One-Dimensional Non-Linear Non-Stationary System of Boltzmann Moment Equations in the Fifth Approximation With A Macroscopic Boundary Condition
Abstract
The present study is devoted to the one-dimensional system of Boltzmann moment equations in the fifth approximation and macroscopic boundary conditions. The microscopic Maxwell boundary condition for the one-dimensional Boltzmann equation was approximated and boundary conditions for the one-dimensional non-linear non-stationary Boltzmann moment system in the fifth approximation were derived. The initial boundary value problems for the fifth approximation of the Boltzmann moment system with macroscopic boundary conditions were formulated. The system of Boltzmann moment equations represents a non-linear symmetric system of hyperbolic equations. The first part substantiates the existence and uniqueness of the solution to the initial boundary value problem for the one-dimensional system of Boltzmann moment equations in the fifth approximation with macroscopic boundary conditions in the space of functions that are continuous in time and square-summable over the spatial variable. In the second part, using a numerical method, an approximate solution to the initial boundary value problem for the system of Boltzmann moment equations is determined. The differential problem is approximated by a finite-difference scheme, and an algorithm and program for numerical implementation on a computer are compiled.