Coupling of the navier-stokes and the boltzmann equations with a meshfree particle and kinetic particle methods for a micro cavity

Abstract

We present a coupling procedure of a meshfree particle method to solve the Navier-Stokes equations and a kinetic particle method, a variant of the Direct Simulation Monte Carlo(DSMC) method, to solve the Boltzmann equation. A 2D micro cavity problem has been simulated for different Knudsen numbers. An adaptive domain decomposition approach has been implemented with the help of a continuum breakdown criterion. The solutions from the Navier-Stokes equations and the coupling algorithm are compared with the ones from the Boltzmann equation. Moreover, it is shown that for larger Knudsen numbers, where the Navier-Stokes equations fail to predict the correct flow behaviors, its stationary solutions are still good candidate to initialize a Boltzmann solver. The CPU time for the coupling code is upto 5 times faster than the CPU time for the code solving Boltzmann equation for the same accuracy of the solutions. © 2011 Springer-Verlag Berlin Heidelberg.