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Discrete-Velocity-Direction Models of BGK-Type with Minimum Entropy: II—Weighted Models

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Abstract

In this series of works, we develop a discrete-velocity-direction model (DVDM) with collisions of BGK-type for simulating gas flows, where the molecular motion is confined to some prescribed directions but the speed is still a continuous variable in each orientation. In this article, we introduce a weighted function in each orientation when recovering the macroscopic parameters. Moreover, the internal molecular degrees of freedom are considered. With this weighted DVDM, we develop three submodels by incorporating the discrete velocity method, the Gaussian-extended quadrature method of moments and the Hermite spectral method in each direction. These spatial-time submodels are novel multidimensional versions corresponding to the three approaches. Numerical tests with a series of 1-D and 2-D flow problems show the efficiency of the weighted DVDM.

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The data in this article are available from the corresponding author upon reasonable request.

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Acknowledgements

This work is supported by the National Key Research and Development Program of China (Grant No. 2021YFA0719200) and the National Natural Science Foundation of China (Grant Nos. 51906122 and 12071246).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Bei**g, 100084, China

    Yihong Chen & Wen-An Yong

  2. Department of Energy and Power Engineering, Tsinghua University, Bei**g, 100084, China

    Qian Huang

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  1. Yihong Chen
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Chen, Y., Huang, Q. & Yong, WA. Discrete-Velocity-Direction Models of BGK-Type with Minimum Entropy: II—Weighted Models. J Sci Comput 99, 84 (2024). https://doi.org/10.1007/s10915-024-02531-3

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