By Giovanni P. Galdi, John G. Heywood, Rolf Rannacher
The mathematical conception of the Navier-Stokes equations offers nonetheless basic open questions that symbolize as many demanding situations for the mathematicians. This quantity collects a chain of articles whose target is to provide new contributions and ideas to those questions, with specific regard to turbulence modelling, regularity of ideas to the initial-value challenge, circulate in quarter with an unbounded boundary and compressible flow.
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Extra resources for Contributions to current challenges in mathematical fluid mechanics
In the first, the problem at hand is simplified as much as possible and conclusions are drawn based on a basic analysis of the simplified problem. ” In the second approach, the exact opposite is done. The problem is modeled as accurately as possible. The resulting model will normally be much more complex. ” Which approach one should take depends on the importance of the problem. Thus, before modeling, there is the need to classify the importance of the problem. The decision regarding the choice of approach may be made following a flow chart such as Fig.
2. Vibration induced by parallel flow (Leader: Fumio Inada). 3. Vibration of piping conveying fluid, pressure fluctuation, and thermal excitation (Leader: Minoru Kato). 4. Fluid–structure interactions. 5. Vibration of rotating structures in flow. This book presents, as the first step, the results of work on the first three fields (1–3). An effort was made to include examples from actual practical experience to the extent possible. The description of a practical problem is followed by presentation of the evaluation method, the vibration mechanisms, and, finally, practical hints for vibration prevention.
Introduction 21 The first and the third terms on the left hand side above express the increase of the kinetic energy and potential energies. The sum of these terms corresponds to the net increase in the system energy E. The second term on the left hand side is zero since [C2] is a skewsymmetric matrix. The right hand side term of Eq. 26) must be positive for fluid-force-induced oscillations to occur. 28) and self-excited vibration occurs. ” On the other hand, when the system has two or more degrees-of-freedom, there is the case where EK contributes to the increase of the kinetic energy E rather than the other components.