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Boundary Scheme for a Discrete Kinetic Approximation of the Navier–Stokes Equations

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Abstract

This paper is concerned with boundary treatments of a discrete kinetic approximation proposed in Guo et al. (J Sci Comput 16(4):569–585, 2001) for the Navier–Stokes equations. For this approximation we find that the widely used bounce-back scheme does not have second-order accuracy even the boundary is located at the middle of two neighbouring grid points. To remedy this, a new boundary scheme is proposed. It is shown with the Maxwell iteration that the new scheme is second-order accurate if the boundary is located at the middle of two neighbouring grid points, and is first-order accurate otherwise. In this regard, the present boundary scheme is a natural extension of the bounce-back scheme to the discrete kinetic approximation. Numerical experiments are conducted to validate the accuracy of the scheme and show its utility for both straight and curved boundaries.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 11471185, 11801030 and 11861131004) and by the Tsinghua University Initiative Scientific Research Program (20151080424).

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Science and Technology Beijing, Beijing, 100083, People’s Republic of China

    Weifeng Zhao

  2. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China

    Wen-An Yong

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  1. Weifeng Zhao
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Correspondence to Weifeng Zhao.

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Zhao, W., Yong, WA. Boundary Scheme for a Discrete Kinetic Approximation of the Navier–Stokes Equations. J Sci Comput 82, 71 (2020). https://doi.org/10.1007/s10915-020-01180-6

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  • DOI: https://doi.org/10.1007/s10915-020-01180-6

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