# Slow nonisothermal flows: numerical and asymptotic analysis of the Boltzmann equation

## TL;DR

This paper analyzes slow, nonisothermal gas flows using asymptotic and numerical methods, deriving boundary conditions from the Boltzmann equation and exploring the interplay of thermal stresses.

## Contribution

It introduces second-order boundary conditions for the Boltzmann equation and compares asymptotic and numerical solutions for nonisothermal flows.

## Key findings

- Boundary conditions up to second order are derived from the Boltzmann equation.
- Numerical solutions support the asymptotic analysis.
- The competition between first- and second-order thermal-stress flows is characterized.

## Abstract

Slow flows of a slightly rarefied gas under high thermal stresses are considered. The correct fluid-dynamic description of this class of flows is based on the Kogan--Galkin--Friedlander equations, containing some non-Navier--Stokes terms in the momentum equation. Appropriate boundary conditions are determined from the asymptotic analysis of the Knudsen layer on the basis of the Boltzmann equation. Boundary conditions up to the second order of the Knudsen number are studied. Some two-dimensional examples are examined for their comparative analysis. The fluid-dynamic results are supported by numerical solution of the Boltzmann equation obtained by the Tcheremissine's projection-interpolation discrete-velocity method extended for nonuniform grids. The competition pattern between the first- and the second-order nonlinear thermal-stress flows has been obtained for the first time.