Computational fluid dynamics : principles and applications / Jiri Blazek.

Format:

Book

Author/Creator:

Blazek, Jiri, author.

Language:

English

Subjects (All):

Computational fluid dynamics.

Physical Description:

1 online resource (466 pages) : illustrations

Edition:

Third edition.

Place of Publication:

Boston, Massachusetts : Elsevier, [2015]

Summary:

Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics. By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques. This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization. An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques. Will provide you with the knowledge required to develop and understand modern flow simulation codes Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques.

Contents:

Front Cover

Computational Fluid Dynamics: Principles and Applications

Copyright

Contents

Acknowledgments

List of Symbols

Abbreviations

Chapter 1: Introduction

Chapter 2: Governing Equations

2.1 The Flow and Its Mathematical Description

2.1.1 Finite control volume

2.2 Conservation Laws

2.2.1 The continuity equation

2.2.2 The momentum equation

2.2.3 The energy equation

2.3 Viscous Stresses

2.4 Complete System of the Navier-Stokes Equations

2.4.1 Formulation for a perfect gas

2.4.2 Formulation for a real gas

2.4.3 Simplifications to the Navier-Stokes equations

Thin shear layer approximation

Parabolized Navier-Stokes equations

Euler equations

References

Chapter 3: Principles of Solution of the Governing Equations

3.1 Spatial Discretization

3.1.1 Finite-difference method

3.1.2 Finite-volume method

3.1.3 Finite-element method

3.1.4 Other discretization methods

Spectral-element method

Lattice Boltzmann method

Gridless method

3.1.5 Central and upwind schemes

Central schemes

Upwind schemes

Flux-vector splitting schemes

Flux-difference splitting schemes

TVD Schemes

Fluctuation-splitting schemes

Solution reconstruction

First- and second-order schemes

ENO/WENO Schemes

Central versus upwind schemes

Upwind schemes for real gas flows

3.2 Temporal Discretization

3.2.1 Explicit schemes

3.2.2 Implicit schemes

3.3 Turbulence Modeling

3.4 Initial and Boundary Conditions

Chapter 4: Structured Finite-Volume Schemes

4.1 Geometrical Quantities of a Control Volume

4.1.1 Two-dimensional case

4.1.2 Three-dimensional case

4.2 General Discretization Methodologies

4.2.1 Cell-centered scheme

4.2.2 Cell-vertex scheme: overlapping control volumes

4.2.3 Cell-vertex scheme: dual control volumes.

4.2.4 Cell-centered versus cell-vertex schemes

4.3 Discretization of the Convective Fluxes

4.3.1 Central scheme with artificial dissipation

Scalar dissipation scheme

Matrix dissipation scheme

4.3.2 Flux-vector splitting schemes

Van Leer's scheme

AUSM

CUSP scheme

4.3.3 Flux-difference splitting schemes

Roe upwind scheme

4.3.4 Total variation diminishing schemes

Upwind TVD scheme

4.3.5 Limiter functions

Limiter functions for MUSCL interpolation

MUSCL scheme with =0

MUSCL scheme with =1/3

Limiter for CUSP scheme

Limiter for TVD scheme

4.4 Discretization of the Viscous Fluxes

4.4.1 Cell-centered scheme

4.4.2 Cell-vertex scheme

Chapter 5: Unstructured Finite-Volume Schemes

5.1 Geometrical Quantities of a Control Volume

5.1.1 Two-dimensional case

Triangular element

Quadrilateral element

Element center

5.1.2 Three-dimensional case

Triangular face

Quadrilateral face

Volume

Cell centroid

5.2 General Discretization Methodologies

5.2.1 Cell-centered scheme

5.2.2 Median-dual cell-vertex scheme

5.2.3 Cell-centered versus median-dual scheme

Accuracy

Computational work

Memory requirements

Grid generation/adaptation

5.3 Discretization of the Convective Fluxes

5.3.1 Central scheme with artificial dissipation

5.3.2 Upwind schemes

5.3.3 Solution reconstruction

Reconstruction based on MUSCL approach

Piecewise linear reconstruction

Linear reconstruction based on nodal weighting procedure

Piecewise quadratic reconstruction

5.3.4 Evaluation of the gradients

Green-Gauss approach

Median-dual scheme

Cell-centered scheme

Mixed grids

Least-squares approach

5.3.5 Limiter functions

Limiter of Barth and Jespersen

Venkatakrishnan's limiter

5.4 Discretization of the Viscous Fluxes.

5.4.1 Element-based gradients

Face-centered control volume

Approximate Galerkin finite-element approach

Average of nodal values

5.4.2 Average of gradients

Chapter 6: Temporal Discretization

6.1 Explicit Time-Stepping Schemes

6.1.1 Multistage schemes (Runge-Kutta)

6.1.2 Hybrid multistage schemes

6.1.3 Treatment of the source term

6.1.4 Determination of the maximum time step

Time step on structured grids

Navier-Stokes equations

