In our view, perhaps the most important aspect of numerical methods is that they provide solutions to problems that would otherwise require extensive experimentation or would otherwise be intractable. In this chapter, we intend to briefly discuss the historical development of this science before quickly moving into the essential aspect of its practice. It is not an overstatement to call numerical methods in general, and numerical simulation of fluid flow, in particular, a critical development in science in the past 100 years. Those tools of numerical simulation are the focus of this chapter and this book. But at a risk of being brazen, we may now have the critical tools necessary to solve complex fluid flow problems with acceptable accuracy and fidelity. And while these statements were reportedly made many decades ago, there is still truth to them. But they nevertheless help provide context for our current understanding of fluid flow. These quotes, both from Nobel prize winning scientists, may be apocryphal. It is the analysis of circulating or turbulent fluids.” Nobody in physics has been able to analyze it satisfactorily in spite of its importance to the sister sciences. It is not the there is a problem of finding new fundamental particles, but something left over from a long time ago … over a hundred years. Richard Feynman: “ There is a physical problem that is common to many fields, that is very old, and that has not been solved. Why relativity and why turbulence? I really believe he will have an answer for the first.” Werner Heisenberg: “ When I meet God, I am going to ask him two questions.
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