Матричный метод построения символа функции Грина для стационарных задач турбулентной диффузии в многослойных средах

Abstract

In this paper were considered boundary value problems of the third type for three-dimensional stationary equations of turbulent diffusion in multilayer semibounded media. An effective recurrent matrix algorithm for constructing the Fourier symbol of the Green's function is developed, in which all the intermediate quantities are presented in an explicit form. The method was developed for piecewise homogeneous media, but it allows solving similar problems for continuously stratified media by means of the approximation of a gradient medium by a multilayer medium with piecewise constant coefficients. This method is stable for any Peclet numbers. An economical and simple method for calculating the two-dimensional inverse Fourier transform is proposed. The solutions of the Dirichlet and Neumann space problems for a packet of 50 layers are given, all parameters of each lay vary linearly with the vertical coordinate. The proposed methods may be of interest for solving direct and inverse problems of modeling the scattering of impurities.