Application of the analytical discrete velocities method for calculating mass and heat fluxes of rarefied gas in the problem of the Poiseuille flow

Abstract

Analytical version of the discrete ordinates method is used to for calculating the gas macroparameters in a plane channel in the problem of Poiseuille flow. The system of finite-difference equations that determine the general solution of a homogeneous integro-differential equation after separation of variables is written in a matrix form. Householder algorithm is used for reducing the coefficient matrix to a tridiagonal one. QL algorithm with implicit shifts is applied for searching eigenvalues. The Gauss method with a permutation of the rows is used to determine the coefficients in the expansion of the solution of the required boundary value problem with allowance for the boundary conditions on the channel walls. The software implementation of the algorithm is developed using the C ++ programming language. The mass velocity profile and the heat flow profile of the gas, the flow rate and heat flow through the cross section of the channel are calculated for a wide range of the Knudsen number. The comparison with similar results presented in the open press is performed.