Lagrangian and eulerian descriptions of phenomena

AI Thread Summary
The discussion contrasts Lagrangian and Eulerian descriptions in fluid mechanics, highlighting their respective advantages. The Lagrangian perspective focuses on individual particles moving through a field, making it useful for classical mechanics, while the Eulerian viewpoint examines fluid flow at fixed points in space, which is often preferred for analyzing deformation and momentum transfer. The Eulerian approach utilizes the total derivative to describe changes over time, making it more intuitive for fluid dynamics. Participants clarify the distinction between the two perspectives, noting that Euler remains stationary while Lagrange follows the particle. Overall, both descriptions are equivalent but serve different purposes depending on the problem at hand.
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lagrangian and eulerian descriptions of phenomena...

hello everyone,

some differential equations are written in terms of a field perspective, some from the point of view of a particle moving through the field...
Navier-stokes eqns can be derived from Newton' s 2nd law applied to a particle.

What advantage is there in viewing things from a particle point of view( Lagrangian view)?
I guess classica mechanics is based on this view.
 
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The two viewpoints are equivalent, but some problems are easier to write down in one particular choice of coordinates. For example, if you want to describe the flow of fluid through a channel, IIRC the Lagrangian viewpoint means you pick a control volume dV and watch the fluid flow through it (i.e. stand on the river bank and watch a static point in space), while the Eulerian view means you choose a fluid element dv and watch it deform over time (i.e. follow a material point in time).

In continuum mechanics, especially fluid mechanics, the Eulerian description is preferred because it's a more natural way to describe how deformation and flow carry momentum and energy, by using the total derivative D/Dt =\frac{\partial}{\partial t} + v\bullet \nabla.
 


Isn't it the other way around? Euler stays put, while Lagrange moves around with the particle?
 
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Heirot said:
Isn't it the other way around? Euler stays put, while Lagrange moves around with the particle?

It could be- I always forget which is which :)
 
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