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
flowfields 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 solution
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.