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Information × Registration Number 0215U003105, 0112U001014 , R & D reports Title Spatial analogues of boundary problems for quasi-reflection and problem of modeling nonlinear processes in porous media popup.stage_title Head Bomba Andriy Yaroslavovych, Registration Date 15-01-2015 Organization Rivne State Humanitarian University popup.description2 Scientifically-research work report: 367 p., 52 images, 8 tables, 235 sources. . Object of research is different component nonlinear processes such as "filtering-suffusion-convection-diffusion and mass transfer" in environments prone to deformation and free boundaries in terms of incomplete data. The aim of the project is to develop a three-dimensional analogue of boundary value problems for quasi-conformal mapping, and on this basis, the simulation of multicomponent nonlinear processes in porous media provided accounting inverse effect on the performance characteristics of the process environment, management, optimization and parameter identification. By constructing a three-dimensional analogue of difference boundary value problems on conformal, and piecewise quasi conformal mappings and their numerical solutions developed a general approach to the modeling of spatial and quasiideal ideal filtration processes in porous media - model complex geometry regions bounded equivalence or kvaziekvipotentsialnimy surfaces and flow as well as the corresponding numerical calculation algorithms fields. Based on them, formed new spatial process models predicting the spread of contaminants in porous media, taking into account different kinds of dependencies of the diffusion coefficient on the concentration of solute (polynomial, integral, with a delay in time), the nature of convection-diffusion supply and discharge of the pollutant, the anisotropic properties of the medium and The development of efficient numerical-asymptotic method for solving the corresponding spatial nonlinear singularly perturbed problems. Appropriate methodology for modeling generalized migration of solutes in nonlinear-layered "sensitive" to existing filtration pressure (potential) media (when the interface between homogeneous layers are formed depending on the decisions of the filtration problems), with a new type of correction obtained in the asymptotic expansions of solutions corresponding to singularly perturbed problems with discontinuous coefficients characterizing the mechanism of convection-diffusion redistribution of concentrations in the vicinity of portions of the layers. A new methodology for modeling quasi-ideal (ideal) flow filtration in maloprostorovih curved regions bounded kvaziekvipotentsialnymi (equipotential) surface and the surface currents, in particular: developed a new mathematical model and numerical algorithm for solving three-dimensional model of nonlinear boundary value problems on spatial quasi-conformal mappings in the case where one of the parts of the border area has an unknown (free) surface, which is designed on the basis of a comprehensive approach to the modeling of nonlinear filtering and suffusion of interaction in the presence of a subsurface dam period such as "seepage" surface depression of water downstream, also considered the case of longitudinal drainage; an integrated approach to mathematical modeling of two-phase flow, to predict the changes in the characteristics of reservoir system under different conditions of exposure to it, the specifics of filtering privyboynyh areas: to the case of a spatially curved layers of variable thickness; on the basis of a systematic description of all possible cases form the perfect flow in limited surface flow and equipotential surfaces curved parallelepiped depending on the intensity (as a control parameter) of the additional line source (located on one of the limiting surface currents) and the curvilinear parallelepiped with a cylindrical cavity bounded four surfaces flow and three equipotential surfaces, first solved the problem of the ambiguity of the related non-linear boundary value problems on conformal mappings of space using automated procedures developed by selecting a suitable case. Solved scientific problems of modeling of filtration through porous media, with the inverse dependence of the process (the concentration of fluid contamination and sediment) on the characteristics of the environment (void ratio, filtration, diffusion, mass transfer, etc.), as well as the diffusion-indignation and mass transfer developed numerical and asymptotic methods of solving the corresponding nonlinear singularly perturbed boundary value problems with incomplete data. Established software systems for forecasting and management of the respective filter systems, including the calculation of the optimal size of the filter, since its protective action, sediment load limit, head loss and the like. A method for numerical-asymptotic expansions of solutions of inverse singularly perturbed boundary value problems "convection-diffusion" with an unknown right-hand side, represented as a product of two functions, provided naperedzadaniya. Appropriate methodology extended to solution of nonlinear singularly perturbed problems such as "filtration-convection-diffusion-mass exchange" with the thermo. Keywords: mathematical modeling, spatial boundary value problems, spatial piecewise conformal mapping, spatial quasi-conformal mappings, inverse problems, the complex potential, porous media, suffoznye phenomenon of convection-diffusion processes, mass transfer processes, filtration processes, regular and singular perturbations, chislenno- asymptotic methods, incomplete data, systems approach, free boundary, the filter coefficients, diffusion and porosity gradient of pressure, flow, filtration deformation. Product Description popup.authors Абрамович О.В. Бомба А. Я. Гаврилюк В. І. Гладка О.М. Климюк Ю.Є. Крока Л.Л. Пригорницький Д.О. Присяжнюк І.М. Присяжнюк О.В. Рожко Р.А. Сінчук А.М. Савюк Є.В. Сафоник А. П. Теребус А.В. Фурсачик О.А. Шепетько Ю.О. Ярощак С.В. popup.nrat_date 2020-04-02 Close