The alternative approach works in the Lagrangian description. The bracket algebra between the canonical Lagrangian variables is extended in noncommutative space, and then a map  from the Lagrangian variables to Eulerian variables is applied to obtain the noncommutative corrections in the fluid field theory.
This is the momentum equation of motion in conservative form, and clearly it has completely the same expression form with the ones in Lagrangian description. The first term in the right-hand side represents the change in the ith component of momentum due to a mismatch in 'i-momentum' carried through a cell in each of the three orthogonal directions, and the second term stands for the external force which is [mathematical expression not reproducible] for gravity field.
(8.) arXiv:1509.02442 [pdf] Lagrangian Description
for Particle Interpretations of Quantum Mechanics--Entangled Many-Particle Case Roderick Sutherland
Thus, we need a Lagrangian description
of the boundary.
In a relativistic aether, using the Levi-Civita connection produces the Lagrangian description
while using the Weitzenbock connection produces the Eulerian description.
The canopy (Lagrangian description
) and fluid domain (Eulerian description) interpenetrate with each other.
The continuum formulation using a total Lagrangian description
is presented using an isoparametric linear triangular element.
In a Lagrangian description
, individual elements represent the same material points throughout the step by-step analysis.
In solids mechanics, models are usually built according to Lagrangian descriptions
of motion, where motion is traced using a fixed point of reference.