Dynamic coupling of kinetic and continuum solvers for micro gas flow computations

O Rovenskaya,G Croce

doi:10.1088/1742-6596/501/1/012029

Abstract

A hybrid method, dynamic coupling the direct numerical solution of the Bhatnagar-Gross-Krook (BGK) kinetic equation and hydrodynamic Navier-Stokes equations is presented. The decomposition of the physical domain into kinetic and hydrodynamic sub-domains is based on the local Knudsen number and macroparameters gradients. The size of these domains will change during the evolution depending on the current value of the criteria. 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. The accuracy and properties of the proposed method is assessed via successful computation of the flow through a slit, at pressure ratio of 0.5 and for wide range of Knudsen number.

Highlights

The coexistence of rarefied continuum flow regime areas and relatively small elements in which rarefaction effects become important is a typical feature of many complex gas flows in micro systems
In micro flows the mean free path of gas molecules is comparable to the characteristic scales of the system. These domains are naturally described by kinetic equation for the velocity distribution function, which involve a considerable effort in terms of CPU time and memory requirements, due to the discretization in both physical and velocity spaces
The solution is advanced in time simultaneously in both kinetic and continuum domains: the coupling is achieved by matching half fluxes at the interface of the kinetic and NS domains, taking care of the conservation of momentum, energy and mass through the interface

Summary

Introduction

The coexistence of rarefied continuum flow regime areas and relatively small elements in which rarefaction effects become important is a typical feature of many complex gas flows in micro systems. The continuum domains are well described by the fluid, Euler or Navier–Stokes (NS) equations in terms of average gas flow velocity, gas density and temperature. This allows the combination of existing in-house codes for numerical solution of both BGK based on the discrete velocity method and a finite-difference finite volume scheme for the NS equations.

Results

Conclusion