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2. Introduction to Numerical Methods
allows matching of both parameters. For ships, the issue is to match both the
Reynolds and Froude numbers, which is nearly impossible.
In other cases, experiments are very difficult if not impossible. For example, the measuring equipment might disturb the flow or the flow may be
inaccessible (e.g. flow of a liquid silicon in a crystal growth apparatus). Some
quantities are simply not measurable with present techniques or can be measured only with an insufficient accuracy.
Experiments are an efficient means of measuring global parameters, like
the drag, lift, pressure drop, or heat transfer coefficients. In many cases,
details are important; it may be essential to know whether flow separation
occurs or whether the wall temperature exceeds some limit. As technological
improvement and competition require more careful optimization of designs
or, when new high-technology applications demand prediction of flows for
which the database is insufficient, experimental development may be too
costly and/or time consuming. Finding a reasonable alternative is essential.
An alternative - or at least a complementary method - came with the
birth of electronic computers. Although many of the key ideas for numerical solution methods for partial differential equations were established more
than a century ago, they were of little use before computers appeared. The
performance-to-cost ratio of computers has increased at a spectacular rate
since the 1950s and shows no sign of slowing down. While the first computers built in the 1950s performed only a few hundred operations per second,
machines are now being designed to produce teraflops - 1012 floating point
operations per second. The ability to store data has also increased dramatically: hard discs with ten gigabyte (10" bytes or characters) capacity could
be found only on supercomputers a decade ago - now they are found in personal computers. A machine that cost millions of dollars, filled a large room,
and required a permanent maintenance and operating staff is now available
on a desktop. It is difficult to predict what will happen in the future, but further increases in both computing speed and memory of affordable computers
are certain.
It requires little imagination to see that computers might make the study
of fluid flow easier and more effective. Once the power of computers had been
recognized, interest in numerical techniques increased dramatically. Solution
of the equations of fluid mechanics on computers has become so important
that it now occupies the attention of perhaps a third of all researchers in
fluid mechanics and the proportion is still increasing. This field is known
as computational fluid dynamics (CFD). Contained within it are many subspecialties. We shall discuss only a small subset of methods for solving the
equations describing fluid flow and related phenomena.
2. Introduction to Numerical Methods
allows matching of both parameters. For ships, the issue is to match both the
Reynolds and Froude numbers, which is nearly impossible.
In other cases, experiments are very difficult if not impossible. For example, the measuring equipment might disturb the flow or the flow may be
inaccessible (e.g. flow of a liquid silicon in a crystal growth apparatus). Some
quantities are simply not measurable with present techniques or can be measured only with an insufficient accuracy.
Experiments are an efficient means of measuring global parameters, like
the drag, lift, pressure drop, or heat transfer coefficients. In many cases,
details are important; it may be essential to know whether flow separation
occurs or whether the wall temperature exceeds some limit. As technological
improvement and competition require more careful optimization of designs
or, when new high-technology applications demand prediction of flows for
which the database is insufficient, experimental development may be too
costly and/or time consuming. Finding a reasonable alternative is essential.
An alternative - or at least a complementary method - came with the
birth of electronic computers. Although many of the key ideas for numerical solution methods for partial differential equations were established more
than a century ago, they were of little use before computers appeared. The
performance-to-cost ratio of computers has increased at a spectacular rate
since the 1950s and shows no sign of slowing down. While the first computers built in the 1950s performed only a few hundred operations per second,
machines are now being designed to produce teraflops - 1012 floating point
operations per second. The ability to store data has also increased dramatically: hard discs with ten gigabyte (10" bytes or characters) capacity could
be found only on supercomputers a decade ago - now they are found in personal computers. A machine that cost millions of dollars, filled a large room,
and required a permanent maintenance and operating staff is now available
on a desktop. It is difficult to predict what will happen in the future, but further increases in both computing speed and memory of affordable computers
are certain.
It requires little imagination to see that computers might make the study
of fluid flow easier and more effective. Once the power of computers had been
recognized, interest in numerical techniques increased dramatically. Solution
of the equations of fluid mechanics on computers has become so important
that it now occupies the attention of perhaps a third of all researchers in
fluid mechanics and the proportion is still increasing. This field is known
as computational fluid dynamics (CFD). Contained within it are many subspecialties. We shall discuss only a small subset of methods for solving the
equations describing fluid flow and related phenomena.