Optimization and Computational Fluid Dynamics - Department of ...

12 Dominique Thévenin
three-dimensional flow geometry discretized using millions of elements and
involving complex physics, typical computing times will be days or weeks.
Should we abandon the hope of any optimization for such interesting problems?
Not necessarily! Since the duration of the complete optimization process
reads in principle “(number of evaluations)×(duration of a single CFD evaluation)”,
there are at least two clear possibilities to still use CFD-O for such
problems:
1. the first one consists in speeding-up as much as possible the evaluation
procedure;
2. the second one consists in reducing as much as possible the number of
required evaluations.
To speed-up each CFD-based evaluation, different solutions might again
be employed and intelligently combined. It is in principle possible to use,
separately or simultaneously, a physical, a mathematical or an algorithmic
point of view:
• From the physical point of view, speeding-up the evaluation means reducing
the model complexity while keeping all (or most) of the needed
coupling processes describing the important physics. This will for example
be demonstrated in the last chapter of this book, where reduced equations
will be partly used instead of the full Navier-Stokes equations, leading
to a tremendous reduction in the needed computing time. It is also employed
in the next chapter when considering optimization of turbulence
model parameters: instead of solving the full multi-dimensional Reynolds-
Averaged Navier-Stokes (RANS) equations to describe turbulent channel
flows, a reduced model will be used instead. Model reduction is clearly
a very efficient procedure and should be used every time this is possible.
But it requires of course a clear understanding of all physical processes
controlling the application considered!
• Applied mathematics should also be considered to reduce as much as possible
the needed computing time and computer memory needed by CFD.
This means that the most efficient solution procedures should be employed.
This can lead for example to multigrid acceleration, perhaps to solve the
pressure/velocity coupling equation; or to the implementation of a highly
complex, three-dimensional adaptive unstructured grid or Adaptive Mesh
Refinement, in order to drastically reduce the needed number of discretization
elements; or to an efficient pre-conditioning of the system. None of
these are specific to CFD-O. But clearly, an experienced CFD specialist
has a better chance to succeed also in CFD-O!
• Finally, the practical coding of the CFD evaluation should also be improved
as much as possible. From an algorithmic point of view, this will
mean in particular the adaptation of the code to the properties of the
employed computer: perhaps a vector, more often today a parallel system.