  In multiscale, multi-physics applications, there is an increasing need for
coupling numerical solvers that are each applied to a different part of the
problem. Here we consider the case of coupling a Lattice Boltzmann fluid model
and a Finite Difference Navier-Stokes solver. The coupling is implemented so
that the entire computational domain can be divided in two regions, with the FD
solver running on one of them and the LB one on the other.
  We show how the various physical quantities of the two approaches should be
related to ensure a smooth transition at the interface between the regions. We
demonstrate the feasibility of the method on the Poiseuille flow, where the LB
and FD schemes are used on adjacent sub-domains.
  The same idea can be also developed to couple LB models with Finite Volumes,
or Finite Elements calculations.
  The motivation for developing such a type of coupling is that, depending on
the geometry of the flow, one technique can be more efficient, less memory
consuming, or physically more appropriate than the other in some regions (e.g.
near the boundaries), whereas the converse is true for other parts of the same
system. We can also imagine that a given system solved, say by FD, can be
augmented in some spatial regions with a new physical process that is better
treated by a LB model. Our approach allows us to only modify the concerned
region without altering the rest of the computation.
