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I have worked with the Navier Stokes equations before but I'm a physicist. I was talking to a mathematician and they use a complete different notation and I am very lost.

First of all, I use the Control Volume method for discretization and they use Finite Element.

Second, they talk about variational forms and H and Q spaces \Omega domains, which I have seen for the first time.

Can anybody point my way to a document, or book, or small chapter where I can understand the mathematical variational point of view of the Navier Stokes equation as simple as possible? (I'm interested in the incompressible stationary case for a fluid, so, very simple.)

Qmechanic
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Karla
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2 Answers2

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I found two books which look interesting but still feel it is not "for dummies" enough.

  • The Finite Element Method: Theory, Implementation, and Applications, Texts in Computational Science and Engineering, by M. G. Larson and F. Bengzon

  • A Mathematical Introduction to Fluid Mechanics by Chorin and Marsden

But still if someone has a better suggestion for a variational Navier Stokes derivation that is not so mathematical for a physicist to understand, please let me know.

Karla
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I'm a physics undergrad student. I've been to self-studying continuum mechanics, and as a part of that reading some fluid dynamics stuff. At first I faced similar difficulties. Kip S Thorne's Modern Classical Physics helped me to grasp the physical intuition behind most of the concepts. Then I was motivated to study the variational formulation of fluid. It uses physicist's familiar language.

  • Badin, Gualtiero, Crisciani, Fulvio; Variational Formulation of Fluid and Geophysical Fluid Dynamics: Mechanics, Symmetries and Conservation Laws
Minotaur
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