Lagrangian and Eulerian specification of the flow field

In classical field theories, the Lagrangian specification of the flow field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time. Plotting the position of an individual parcel through time gives the pathline of the parcel. This can be visualized as sitting in a boat and drifting down a river.

This article is about continuum mechanics. For the use of generalized coordinates in classical mechanics, see generalized coordinates, Lagrangian mechanics and Hamiltonian mechanics

The Eulerian specification of the flow field is a way of looking at fluid motion that focuses on specific locations in the space through which the fluid flows as time passes. This can be visualized by sitting on the bank of a river and watching the water pass the fixed location.

The Lagrangian and Eulerian specifications of the flow field are sometimes loosely denoted as the Lagrangian and Eulerian frame of reference. However, in general both the Lagrangian and Eulerian specification of the flow field can be applied in any observer's frame of reference, and in any coordinate system used within the chosen frame of reference.

These specifications are reflected in computational fluid dynamics, where "Eulerian" simulations employ a fixed mesh while "Lagrangian" ones (such as meshfree simulations) feature simulation nodes that may move following the velocity field.

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