytical
Solution, Numerical
Solutions, Grid
Clustering, Global Time Step and Local Time Step, Application 2: Shock Tube or Riemann Problem,
Problem Description, Analytical
Solution, Numerical
Solution, Two-Dimensional
Planar and Axisymmetric Euler Equations,
Numerical Considerations,
Explicit Formulations,
Steger and Warming Flux Vector Splitting,
Matrix Manipulations,
Existence of Zero Metrics Within the Domain,
Eigenvector Matrices,
Van Leer Flux Vector Splitting,
Modified Runge-Kutta Formulation,
Second-Order TVD Formulation,
Harten-Yee Upwind TVD,
Roe Sweby Upwind TVD,
David-Yee Symmetric TVD,
Modified Runge-Kutta Scheme with TVD,
Boundary Conditions, Body
Surface, Symmetry, Inflow,
Outflow, Boundary
Conditions Based on Characteristics, Inflow Boundary, Outflow
Boundary, Determination
of Flow Variables, Implicit
Formulations, Steger
and Warming Flux Vector Splitting,
Computation of the Jacobian Matrices,
Boundary Conditions, Application: Axisymmetric/Two-Dimensional Problems, Supersonic Channel Flow,
Grid Generation, Numerical
Scheme, Analytical
Solution, The
Physical Domain and Flow Conditions,
Initial Conditions and Time Step,
Results, Axisymmetric
Blunt Body, Concluding
Remarks, Problems.
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Chapter Thirteen:
Parabolized Navier-Stokes Equations |
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Introductory Remarks,
Governing Equations of Motion,
Streamwise Pressure Gradient,
Numerical Algorithm, Boundary
Conditions, Extension
to Three Dimensions, Numerical
Algorithm, Numerical
Damping Terms, Shock
Fitting Procedure, Extension
to Three-Dimensions, Application, Summary Objectives, Problems.
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Chapter Fourteen:
Navier-Stokes Equations
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Introductory Remarks,
Navier-Stokes Equations ,Thin-Layer Navier-Stokes
Equations, Numerical
Algorithms, Explicit
Formulations, MacCormack
Explicit Formulation, Flux
Vector Splitting, Modified
Runge-Kutta Scheme, Boundary
Conditions, Implicit
Formulations, Flux
Vector Splitting, Higher-Order
Flux-Vector Splitting, Second-Order
Accuracy in Time, LU
Decomposition, Extension to three-Dimensions,
Explicit Flux Vector Splitting Scheme,
Implicit Formulation,
Concluding Remarks, Problems.
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Chapter Fifteen:
Boundary Conditions
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Introductory Remarks,
Classification of Schemes for Specification of Boundary
Conditions, Category
Two Boundary Conditions: Characteristics Based Boundary
Conditions, Mathematical
Developments, Slip
Wall Boundary Condition, Nonconservative
(Primitive) Variables, Conservative
Variables, No-Slip
Wall Boundary Condition, Nonconservative
(Primitive) Variables, Conservative
Variables, Inflow/Outflow
Boundary Conditions, Category
Three Boundary Conditions: Addition of Buffer Layer,
Applications, Application
1: Moving Shock Wave, Application
2: Flow Over a Compression Corner,
Concluding Remarks.
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Chapter Sixteen:
An Introduction to High Temperature Gases
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Introductory Remarks,
Fundamental Concepts,
Real Gas and Perfect Gas,
Partial Pressure, Frozen
Flow, Equilibrium Flow, Nonequilibrium
Flow, Various Modes
of Energy, Reaction
Rates, Five-Species
Model, Quasi
One-Dimensional Flow/Equilibrium Chemistry,
Quasi One-Dimensional Flow/Nonequilibrium Chemistry,
Species Continuity Equation,
Coupling Schemes, Numerical
Procedure for the Loosely Coupled Scheme,
Applications, Quasi
One-Dimensional Flow, Two-Dimensional
Axisymmetric Flow, Concluding
Remarks.
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Chapter Seventeen:
Grid Generation - Unstructured Grids
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Introductory Remarks,
Domain Nodalization, Domain
Triangulation, The
Advancing Front Method, Simply-Connected
Domain, Multiply-Connected
Domain, The Delaunay
Method, Geometrical
Description, Outline
of the Algorithm, An
Illustrative Example, Concluding
Remarks, Problems.
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Chapter Eighteen:
Finite Volume Method
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Introductory Remarks,
General Description of the Finite Volume Method,
Cell Centered Scheme,
Nodal Point Scheme, Two-Dimensional
Heat Conduction Equation, Interior
Triangles, Boundary
Triangles, Dirichlet
Type Boundary Condition, Neumann
Type Boundary Condition, Flux
Vector Splitting Scheme, Interior
Triangles, Boundary
Triangles, Concluding
Remarks, Problems.
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Chapter Nineteen:
Finite Element Method
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Introductory Remarks,
Optimization Techniques,
General Description and Development of the Finite Element
Method, Two-Dimensional
Heat Conduction Equation, Construction
of the Global Matrix, Boundary
Conditions, Reduction
of the Half-Bandwidth of the Global Matrix.
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