Nonequilibrium Molecular Velocity Distribution Functions Predicted by Macroscopic Gas Dynamic Models

Maksim Timokhin () and Yevgeniy Bondar
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Maksim Timokhin: Faculty of Physics, Lomonosov Moscow State University, 1-2 Leninskie Gory, 119991 Moscow, Russia
Yevgeniy Bondar: Faculty of Physics, Lomonosov Moscow State University, 1-2 Leninskie Gory, 119991 Moscow, Russia

Mathematics, 2025, vol. 13, issue 8, 1-15

Abstract: In the present study, abilities of various macroscopic models (Navier–Stokes–Fourier, Burnett, original and regularized Grad’s 13-moment equations) in predicting the nonequilibrium molecular velocity distribution are examined. The results of the local distribution function reconstruction from flow macroparameters for the models considered are compared with each other and with the reference solution. Two different flows are considered: normal shock wave and stationary regular reflection of oblique shock waves. The Direct Simulation Monte Carlo method is used to obtain the reference solution and the flow macroparameters required for the distribution function reconstruction. All models under consideration predict the distribution function in the upstream low-density region rather poorly, with strong oscillations and unphysical negative values (especially regularized Grad’s 13-moment equations). In the high-density downstream region, the shape of the reference distribution is close to equilibrium, and all macroscopic models predict it rather accurately.

Keywords: rarefied gas dynamics; kinetic theory of gases; velocity distribution function; shock wave; nonequilibrium; DSMC method; Grad’s moment method; Chapman–Enskog method; regularized 13-moment equations; regular reflection of shock waves (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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