Coupling kinetic and continuum equations for micro scale flow computations

A hybrid method, coupling the direct numerical solution of the Bhatnagar-Gross-Krook (BGK) kinetic equation and hydrodynamic (Navier-Stokes) equations is presented. The computational physical domain is decomposed into kinetic and continuum sub-domains using an appropriate criterion based on the local Knudsen number and proper gradients of macro-parameters, computed via a preliminary Navier-Stokes solution throughout the whole physical domain. The coupling is achieved by matching half fluxes at the interface of the kinetic and Navier-Stokes domains, thus taking care of the conservation of momentum, energy, and mass through the interface. The advantage of the presented hybrid algorithm is that it easily allows the coupling of existing codes for the numerical solution of the BGK and Navier-Stokes equations. To validate and estimate the efficiency of the proposed method the simulation of the monatomic gas flow through a slit has been considered for outlet to inlet pressure ratio of 0.1, 0.5, and 0.9, and a wide range of Knudsen number. The comparison of local parameters (density, velocity, and temperature) with pure kinetic solutions shows satisfactory agreement with those computed by the hybrid solver