Lagrangian and Eulerian Specifications

[swmmr1928]

This is not a homework or test or textbook question or exercise. I am asking purely out of curiosity. Please do not tell me to post this in homework help or give me another infraction.

I have gathered that the Lagrangian approach will follow an individual particle to record some streamline and the Eulerian approach will stay at a point. The Eurlerian neglects time effects and so the material derivative is needed.

My question is will the Lagrangian follow an individual particle in time and in space or in space only? In the weather analogy where you can measure pressure by moving in space or by staying in place, will time be changing while you move through space?

I can imagine two approaches that differ from the Eulerian approach:
1) You follow an individual particle in space as it moves in time
2) You follow the path, at constant time, of a streamline

Which of these two is the Lagrangian approach?

I read some more and my understanding was way off when I posted this, but I am still confused.
The Eulerian approach can use streamlines. The Lagrangian also needs the material derivative. True?

 

[PhilDSP]

Hi swmmr1928,

Both approaches involve (or can involve) following a particle in space and time. Neither neglects time effects. The Lagrangian approach assigns the initial coordinates to where a particular particle (that is presumably traveling in a stream) has been at a particular time while the Eulerian approach assigns the initial coordinates to something outside the local flow of the stream.

Since the Eulerian approach requires you to specify information about the flow of the stream AND the local displacement in the stream of the particle, the material derivative is required. In the Lagrangian approach, you are only concerned with the local displacement of that particular particle for a given time. The Eulerian approach allows you to more naturally track the position of different particles that may or may not be traveling at different velocities within the stream.

The Navier-Stokes equation for Fluid Dynamics incorporates the Eulerian approach.