The **Eulerian** equations watch the fluid move thru a mesh which stands still.
The dynamic variables at a point in the mesh are density, temperature, fluid velocity.
Static information for the mesh point is the geometric details.
Often the mesh is layer out in a rectangular fashion which eliminates per mesh point information.

For the **Lagrangian** equations the mesh moves with the fluid and the dynamic variables are temperature, the positions and velocities of the mesh point.
Each mesh point has an associated constant mass.