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A meshfree method for the BGK model for rarefied gas dynamics

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Abstract

In this paper, we have applied semi-Lagrangian schemes with meshfree interpolation, based on a moving least squares method, to solve the BGK model for rarefied gas dynamics. Sod’s shock tube problems are presented for a large range of mean free paths in one-dimensional physical space and three-dimensional velocity space. In order to validate the solutions obtained from the meshfree method, we have used the piecewise linear spline interpolation. Furthermore, we have compared the solutions of the BGK model with the solutions obtained from direct simulation Monte Carlo method. In the case of a very small mean free path, the numerical solutions are compared with the exact solutions of the compressible Euler equations. Overall, we found that the meshfree interpolation gives better approximation than the piecewise linear spline interpolation.

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Acknowledgements

This work is supported by the DFG (German research foundation) under Grant No. KL 1105/30-1 and by the ITN-ETN Marie-Curie Horizon 2020 program ModCompShock, Modeling and computation of shocks and interfaces, Project ID: 642768.

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Authors and Affiliations

  1. Department of Mathematics, Technische Universität Kaiserslautern, Erwin-Schrödinger-Straße, 67663, Kaiserslautern, Germany

    Sudarshan Tiwari & Axel Klar

  2. Fraunhofer ITWM, Fraunhoferplatz 1, 67663, Kaiserslautern, Germany

    Axel Klar

  3. Department of Mathematics and Computer Science, University of Catania, Catania, Italy

    Giovanni Russo

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  1. Sudarshan Tiwari
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  2. Axel Klar
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  3. Giovanni Russo
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Correspondence to Sudarshan Tiwari.

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Tiwari, S., Klar, A. & Russo, G. A meshfree method for the BGK model for rarefied gas dynamics. Int J Adv Eng Sci Appl Math 11, 187–197 (2019). https://doi.org/10.1007/s12572-019-00254-5

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  • DOI: https://doi.org/10.1007/s12572-019-00254-5

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