Coupling of the Navier-Stokes and the Boltzmann equations with a meshfree particle and kinetic particle methods for a micro cavity

  • Sudarshan TiwariEmail author
  • Axel Klar
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 79)


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.

Key words

meshfree method DSMC micro fluidics coupling Boltzmann and Navier-Stokes 


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This work was supported by the German Research Foundation (DFG), KL 1105/17-1. We would like to thank the (DFG) for the financial support.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of MathematicsTU KaiserslauternKaiserslauternGermany

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