A compressible fluid particle model based on the Voronoi ...

Conclusions
-The discrete <strong>model</strong> formulated on physical grounds can be interpreted
as a Lagrangian discretization of the continuum Navier Stokes
equations that preserves First and Second law of thermodynamics.
Any physical reasonable <strong>model</strong> should be compatible with the
thermodynamic laws.
-In order to be able to include thermal fluctuations in any <strong>model</strong> we have
to be sure that the dissipative matrix M(x) of the irreversible dynamics is
positive definite.
-In order to be able to exploit the Lagrangian power of the techniques for
applications to complex <strong>fluid</strong>s some more theoretical work has to be
done to get good discrete versions of the second derivative operators
in non uniform grids.