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Meshfree Methods for Partial Differential Equations V pp 155–171Cite as

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

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 79))

Summary

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.

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Acknowledgment

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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Authors and Affiliations

  1. Department of Mathematics, TU Kaiserslautern, 67663, Kaiserslautern, Germany

    Sudarshan Tiwari & Axel Klar

Authors
  1. Sudarshan Tiwari
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  2. Axel Klar
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Correspondence to Sudarshan Tiwari .

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Editors and Affiliations

  1. Inst. Numerische Simulation, Universität Bonn, Wegelerstr. 6, Bonn, 53115, Germany

    Michael Griebel

  2. Inst. f. Parallele und Verteilte Systeme, Universität Stuttgart, Universitätsstr. 38, Stuttgart, 70569, Germany

    Marc Alexander Schweitzer

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Tiwari, S., Klar, A. (2011). Coupling of the Navier-Stokes and the Boltzmann equations with a meshfree particle and kinetic particle methods for a micro cavity. In: Griebel, M., Schweitzer, M. (eds) Meshfree Methods for Partial Differential Equations V. Lecture Notes in Computational Science and Engineering, vol 79. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16229-9_10

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