Two-Dimensional System of Moment Equations and Macroscopic Boundary Conditions Depending on the Velocity of Movement and the Surface Temperature of a Body Moving in Fluid

Auzhan Sakabekov, Yerkanat Auzhani () and Shinar Akimzhanova
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Auzhan Sakabekov: Department of Higher Mathematics and Modeling, Satbayev University, Almaty 050013, Kazakhstan
Yerkanat Auzhani: Department of Higher Mathematics and Modeling, Satbayev University, Almaty 050013, Kazakhstan
Shinar Akimzhanova: Department of Higher Mathematics and Modeling, Satbayev University, Almaty 050013, Kazakhstan

Mathematics, 2024, vol. 12, issue 10, 1-30

Abstract: This article is dedicated to the derivation of a two-dimensional system of moment equations depending on the velocity of movement and the surface temperature of a body submerged in fluid, and macroscopic boundary conditions for the system of moment equations approximating the Maxwell microscopic boundary condition for the particle distribution function. The initial-boundary value problem for the Boltzmann equation with the Maxwell microscopic boundary condition is approximated by a corresponding problem for the system of moment equations with macroscopic boundary conditions. The number of moment equations and the number of macroscopic boundary conditions are interconnected and depend on the parity of the approximation of the system of moment equations. The setting of the initial-boundary value problem for a non-stationary, nonlinear two-dimensional system of moment equations in the first approximation with macroscopic boundary conditions is presented, and the solvability of the above-mentioned problem in the space of functions continuous in time and square-integrable in spatial variables is proven.

Keywords: Boltzmann equation; two-dimensional system of moment equations; Maxwell microscopic boundary condition; macroscopic boundary conditions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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