  In this work we discuss the coupling of two mesoscopic approaches for fluid
dynamics, namely the lattice Boltzmann method (LB) and the multiparticle
collision dynamics (MPCD) \cite{kapral2008multiparticle} to design a new class
of flexible and efficient multiscale schemes based on a dual representation of
the fluid observables.
  At variance with other commonly used multigrid methods, mostly oriented to
high Reynolds and turbulent flows, the present approach is designed to capture
the physics at the smallest scales whenever the lattice Boltzmann alone falls
short of providing the correct physical information due to a lack of
resolution, as it occurs for example in thin films between interacting bubbles
or droplets in microfluidic crystals.
  The coupling strategies employed to pass the hydrodynamic information between
the LB and the MPCD are detailed and the algorithm is tested against the steady
isothermal Poiseuille flow problem for different coupling configurations.
