9.2 Direct Numerical Simulation (DNS)
267
of the problems associated with the numerical solution of equations containing turbulence models are presented later in this chapter.
The fourth type of method is called two-point closure. It uses equations
for the correlation of the velocity components at two spatial points or,
more often, the Fourier transform of these equations. As these methods
are rarely used except for homogeneous turbulence, we shall not consider
them further.
The fifth is large eddy simulation (LES) and solves for the largest scale
motions of the flow while approximating or modeling only the small scale
motions. It can be regarded as a kind of compromise between one point
closure methods (see above) and direct numerical simulation (see below).
Finally, there is direct numerical simulation (DNS) in which the NavierStokes equations are solved for all of the motions in a turbulent flow.
As one progresses down this list, more and more of the turbulent motions
are computed and fewer are approximated by models. This makes the methods close to the bottom more exact but the computation time is increased
considerably.
All of the methods described in this chapter require the solution of some
form of the conservation equations for mass, momentum, energy, or chemical species. The major difficulty is that turbulent flows contain variations
on a much wider range of length and time scales than laminar flows. So,
even though they are similar to the laminar flow equations, the equations
describing turbulent flows are usually much more difficult and expensive to
solve.
9.2 Direct Numerical Simulation (DNS)
The most accurate approach to turbulence simulation is to solve the NavierStokes equations without averaging or approximation other than numerical
discretizations whose errors can be estimated and controlled. It is also the
simplest approach from the conceptual point of view. In such simulations, all
of the motions contained in the flow are resolved. The computed flow field
obtained is equivalent to a single realization of a flow or a short-duration laboratory experiment; as noted above, this approach is called direct numerical
simulation (DNS).
In a direct numerical simulation, in order to assure that all of the significant structures of the turbulence have been captured, the domain on which
the computation is performed must be at least as large as the physical domain to be considered or the largest turbulent eddy. A useful measure of
the latter scale is the integral scale (L) of the turbulence which is essentially
the distance over which the fluctuating component of the velocity remains
correlated. Thus, each linear dimension of the domain must be a t least a few
267
of the problems associated with the numerical solution of equations containing turbulence models are presented later in this chapter.
The fourth type of method is called two-point closure. It uses equations
for the correlation of the velocity components at two spatial points or,
more often, the Fourier transform of these equations. As these methods
are rarely used except for homogeneous turbulence, we shall not consider
them further.
The fifth is large eddy simulation (LES) and solves for the largest scale
motions of the flow while approximating or modeling only the small scale
motions. It can be regarded as a kind of compromise between one point
closure methods (see above) and direct numerical simulation (see below).
Finally, there is direct numerical simulation (DNS) in which the NavierStokes equations are solved for all of the motions in a turbulent flow.
As one progresses down this list, more and more of the turbulent motions
are computed and fewer are approximated by models. This makes the methods close to the bottom more exact but the computation time is increased
considerably.
All of the methods described in this chapter require the solution of some
form of the conservation equations for mass, momentum, energy, or chemical species. The major difficulty is that turbulent flows contain variations
on a much wider range of length and time scales than laminar flows. So,
even though they are similar to the laminar flow equations, the equations
describing turbulent flows are usually much more difficult and expensive to
solve.
9.2 Direct Numerical Simulation (DNS)
The most accurate approach to turbulence simulation is to solve the NavierStokes equations without averaging or approximation other than numerical
discretizations whose errors can be estimated and controlled. It is also the
simplest approach from the conceptual point of view. In such simulations, all
of the motions contained in the flow are resolved. The computed flow field
obtained is equivalent to a single realization of a flow or a short-duration laboratory experiment; as noted above, this approach is called direct numerical
simulation (DNS).
In a direct numerical simulation, in order to assure that all of the significant structures of the turbulence have been captured, the domain on which
the computation is performed must be at least as large as the physical domain to be considered or the largest turbulent eddy. A useful measure of
the latter scale is the integral scale (L) of the turbulence which is essentially
the distance over which the fluctuating component of the velocity remains
correlated. Thus, each linear dimension of the domain must be a t least a few