We go back to the question of the regularity of the “velocity average”
when
and
both belong to
, and the variable
lies in a discrete
subset of
.
First of all, we provide a rate, depending on the number of velocities, for the defect of
regularity which
is reached when
ranges over a continuous set. Second of all, we show that the
regularity holds in expectation when the set of velocities is chosen randomly. We
apply this statement to investigate the consistency with the diffusion asymptotics of
a Monte Carlo-like discrete velocity model.
Keywords
average lemma, discrete velocity models, random velocity
grids, hydrodynamic limits
Inria Rennes-Bretagne Atlantique,
IPSO
Research team
IRMAR, UMR CNRS 6625
Campus de Beaulieu
Bâtiment 22/23
263 Avenue du Général Leclerc
35042 Rennes
France