Ivanchuk N. Mathematical modeling of filtration processes in soil environments taking into account the influence of elements of engineering structures

The dissertation is devoted to the development of new mathematical models of filtration processes in porous media under the conditions of elements of engineering structures presence, taking into account the influence of technogenic factors. Existing mathematical models of filtration problems, consolidation of completely saturated porous environments, their filtration destruction, heat and salt transfer in the case of elements of engineering structures presence in porous environments have been improved. The kinematic boundary condition on the mobile depression surface of the soil massif has been modified, taking into account the variable porosity and the influence of physico-chemical factors. An approach to the numerical solution of the corresponding nonlinear boundary value problems for systems of differential equations in domains with inclusions is developed. According to the developed approach, the FreeFem++ package has been used to find approximate solutions of the corresponding nonlinear boundary value problems using the finite element method in the domains with moving boundaries, using the features of the FreeFem++ package for the parallelization of computations to reduce the machine time to solve the boundary value problems. The algorithms were developed, corresponding software implementations of the developed algorithms were created, and a series of numerical experiments were conducted in relation to the study of the influence of elements of engineering structures on filtration processes in porous environments. It was revealed that the presence of these elements of engineering structures (especially their damage) significantly influence the filtration processes in these environments. Also, the influence of variable porosity and suffusion, and colmatage processes on the processes of filtration in a bioplato filter and their influence on its (bioplato) predictive productivity is studied. The study also offers to consider the concentrated ways of filtration in soil massifs as a generalization of elements of engineering structures. The results of dissertational work have been used during the development of the design documentation for reconstruction of the water supply network in Ozhenyn village in Ostroh region of Rivne oblast by “BTS-ENGINEERING” state enterprise, “BIOTEKHSOIUZ” LLC; during development of the reconstruction project documentation for the sewage system on the manufacturing site of “Mankovychi” distillery, Mankovychi village, Stolin region, Brest oblast, Republic of Belarus. Results obtained in the dissertational work have been introduced into the educational process in development of courses “Mathematical and computer modelling of natural and anthropogenic systems”, “Projection-mesh and mesh-free methods of mathematical physics” for the students of National University of Water and Environmental Engineering of Ministry for Education and Science of Ukraine in specialty 113 “Applied mathematics”. Four authors' rights registration certificates have been obtained.