  In Computational Fluid Dynamics there have been many attempts to combine the
power of a fixed mesh on which to carry out spatial calculations with that of a
set of particles that moves following the velocity field. These ideas indeed go
back to Particle-in-Cell methods, proposed about 60 years ago.
  Of course, some procedure is needed to transfer field information between
particles and mesh. There are many possible choices for this "assignment", or
"projection".
  Several requirements may guide this choice. Two well-known ones are
conservativity and stability, which apply to volume integrals of the fields.
  An additional one is here considered: preservation of information. This means
that mesh interpolation, followed by mesh assignment, should leave the field
values invariant. The resulting methods are termed "mass" assignments due to
their strong similarities with the Finite Element Method.
  We test several procedures, including the well-known FLIP, on three
scenarios: simple 1D convection, 2D convection of Zalesak's disk, and a CFD
simulation of the Taylor-Green periodic vortex sheet. The most symmetric mass
assignment is seen to be clearly superior to other methods.
