Work

Nonequilibrium Molecular Velocity Distribution Functions Predicted by Macroscopic Gas Dynamic Models

Year: 2025

Type: article

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.

Source: Mathematics

DOI: 10.3390/math13081328

Authors: Maksim Timokhin, Yevgeniy Bondar

Institutions: Lomonosov Moscow State University, Institute of Theoretical and Applied Mechanics

Language: English

Topic: Gas Dynamics and Kinetic Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Russian Science Foundation