A Multiresolution Mesoscale Approach for Microscale Hydrodynamics

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.