Download PDF by Professor Dr. Cornelis B. Vreugdenhil (auth.): Computational Hydraulics: An Introduction

By Professor Dr. Cornelis B. Vreugdenhil (auth.)

ISBN-10: 3540506063

ISBN-13: 9783540506065

ISBN-10: 3642955789

ISBN-13: 9783642955785

What is Computational Hydraulics? Computational hydraulics is without doubt one of the many fields of technological know-how within which the appliance of desktops supplies upward thrust to a brand new means of operating, that is intermediate among in simple terms theoretical and experimental. it's all in favour of simulation ofthe stream of water, including its outcomes, utilizing numerical tools on com­ puters. there isn't loads of distinction with computational hydrodynamics or computational fluid dynamics, yet those phrases are an excessive amount of limited to the fluid as such. it kind of feels to be average of sensible difficulties in hydraulics that they're infrequently directed to the stream on its own, yet fairly to a few outcome of it, akin to forces on stumbling blocks, shipping of warmth, sedimentation of a channel or decay of a pollutant. these kinds of matters require very comparable numerical equipment and it's because they're handled jointly during this booklet. accordingly, i've got hottest to exploit the time period computational hydraulics. consequently, i've got tried to teach the large box of software by way of giving examples of an exceptional number of such useful difficulties. function of the publication it really is getting a typical scenario that an engineer is needed to resolve a few engineering challenge concerning fluid stream, utilizing typical and general-purpose machine courses to be had in lots of corporations. usually, the software program has been designed with the declare that no numerical or computer-science services is required in utilizing them.

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2 Illustration of the CFL condition. 9) is necessary but not sufficient. This can be seen in the case of the modified Lax method, where a value of IX < 1 gives rise to a more restricting condition. 4 Truncation Error A stable finite-difference method is not necessarily an accurate one. There are two ways of investigating the accuracy, one of which is determining the truncation error. If you substitute the solution of the differential equation (which is normally unknown, so it is a mental exercise) into the difference equation, you do not get the differential equation again, but something deviating from it by a (hopefully) small amount.

This is apparently the relevant factor determining the numerical accuracy. In Fig. 4, the numerical transfer function is shown as a function of this parameter. The analytical value e - 1 is also indicated. A few conclusions can be drawn: (i) the factor () has a very great influence. 5 or close to that are clearly preferable; (ii) the time step should be less than 10% of the relaxation time to have any accuracy at all, if () = 0 or 1. 5, a time step 5 times greater is acceptable; (iii) for () = 1, the accuracy is about as bad as for () = O.

4 T/ At. It turns out that for L/ Ax = 50 to 100 the required accuracy is met. Note that the value of Cr is of no interest here as no conditions of accuracy for the time of arrival of the wave have been given; it is however quite close to unity. 2 Example 250 h 300 t- 33 Fig. 2 Existing situation; water level as a function of time at four locations. m 250 h 300 t- Fig. 3 Situation with storage basin; same locations. ingly (from the Courant number) M = 1 to 2 h. The smaller values have been used for the numerical example.

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Computational Hydraulics: An Introduction by Professor Dr. Cornelis B. Vreugdenhil (auth.)

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