Solution by the factorization method of a mixed boundary value problem of diffusion-convection-decay for a homogeneous layer based on the equations of turbulent diffusion

Abstract

Mixed boundary value problems of diffusion-convection-decay are of great interest to researchers, since they describe different physical processes most accurately in comparison with solutions of similar homogeneous problems. The investigated boundary value problems can have different physical interpretations. In this work, they are considered as processes of propagation of substances in a diffusion layer with different properties of reflection and absorption of impurities by the boundaries of the layer. The constructed mathematical model of a mixed stationary boundary value problem of diffusion-convection-decay for a homogeneous layer and numerical algorithms allow solving the problem with the Dirichlet and Neumann boundary conditions and conditions of the third kind (in their various combinations) with high accuracy. In a two-dimensional formulation, the mixed boundary value problem for the diffusion layer is reduced to the Wiener-Hopf integral equation. The integral equation is solved by the factorization method. A large number of numerical examples are presented. The influence of the solution to the integral equation most significantly affects the nature of the distribution of the substance in the near zone. The influence of boundary conditions is more global in nature. The developed model is applicable without fundamental changes for solving a mixed problem with a multilayer package of layers with different properties of each layer.