  We present a method to derive macroscopic fluid-dynamic models from
microscopic car-following models via a coarse-graining procedure. The method is
first demonstrated for the optimal velocity model. The derived macroscopic
model consists of a conservation equation and a momentum equation, and the
latter contains a relaxation term, an anticipation term, and a diffusion term.
Properties of the resulting macroscopic model are compared with those of the
optimal velocity model through numerical simulations, and reasonable agreement
is found although there are deviations in the quantitative level. The
derivation is also extended to general car-following models.
