History reminds us of ancient examples of fluid dynamics applications such as
the Roman baths and aqueducts that fulfilled the requirements of the engineers
who built them; of ships of various types with adequate hull designs, and of wind
energy systems, built long before the subject of fluid mechanics was formalized
by Reynolds, Newton, Euler, Navier, Stokes, Prandtl and others. The twentieth
century has witnessed many more examples of applications of fluid dynamics
for the use of humanity, all designed without the use of electronic computers.
They include prime movers such as internal-combustion engines, gas and steam
turbines, flight vehicles, and environmental systems for pollution control and
ventilation.
Computational Fluid Dynamics (CFD) deals with the numerical analysis of
these phenomena. Despite impressive progress in recent years, CFD remains
an imperfect tool in the comparatively mature discipline of fluid dynamics,
partly because electronic digital computers have been in widespread use for less
than thirty years. The Navier-Stokes equations, which govern the motion of
a Newtonian viscous fluid were formulated well over a century ago. The most
straightforward method of attacking any fluid dynamics problem is to solve these
equations for the appropriate boundary conditions. Analytical solutions are few
and trivial and, even with today's supercomputers, numerically exact solution
of the complete equations for the three-dimensional, time-dependent motion of
turbulent flow is prohibitively expensive except for basic research studies in
simple configurations at low Reynolds numbers. Therefore, the "straightforward"
approach is still impracticable for engineering purposes.
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