Determination of the values of transfer characteristics in multicomponent media on the basis of micro-process analysis

I. V. Anisimova ; V. N. Ignat'ev ; E. Yu. Lapteva

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 81 (2023), pp. 49-56

Résumé

This paper proposes a two-level approach for mathematical modeling of processes in multicomponent gas mixtures. It involves a combination of the description of conservation laws based on macro-equations and the determination of the corresponding transfer coefficients using the analysis of micro-processes. The main purpose of this work is to develop an algorithm for determining transport characteristics in multicomponent media based on the analysis of inner micro-processes. Hence, the kinetic molecular theory of gases and liquids is used, namely, the collision part of the Boltzmann equation. It includes multiple improper integrals taking into account the effect of micro-processes in the medium on the values of transport coefficients. When integrating the Boltzmann equation by the Chapman-Enskog method, the transport coefficients are expressed through integral brackets of the Sonin polynomials, which represent the linear combinations of molecular collision integrals. Their calculations require the use of efficient mathematically sound ways including the elements of parallel computing.

Détail

Keywords: multicomponent medium, Boltzmann equation, interaction potential of molecules, integrals with oscillating integrands, parallel computing.
Mots-clés : transport coefficients