Complete Analytical Exact Solutions of Navier-Stokes Eqs: Fluid Mechanics Book

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Discussion Overview

The discussion revolves around the search for resources that compile all known complete analytical exact solutions of the Navier-Stokes equations, a fundamental topic in fluid mechanics. Participants explore the availability of such materials, the feasibility of compiling them, and the nature of exact solutions in practical applications.

Discussion Character

  • Exploratory, Debate/contested, Technical explanation

Main Points Raised

  • One participant inquires about existing resources that compile exact solutions to the Navier-Stokes equations.
  • Another participant states that, to their knowledge, such compilations do not exist and that information is primarily found in various papers.
  • A participant expresses a desire to undertake the task of compiling a comprehensive resource from existing literature.
  • One participant references a specific journal article related to exact solutions for magnetohydrodynamic flow as a potential resource.
  • Another participant suggests that the conditions under which exact solutions can be found are often not applicable to practical problems in fluid mechanics, emphasizing the preference for methods that yield accurate approximations instead.
  • A later reply advises against the effort of compiling such a resource, implying it may not be worthwhile.
  • It is noted that very few exact solutions exist and that the conditions for solvable cases are typically quite simple.
  • A participant provides a link to an introductory journal paper that may contain relevant information.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the existence of a comprehensive resource for exact solutions. There are competing views regarding the practicality and usefulness of exact solutions versus approximate methods in real-life fluid mechanics problems.

Contextual Notes

Limitations include the potential lack of comprehensive coverage in existing literature and the specific conditions under which exact solutions are applicable, which may not align with practical scenarios.

makethings
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Is there a book, series of notes, lectures, PDF, PPT or anything that contains all known complete analytical exact solutions of the Navier-Stokes equations?
 
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Not to my knowledge. As far as I know, information regarding exact solutions to the N-S equations is mostly just published in several papers.
 
Well then, I wonder if I should make it my mission to search deep into every fluids text and journal paper and compile one myself.
 
An exact solution of the Navier-Stokes equations for magnetohydrodynamic flow

Journal Acta Mechanica
Publisher Springer Wien
ISSN 0001-5970 (Print) 1619-6937 (Online)
Issue Volume 113, Numbers 1-4 / March, 1995


maybe this is what you are looking for
 
makethings said:
Well then, I wonder if I should make it my mission to search deep into every fluids text and journal paper and compile one myself.

You could. But from what I understand, the conditions in which an exact solution can be found are not really applicable to anything useful. So in a nutshell, when people are looking for solutions to real life fluid mechanics problems they don't go looking for an exact solution but a method to give them an accurate approximation.
 
makethings said:
Well then, I wonder if I should make it my mission to search deep into every fluids text and journal paper and compile one myself.

Don't waste your time.
 
To my knowledge, there are very few exact solutions to the NS equations. The conditions that could be solved are very simple.

Here's an intro to a journal paper:
http://arjournals.annualreviews.org/doi/abs/10.1146/annurev.fl.23.010191.001111
 

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