Modeling of Non-Stationary Diffusion Processes - Convections - Reactions in Multi-Layer Half-Spaces and Connected Half-Spaces

Abstract

A matrix method is developed for constructing the Fourier-Laplace symbol of the Green's function for a multilayer half-space and linked half-spaces for three-dimensional non-stationary problems of turbulent diffusion. The sources of emission of impurities can be external or internal, the number of considered layers can be large. The method allows solving boundary-value convection-diffusion-decay problems not only for piecewise constant media, but also for gradient media, all parameters of which depend on the vertical coordinate by discretization with a small vertical step. The multilayer half-space model is a better physical model of the atmosphere than the multilayer packet of layers, since the decrease in concentration in the upper layers in the half-space is caused not by the introduction of special boundary conditions, but by the natural decrease of the solution at infinity for half-space.

It is shown that for a boundary value problem of the third kind for a homogeneous half-space in the non-stationary case, the occurrence of real poles is possible, as well as in the stationary case. For the case of the occurrence of real poles, a method for determining the correct integration contour for the Laplace transform is indicated.

The proposed method for the numerical inversion of three-dimensional Fourier-Laplace integrals based on standard algorithms for integrating rapidly oscillating functions is very effective, which allows us to solve not only direct, but also some inverse problems of turbulent diffusion.

The given example of the numerical solution of a three-dimensional non-stationary problem for two linked half-spaces can be considered as a model of impurity propagation at the boundary of the atmosphere and the ocean.