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Application of moment equations to the mathematical simulation of gas microflows

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Abstract

An approach to the simulation of moderately rarefied gas flows in a transition zone is developed. The applicability of the regularized Grad 13-moment (R13) equations to the numerical simulation of a transition flow between the continual and free-molecular gas flow regimes is explored. For the R13 equations, a numerical method is proposed that is a higher order accurate version of Godunov’s explicit method. A numerical procedure for implementing solid-wall boundary conditions is developed. One- and two-dimensional test problems are solved, including the shock wave structure and the Poiseuille flow in a plane channel. The possibility of applying the R13 equations to the simulation of plane channel and jet flows in a transition regime is explored. To this end, the flow in a square cavity generated by the motion of one of the walls is studied and the operation of the Knudsen pump is analyzed.

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Authors and Affiliations

  1. Faculty of Physics, Moscow State University, Moscow, 119992, Russia

    I. E. Ivanov & M. Yu. Timokhin

  2. Institute for Problems of Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, Moscow, 119526, Russia

    I. A. Kryukov

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  1. I. E. Ivanov
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  2. I. A. Kryukov
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  3. M. Yu. Timokhin
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Correspondence to M. Yu. Timokhin.

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Original Russian Text © I.E. Ivanov, I.A. Kryukov, M.Yu. Timokhin, 2013, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2013, Vol. 53, No. 10, pp. 1721–1738.

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Ivanov, I.E., Kryukov, I.A. & Timokhin, M.Y. Application of moment equations to the mathematical simulation of gas microflows. Comput. Math. and Math. Phys. 53, 1534–1550 (2013). https://doi.org/10.1134/S0965542513100084

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  • DOI: https://doi.org/10.1134/S0965542513100084

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