Abstract
A hybrid method dynamically coupling the direct numerical solution of the S-model kinetic equation and Navier-Stokes equations is applied to a numerical simulation of the flow through the channel of a finite length due to arbitrarily pressure ratios and for a wide range of Knudsen number. The decomposition of the physical domain into kinetic and hydrodynamic sub-domains is updated at each time step. The solution is advanced in time simultaneously in both kinetic and hydrodynamic domains: 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. Solver efficiency is increased via MPI (Message Passing Interface) parallelization. Accuracy and reliability of the method, for different decomposition criteria, are assessed via comparison with a pure kinetic solution.
Highlights
At microscale, the analysis of gaseous flow may require to take into account rarefaction effects
The first area where such effect becomes significant is the near-wall region. This is due to the well known fact that the flow near a solid surface can be divided into a thin boundary layer, of the order of a few mean free path, which is a rarefied regime area and the internal core flow, which is a continuum one
A hybrid algorithm based on the direct numerical solution of the kinetic S-model equation coupled with a Navier-Stokes model was applied to the numerical investigation of a gas flow through the channel
Summary
The analysis of gaseous flow may require to take into account rarefaction effects. The first area where such effect becomes significant is the near-wall region This is due to the well known fact that the flow near a solid surface can be divided into a thin boundary layer, of the order of a few mean free path (so thin to be negligible for macro configuration), which is a rarefied regime area and the internal core flow, which is a continuum one. The continuum domain is well described by the fluid Navier-Stokes (NS) equations in terms of mere average flow velocity, gas density and temperature. These equations are more efficient, but less accurate in critical rarefied areas. As indicated in the literature, the slip conditions are valid only for the local Knudsen number
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