Mandzak T. Mathematical modeling and numerical analysis of advection-diffusion in nonhomogeneous media

Methodology of modeling the influence of thin inclusions on transport processes has been generalized and developed in area of adequate consideration of the dominant advective flux component and configuration of thin inclusion. New polydimensional advection-diffusion boundary value problem in media with included curvilinear layer has been formulated. Correctness of the dimensional reduction procedure has been investigated. The approximation of thought field by the thickness of the inclusion has been proposed. Error bounds that concerns polydimensional approach have been presented. Numerical experiments that have been carried out in present work confirm theoretical results and let make important conclusions. Developed software is adopted in educational process in Ivan Franko national university of L’viv and can be applied as a kernel of a system of quantitative analysis and prognosis of transfer processes in multicomponent, particularly, soil media.