Software Implementation of the discrete ordinates method in the problem of the Poiseuille flow in a plane channel with infinite parallel walls

Abstract

The algorithm for calculating the gas macroparameters in a channel using the discrete ordinates method was considered. The system of finite-difference equations that determine the general solution of a homogeneous integro-differential equation after separation of variables was written in a matrix form. The coefficient matrix in the resulting system of equations was reduced to a symmetric one and then to a tridiagonal matrix using the Householder algorithm. The search for the eigenvalues of the tridiagonal matrix was performed using a QL algorithm with implicit shifts. The determination of the coefficients in the expansion of the solution of the required boundary value problem with allowance for the boundary conditions on the channel walls was reduced to a system of linear algebraic equations. The Gauss method with a permutation of the rows was used to solve it. The software implementation of the algorithm was carried out using the C++ programming language. The mass velocity profile of the gas and the flow rate through the cross section of the channel in the Poiseuille flow problem were calculated as an application. The comparison with similar results presented in the open press was performed.