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)  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.
Montessori, A., Tiribocchi, A., Lauricella, M., Succi, S. (2020). A coupled lattice Boltzmann-Multiparticle collision method for multi-resolution hydrodynamics. JOURNAL OF COMPUTATIONAL SCIENCE, 44, 101160 [10.1016/j.jocs.2020.101160].