Jens-Dominik Mueller

Essentials of Computational Fluid Dynamics

• Broschiertes Buch

Produktbeschreibung

Approaching the material from the viewpoint of a user of a commercial flow package, this book initially limits the description of the mathematics to the level that is strictly needed to make the correct choices when setting up a case in a commercial flow solver. It discusses the sources of errors in FD solutions using simple examples with finite differences, and they are demonstrated with mesh convergence studies. It focuses on the understanding of how the flow physics interact with a typical finite-volume discretization.

Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 238
• Erscheinungstermin: 11. November 2015
• Englisch
• Abmessung: 233mm x 154mm x 17mm
• Gewicht: 415g
• ISBN-13: 9781482227307
• ISBN-10: 1482227304
• Artikelnr.: 40039466

Autorenporträt

Dr. Jens-Dominik Mueller is a senior lecturer in the School of Engineering and Materials Science at Queen Mary, University of London, UK. He graduated with a Dipl.-Ing in mechanical engineering in 1989 from the Technical University of Munich, obtained a VKI Diploma in aeronautics from the Von Karman Institute in Brussels in 1990, and an MSc and PhD in aerospace engineering from the University of Michigan, Ann Arbor, in 1996. He held research and academic positions at CERFACS, Toulouse, Oxford University and Queen's University Belfast. He is the author of more than 40 publications and has organized numerous international conferences.

