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Mathematical Fluid Dynamics

  1. Nov 10, 2013 #1
    Hi guys,

    I studied mechanical engineering and I am currently a graduate student (turbulence modeling).

    I am interested in the more formal/mathematical aspects of fluid dynamics, which are mainly worked in mathematical faculties and I would like to know if someone knows/have an idea about how difficult is, for someone with an engineering background to switch from numerical/applied research to more analytical/formal mathematical fluid dynamics research.

    There is someone there working in mathematical fluid dynamics?..

    I thank you in advance for any answer...
  2. jcsd
  3. Nov 11, 2013 #2

    Andy Resnick

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    I have only peripheral exposure to mathematical fluids dynamics research- the current work I see has a lot of functional analysis and differential geometry. Some relevant texts you may wish to consult:

    Pozrikidis "Introduction to theoretical and computational fluid mechanics", aimed at the advanced undergrad/grad
    Holmes, Lumley, Berkooz, Rowley "Turbulence, Coherent structures, Dynamical systems and Symmetry"
    Lions "Mathematical topics in fluid mechanics"
    Galdi, Rannacher, Robertson and Turek "Hemodynamical flows: Modeling, Analysis and Simulation"
  4. Nov 11, 2013 #3


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    Most of the research these days is devoted to the computational aspects of fluid dynamics. Until recently, the flow of the so-called perfect fluids (inviscid and irrotational) was what could be handled computationally. Now, additional research has gone into modelling fluids with turbulence, which better simulates real-world fluids, like air and water. One of the goals is to match computationally the results which are usually obtained from model testing, either in a towing tank or a wind tunnel. Not only are aircraft and ships being modelled numerically, but as fuel economy becomes ever more important, all sorts of powered automotive vehicles are being designed numerically to minimize drag and noise.

    Computational fluid dynamics is also used to model flows through devices like turbo-machinery, where there are the usual fluid flow problems which are analyzed, but with the addition of analyzing situations where combustion of fuels is present. These techniques have also been applied to conventional Otto and Diesel cycle engines as well.
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