Time step on unstructured grids

Method 1

Method 2

6.2 Implicit Time-Stepping Schemes

6.2.1 Matrix form of the implicit operator

Implicit operator on structured grids

Implicit operator on unstructured grids

6.2.2 Evaluation of the flux Jacobian

Central scheme

Flux-vector splitting scheme

Flux-difference splitting scheme

Viscous flows

6.2.3 Alternating direction implicit scheme

6.2.4 Lower-upper symmetric Gauss-Seidel scheme

LU-SGS on structured grids

LU-SGS on unstructured grids

6.2.5 Newton-Krylov method

GMRES method

Computation of the flux Jacobian

Preconditioning

Start-up problem

6.2.6 Implicit Runge-Kutta schemes

6.3 Methodologies for Unsteady Flows

6.3.1 Dual time-stepping for explicit multistage schemes

6.3.2 Dual time-stepping for implicit schemes

Chapter 7: Turbulence Modeling

7.1 Basic Equations of Turbulence

7.1.1 Reynolds averaging

7.1.2 Favre (mass) averaging

7.1.3 Reynolds-averaged Navier-Stokes equations

7.1.4 Favre- and Reynolds-averaged Navier-Stokes equations

7.1.5 Eddy-viscosity hypothesis

7.1.6 Non-linear eddy viscosity

7.1.7 Reynolds-stress transport equation

7.2 First-Order Closures

7.2.1 Spalart-Allmaras one-equation model

Differential form

Integral form

Initial and boundary conditions.

7.2.2 K - two-equation model

Initial and boundary conditions

Wall functions

7.2.3 SST two-equation model of Menter

Boundary conditions

7.3 Large-Eddy Simulation

7.3.1 Spatial filtering

7.3.2 Filtered governing equations

Incompressible Navier-Stokes equations

Compressible Navier-Stokes equations

7.3.3 Subgrid-scale modeling

Eddy-viscosity models

Smagorinsky SGS model

Dynamic SGS models

7.3.4 Wall models

7.3.5 Detached eddy simulation

Chapter 8: Boundary Conditions

8.1 Concept of Dummy Cells

8.2 Solid Wall

8.2.1 Inviscid flow

Structured cell-centered scheme

Structured cell-vertex scheme

Unstructured cell-centered scheme

Unstructured median-dual scheme

8.2.2 Viscous flow

Cell-vertex scheme

8.3 Far-Field

8.3.1 Concept of characteristic variables

Supersonic inflow

Supersonic outflow

Subsonic inflow

Subsonic outflow

8.3.2 Modifications for lifting bodies

Vortex correction in 2D

Vortex correction in 3D

8.4 Inlet/Outlet Boundary

Subsonic inlet

Subsonic outlet

Supersonic inlet and outlet

8.5 Injection Boundary

8.6 Symmetry Plane

Cell-vertex scheme (dual control volume)

8.7 Coordinate Cut

8.8 Periodic Boundaries

Rotational periodicity

8.9 Interface Between Grid Blocks

8.10 Flow Gradients at Boundaries of Unstructured Grids

Chapter 9: Acceleration Techniques

9.1 Local Time-Stepping

9.2 Enthalpy Damping

9.3 Residual Smoothing

9.3.1 Central IRS on structured grids

9.3.2 Central IRS on unstructured grids

9.3.3 Upwind IRS on structured grids

9.4 Multigrid

9.4.1 Basic multigrid cycle.

Transfer of the solution and residuals to the coarser grid

Computation of a new solution on the coarse grid

Solution interpolation from the coarse to the fine grid

9.4.2 Multigrid strategies

Number of time steps

Starting grid

Accuracy of transfer operators

9.4.3 Implementation on structured grids

Transfer operators for the cell-centered scheme

Transfer operators for the cell-vertex scheme

Upwind prolongation (cell-vertex scheme)

9.4.4 Implementation on unstructured grids

Nonnested grids

Topological methods

Agglomeration multigrid method

Generation of coarse grids by volume agglomeration

Problems of agglomeration multigrid

9.5 Preconditioning for Low Mach Numbers

9.5.1 Derivation of preconditioned equations

9.5.2 Implementation

9.5.3 Form of the matrices

Transformation matrices

Preconditioning matrices

Weiss and Smith preconditioner

Eigenvalues of the preconditioned system

Eigenvectors of the preconditioned system

9.6 Parallelization

9.6.1 MPI

9.6.2 OpenMP

9.6.3 CUDA

9.6.4 OpenCL

Chapter 10: Consistency, Accuracy, and Stability

10.1 Consistency Requirements

10.2 Accuracy of Discretization Scheme

10.3 Von Neumann Stability Analysis

10.3.1 Fourier symbol and amplification factor

10.3.2 Convection model equation

Central scheme with artificial dissipation

Upwind scheme

10.3.3 Convection-diffusion model equation

10.3.4 Explicit time-stepping

Examples of Fourier symbols and amplification factors

10.3.5 Implicit time-stepping

Examples of amplification factors

10.3.6 Derivation of the CFL condition

CFL condition by von Neumann analysis

Chapter 11: Principles of Grid Generation

11.1 Structured Grids

11.1.1 C-, H-, and O-grid topology

C-grid topology

H-grid topology

O-grid topology.

11.1.2 Algebraic grid generation.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9780080999951

0080999956

9780128011720

0128011726

OCLC:

908335721