Inhaltsangabe

Foreword
1 Introduction
1.1 CFD, the virtual wind tunnel
1.2 Examples of CFD applications
1.3 Prerequisites
1.4 Literature
1.5 Ingredients
1.6 Organisation of the chapters
1.7 Exercises
2 Physical and mathematical principles of modern CFD
2.1 The physical model
2.1.1 Continuum assumption
2.1.2 Lagrangian vs. Eulerian description
2.1.3 Conservation principles
2.2 The mathematical model: the equations of fluid flow
2.2.1 Mass conservation in 1
D
2.2.2 Mass conservation in 3
D
2.2.3 Divergence and gradient operators, total derivative
2.2.4 The total or material derivative
2.2.5 The divergence form of the total derivative
2.2.6 Reynolds' transport theorem
2.2.7 Transport of a passive scalar
2.3 The momentum equations
2.3.1 Examples of momentum balance
2.3.2 The inviscid momentum equation
the Euler equation
2.3.3 The viscous momentum equations
Navier
Stokes
2.3.4 The incompressible Navier
Stokes equations
2.3.5 Energy balance
2.3.6 Summary of properties for the Navier
Stokes equations
2.4 Simplified model equations
2.4.1 Linear advection equation
2.4.2 Inviscid Burgers' equation
2.4.3 Heat equation
2.5 Excercises
3 Discretisation of the equations
3.1 Discretisation of the linear advection equation
3.1.1 Finite difference discretisation of linear advection .
3.1.2 Solving the finite difference approximation
3.1.3 Mesh refinement
3.1.4 Finite volume discretisation of the 1
D advection .
3.1.5 Solving the finite volume approximation
3.1.6 Finite difference vs. finite volume formulations . .
3.2 Burgers' equation: non
linear advection and conservation
3.3 Heat equation in 1
D
3.3.1 Discretising second derivatives
3.3.2 1
D Heat equation, differential form
3.3.3 Solving the 1
D heat equation
3.4 Advection equation in 2
D
3.4.1 Discretisation on a structured grid
3.5 Solving the Navier
Stokes equations
3.6 The main steps in the finite volume method
3.6.1 Discretisation on arbitrary grids
3.6.2 Transport through an arbitrary face
3.6.3 The concept of pseudotime
stepping
3.6.4 Time
stepping for compressible flows
3.6.5 Iterative methods for incompressible flows
3.6.6 The SIMPLE scheme
3.7 Exercises
4 Analysis of discretisations
4.1 Forward, backward and central differences
4.2 Taylor analysis: consistency, first
and second
order accuracy
4.2.1 Round
off errors
4.2.2 Order of accuracy and mesh refinement
4.3 Stability, artificial viscosity and second
order accuracy . .
4.3.1 Artificial viscosity
4.3.2 Artificial viscosity and finite volume methods
4.3.3 Stable second
order accurate discretisations for CFD
4.3.4 Monotonicity and second
order accuracy: limiters .
4.4 Summary of spatial discretisation approaches
4.5 Convergence of the time
stepping iterations
4.5.1 Explicit methods
4.5.2 Implicit methods
4.5.3 Increasing mesh resolution
4.5.4 Multigrid
4.6 Excercises
5 Boundary conditions and flow physics
5.1 Selection of boundary conditions
5.1.1 Some simple examples
5.1.2 Selecting boundary conditions to satisfy the equations
5.2 Characterisation of partial differential equations
5.2.1 Wave
like solutions: hyperbolic equations
5.2.2 Smoothing
type solutions: elliptic equations
5.2.3 The borderline case
parabolic equations
5.2.4 The domain of dependence, the domain of influence
5.2.5 Example of characterisation: surface waves
5.2.6 Compressible and incompressible flows
5.2.7 Characterisation of the Navier
Stokes equations . .
5.3 Choice of boundary conditions
5.3.1 Boundary conditions for incompressible flow
5.3.2 Boundary conditions for hyperbolic equations
5.4 Exercises
6 Turbulence modelling
6.1 The challenges of turbulent flow for CFD
6.2 Description of turbulent flow
6.3 Self
similar profiles through scaling
6.3.1 Laminar velocity profiles
6.3.2 Turbulent velocity profile
6.4 Velocity profiles of turbulent boundary layers
6.4.1 Outer scaling: friction velocity
6.4.2 Inner scaling: non
dimensional wall distance y+
6.5 Levels of turbulence modelling
6.5.1 Direct Numerical Simulation (DNS)
6.5.2 Reynolds
Averaged Navier
Stokes (RANS)
6.5.3 Large Eddy (LES) & Detached Eddy Simulation (DES)
6.5.4 Summary of approaches to turbulence modelling .
6.6 Eddy viscosity models
6.6.1 Mixing length model
6.6.2 The Spalart
Allmaras model
6.6.3 The k
e model
6.7 Near
wall mesh requirements
6.7.1 Estimating the wall distance of the first point
6.8 Exercises
7 Mesh quality and grid generation
7.1 Influence of mesh quality on the accuracy
7.1.1 Maximum angle condition
7.1.2 Regularity
7.1.3 Size variation
7.2 Requirements for the ideal mesh generator
7.3 Structured grids
7.3.1 Algebraic grids using transfinite interpolation
7.4 Unstructured grids
7.4.1 The Advancing Front Method
7.4.2 Delaunay triangulation
7.4.3 Hierarchical grid Methods
7.4.4 Hexahedral unstructured mesh generation
7.4.5 Hybrid mesh generation for viscous flow
7.5 Mesh adaptation
7.5.1 Mesh movement: r
refinement
7.5.2 Mesh refinement: h
refinement
7.6 Exercises
8 Analysis of the results
8.1 Types of errors
8.1.1 Incorrect choice of boundary conditions
8.1.2 Insufficient convergence
8.1.3 Artificial viscosity
8.1.4 Modelling errors
8.2 Mesh convergence
8.2.1 Cost of error reduction
8.3 Validation
8.4 Summary
8.5 Exercises
9 Case studies
9.1 Aerofoil in 2
D, inviscid flow
9.1.1 Case description
9.1.2 Flow physics
9.1.3 Meshes
9.1.4 Simulation results for the C
mesh
9.1.5 Comparison of C
vs O
mesh
9.1.6 Analysis of lift and drag values
9.2 Blood vessel bifurcation in 2
D
9.2.1 Geometry and flow parameters
9.2.2 Flow physics and boundary conditions
9.2.3 Velocity and pressure fields
9.2.4 Velocity profile in the neck
9.2.5 Effect of outlet boundary condition
9.3 Aerofoil in 2
D, viscous flow
9.3.1 Flow physics
9.3.2 Turbulence modelling
9.3.3 Flow results
9.3.4 Lift and drag
10 Appendix
10.1 Finite
volume implementation of 2
D advection
Bibliography
Index.