Computation of a shock wave structure in a gas mixture based on the Boltzmann equation with accuracy control

Sitnikov S.S., Tcheremissine F.G.
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In this paper, the structure of a shock wave in a binary gas mixture is studied on the basis of direct solution of the Boltzmann kinetic equation. The conservative projection method is used to evaluate the collision integral in the kinetic equation. The applied evaluation formulas and numerical methods are described in detail. The model of hard spheres is used as an interaction potential of molecules. Numerical simulation is performed using the developed simulation environment software, which makes it possible to study both steady and non-steady flows of gas mixtures in various flow regimes and for an arbitrary geometry of the problem. Modeling is performed on a cluster architecture. Due to the use of code parallelization technologies, a significant acceleration of computations is achieved. With a fixed accuracy controlled by the simulation parameters, the distributions of macroscopic characteristics of the mixture components through the shock wave front were obtained. Computations were conducted for various ratios of molecular masses and Mach numbers. The total accuracy of at least 1% for the local values of molecular density and temperature and 3% for the shock front width was achieved. The obtained results were compared with existing computation data. The results presented in this paper are of theoretical significance, and can serve as a test computation, since they are obtained using the exact Boltzmann equation.

Keywords: rarefied gas dynamics, binary gas mixtures, Boltzmann kinetic equation, projection method, numerical simulation, shock wave structure
Citation in English: Sitnikov S.S., Tcheremissine F.G. Computation of a shock wave structure in a gas mixture based on the Boltzmann equation with accuracy control // Computer Research and Modeling, 2024, vol. 16, no. 5, pp. 1107-1123
Citation in English: Sitnikov S.S., Tcheremissine F.G. Computation of a shock wave structure in a gas mixture based on the Boltzmann equation with accuracy control // Computer Research and Modeling, 2024, vol. 16, no. 5, pp. 1107-1123
DOI: 10.20537/2076-7633-2024-16-5-1107-1123
URL: http://crm-en.ics.org.ru/journal/article/3520/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

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