9.2 Direct Numerical Simulation (DNS)
269
Understanding the mechanisms of turbulence production, energy transfer,
and dissipation in turbulent flows;
0 Simulation of the production of aerodynamic noise;
0 Understanding the effects of compressibility on turbulence;
0 Understanding the interaction between combustion and turbulence;
0 Controlling and reducing drag on a solid surface.
Other applications of DNS have already been made and many others will
undoubtedly be proposed in the future.
The increasing speed of computers has made it possible to carry out DNS
of simple flows a t low Reynolds numbers on workstations. By simple flows, we
mean any homogeneous turbulent flow (there are many), channel flow, free
shear flows, and a few others. On large parallel computers, it is now possible
to do DNS with 5 1 2 ~ (N 1.35 x lo8) or more grid points. The computation
time depends on the machine and the number of grid points used so no useful
estimate can be given. Indeed, one usually chooses the flow to simulate and
the number of grid points t o fit the available computer resources. A complete
state of the art simulation generally requires between ten and many hundred
hours. As computers become faster and memories larger, more complex and
higher Reynolds number flows will be simulated.
A wide variety of numerical methods can be employed in direct numerical
simulation and large eddy simulation. Almost any method described in this
book can be used. Because these methods have been presented in earlier
chapters, we shall not give a lot of detail here. However, there are important
differences between DNS and LES and simulations of steady flows and it is
important that these be discussed.
The most important requirements placed on numerical methods for DNS
and LES arise from the need to produce an accurate realization of a flow that
contains a wide range of length and time scales. Because an accurate time
history is required, techniques designed for steady flows are inefficient and
should not be used without considerable modification. The need for accuracy
requires the time step to be small and, obviously, the time-advance method
must be stable for the time step selected. In most cases, explicit methods
that are stable for the time step demanded by the accuracy requirement are
available so there is no reason to incur the extra expense associated with
implicit methods; most simulations have therefore used explicit time advance
methods. A notable (but not the only) exception occurs near solid surfaces.
The important structures in these regions are of very small size and very fine
grids must be used, especially in the direction normal to the wall. Numerical
instability may arise from the viscous terms involving derivatives normal to
the wall so these are often treated implicitly. In complex geometries, it may
be necessary to treat still more terms implicitly.
The time advance methods most commonly used in DNS and LES are of
second to fourth order accuracy; Runge-Kutta methods have been used most
commonly but others, such as the Adams-Bashforth and leapfrog methods
269
Understanding the mechanisms of turbulence production, energy transfer,
and dissipation in turbulent flows;
0 Simulation of the production of aerodynamic noise;
0 Understanding the effects of compressibility on turbulence;
0 Understanding the interaction between combustion and turbulence;
0 Controlling and reducing drag on a solid surface.
Other applications of DNS have already been made and many others will
undoubtedly be proposed in the future.
The increasing speed of computers has made it possible to carry out DNS
of simple flows a t low Reynolds numbers on workstations. By simple flows, we
mean any homogeneous turbulent flow (there are many), channel flow, free
shear flows, and a few others. On large parallel computers, it is now possible
to do DNS with 5 1 2 ~ (N 1.35 x lo8) or more grid points. The computation
time depends on the machine and the number of grid points used so no useful
estimate can be given. Indeed, one usually chooses the flow to simulate and
the number of grid points t o fit the available computer resources. A complete
state of the art simulation generally requires between ten and many hundred
hours. As computers become faster and memories larger, more complex and
higher Reynolds number flows will be simulated.
A wide variety of numerical methods can be employed in direct numerical
simulation and large eddy simulation. Almost any method described in this
book can be used. Because these methods have been presented in earlier
chapters, we shall not give a lot of detail here. However, there are important
differences between DNS and LES and simulations of steady flows and it is
important that these be discussed.
The most important requirements placed on numerical methods for DNS
and LES arise from the need to produce an accurate realization of a flow that
contains a wide range of length and time scales. Because an accurate time
history is required, techniques designed for steady flows are inefficient and
should not be used without considerable modification. The need for accuracy
requires the time step to be small and, obviously, the time-advance method
must be stable for the time step selected. In most cases, explicit methods
that are stable for the time step demanded by the accuracy requirement are
available so there is no reason to incur the extra expense associated with
implicit methods; most simulations have therefore used explicit time advance
methods. A notable (but not the only) exception occurs near solid surfaces.
The important structures in these regions are of very small size and very fine
grids must be used, especially in the direction normal to the wall. Numerical
instability may arise from the viscous terms involving derivatives normal to
the wall so these are often treated implicitly. In complex geometries, it may
be necessary to treat still more terms implicitly.
The time advance methods most commonly used in DNS and LES are of
second to fourth order accuracy; Runge-Kutta methods have been used most
commonly but others, such as the Adams-Bashforth and leapfrog methods