Computational Fluid Dynamics: An Introduction (Von Karman by John F. Wendt PDF

By John F. Wendt

ISBN-10: 3540850554

ISBN-13: 9783540850557

ISBN-10: 3540850562

ISBN-13: 9783540850564

The publication offers an basic instructional presentation on computational fluid dynamics (CFD), emphasizing the basics and surveying numerous answer concepts whose purposes variety from low velocity incompressible circulate to hypersonic move. it really is aimed toward folks who've very little event during this box, either contemporary graduates in addition to specialist engineers, and may supply an perception to the philosophy and tool of CFD, an figuring out of the mathematical nature of the fluid dynamics equations, and a familiarity with quite a few resolution thoughts. For the 3rd variation the textual content has been revised and up-to-date.

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Extra resources for Computational Fluid Dynamics: An Introduction (Von Karman Institute Book)

Sample text

577215664901533 . ). The same method can be used for many other sums or limits of the same kind. For instance, we can easily compute to 15 decimal digits any reasonable value of ζ(s); see Exercise 42. ) = (N + 1/2) log N − N + C + O(1/N ) for a certain constant C. As above, it is easy to compute C numerically. ) = N+ 1 2 log N − N + C + B2 B4 + + ··· . 1 · 2N 3 · 4N 3 However, the constant C can also be computed exactly. 22). 13. Let us explain how this is done, since it can be used in other situations (see Exercise 44).

However, the second one is better suited for numerical computation since there is no problem in computing the integrand close to t = 0, while with the first form we must use some sort of Taylor expansion to obtain the result accurately. 5 Basic Applications of the Euler–MacLaurin Formula As already mentioned, the Euler–MacLaurin formula has many applications. We begin with the easiest. 12. For every k N 1 we have k mk = m=1 k+1 1 k+1 k Bj N k+1−j N k+1 + N + j k+1 2 j=2 = Nk + Bk+1 (N + 1) − Bk+1 (0) Bk+1 (N ) − Bk+1 (0) = , k+1 k+1 and more generally (m + x)k = 0 m

As a toy example, assume for instance that we do not want to use Bernoulli numbers Bj for j > 12. We will thus use k = 12 in the formula. 5 are satisfied, we deduce that the modulus of the remainder r12 is bounded by 1 |B14 | 13! = . 14! 577215664901533 . ). The same method can be used for many other sums or limits of the same kind. For instance, we can easily compute to 15 decimal digits any reasonable value of ζ(s); see Exercise 42. ) = (N + 1/2) log N − N + C + O(1/N ) for a certain constant C.

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Computational Fluid Dynamics: An Introduction (Von Karman Institute Book) by John F. Wendt


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