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Computational Fluid Dynamics
Fourth Edition
Volume 3

2000, 175 PP
    Hoffmann, Chiang
     

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The fundamental concepts and development of computational schemes for the solution of parabolic, elliptic, and hyperbolic equations are established in Volume I and are extended to the Navier-Stokes equations in Volume II.

The primary goal in the third volume is to review the fundamentals of turbulence and turbulent flows and to extend the governing equations and numerical schemes developed in Volume II to include turbulence.

This volume begins with the basic definitions and concepts in turbulence and turbulent flows. Subsequently, the modification of the governing equations and numerical schemes is introduced. There are three approaches by which turbulent flow fields may be computed. The first approach is based on the averaged Navier-Stokes equations either in the form of Reynolds-Averaged Navier-Stokes (RANS) equations or Favre-Averaged Navier-Stokes (FANS) equations. These formulations, along with several turbulence models and numerical considerations for the solutions of equations, are presented in Chapter 21.The second and third approaches are the Large Eddy Simulations (LES) and the Direct Numerical Simulations (DNS), which are presented in Chapter 23.Since typical computations involved in turbulence and, in particular, in DNS, require higher-order schemes such as compact finite difference formulations, these formulations are introduced in Chapter 22.

Finally, a computer code based on the RANS equations and several turbulence models have been developed and included in the text Student Guide for CFD-Volume III.

Table of Contents   

    

Chapter:

    
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20

Turbulence and Turbulent Flows     
21
 
Turbulent Flow and Turbulence Models  
22
  
Compact Finite Difference Formulations  
23
  
Large Eddy Simulation and Direct Numerical Simulation  
  
  

    
Appendices
    

J Transformation of Turbulence Models from Physical Space to Computational Space  
K The Transport Equation for the Turbulence Kinetic Energy
  
References
   
Index
   

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Preface
Introduction
   

Chapter Twenty:
Turbulence and Turbulent Flows
    

Introductory Remarks, Fundamental Concepts and Definitions, Introduction to Transition, Stability Theory, Transition, Conceptual Model for Turbulent Flows, Production, Diffusion, and Dissipation of Turbulence, Length and Time Scales of Turbulence, Free Shear Layer Flows, Numerical Techniques for Turbulent Flows, Concluding Remarks.

  


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Chapter Twenty One:
Turbulent Flow and Turbulence Models
    

Introductory Remarks, Fundamental Concepts, Universal Velocity Distribution, Modification of the Equations of Fluid Motion, Reynolds Averaged Navier-Stokes Equations,  Turbulent Shear Stress and Heat Flux, Flux Vector RANS Formulation, Turbulence Models, Zero-Equation Turbulence Models, One-Equation Turbulence Models, Baldwin-Barth One-Equation Turbulence Model, Nondimensional Form, Baldwin-Barth Turbulence Model in Computational Space, Spalart- Allmaras One-Equation Turbulence Model, Nondimensional Form, Spalart-Allmaras Turbulence Model in Computational Space, Two-Equation Turbulence Models, Two-Equation Turbulence Model, Low Reynolds number     model, Compressibility Correction and Axisymmetric Consideration, Initial and Boundary Conditions, Two-Equation Turbulence Model, Combined         Two-Equation Turbulence Model, Baseline model, Initial and boundary conditions, Shear-stress transport model, Compressibility correction, Nondimensional form,   /  Turbulence Model in Computational Space, Numerical Considerations, Finite Difference Formulations, Baldwin-Barth One-Equation Turbulence Model, Implicit Formulation, Explicit Formulation, Spalart-Allmaras One-Equation Turbulence Model, Implicit Formulation, Explicit Formulation, Two-Equation Turbulence Models, Applications, Shock/Boundary Layer Interaction, Two-Dimensional Base Flow, Axisymmetric, Supersonic, Turbulent Exhaust Flow, Favre-Averaged Navier-Stokes Equations, Turbulent Viscosity, Concluding Remarks.

    


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Chapter Twenty Two:
Compact Finite Difference Formulations
   

Introductory Remarks, Compact Finite Difference Formulations for the First-Order Derivatives, One-Sided Approximations, Compact Finite Difference Formulations for the Second-Order Derivatives, Error Analysis, Applications to the Hyperbolic Equations, Problems.

    


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Chapter Twenty Three:
Large Eddy Simulation and Direct Numerical Simulation

Introductory Remarks,  Large Eddy Simulation,  Filtered Navier-Stokes Equations,  Subgridscale Models,  Eddy Viscosity,  Smagorinsky Model,  Dynamic Model,  Direct Numerical Simulation.
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