  A new class of multiscale scheme is presented for micro-hydrodynamic problems
based on a dual representation of the fluid observables. The hybrid model is
first tested against the classical flow between two parallel plates and then
applied to a plug flow within a micrometer-sized striction and a shear flow
within a microcavity. Both cases demonstrate the capability of the multiscale
approach to reproduce the correct macroscopic hydrodynamics also in the
presence of refined grids (one and two levels), while retaining the correct
thermal fluctuations, embedded in the multiparticle collision method. This
provides the first step toward a novel class of fully mesoscale hybrid
approaches able to capture the physics of fluids at the micro- and nanoscales
whenever a continuum representation of the fluid falls short of providing the
complete physical information, due to a lack of resolution and thermal
fluctuations.
