Kukhars'kyj V. Numerical research of advection-diffusion problem in environments with thin heterogeneity

Object of research - advection-diffusion processes in environments with fine heterogeneities. The purpose of work is construction and research of mathematical models of non-stationary advection-diffusion processes in environments with fine heterogene- ities. In the thesis a technique of numerical research of non-stationary processes of advection-diffusion in the environments with fine hete- rogeneities in the form of curvilinear layers or axisymmetric channels is designed. Numerical problem solving implies using the variational approach, according to which the appropriate settings of the problems are constructed and the questions of their correctness is researched. The questions of stabilization of numerical schemes for the problems with dominating advection are researched. Sphere of application - ecology, hydrodynamics, physiology, microelectronics.