Klymyuk Y. Mathematical modeling of spatial nonlinear singularly perturbed "filtration-convection-diffusion" processes in porous media.

This thesis is devoted to mathematical modeling of "filtration-convection-diffusion-mass exchange" processes in porous media which are singly- and doubly connected model domains, bounded by equi- or quasiequipotential surfaces and surfaces of flow, under the conditions when convective component prevailing over the diffusion one considering retroaction of process characteristics on the medium characteristics and development of numerical-asymptotic methods for solving appropriate spatial nonlinear singular perturbed problems. Numerical algorithms for solving of spatial analogues of the inverse boundary value problems of filtration theory on conformal and quasiconformal mappings are developed, which particular automatically solve the choice problem of estimated net nodes. On this basis efficient numerical-asymptotic method of spatial nonlinear singularly perturbed "convection-diffusion-mass exchange" problems solving for the cases of accounting for polynomial and the integral dependency of diffusion coefficient from the desired concentration and time lag is developed. The solutions of preconceived problems with conditions of convection-diffusion supply (removal) of the pollutant defined on the input (output) of filtration flow are obtained with taking into account the anisotropic properties of the medium. Developed technique has been applied to solving of such problems for the cases of multilayer media, with taking into account for retroaction of the concentrations of the pollutant (in the liquid and onto the skeleton of a porous medium), filtration rate etc on the coefficients of porosity, mass transfer and so on. Particular, the new models of filtration processes through the porous loads are built. Filtration characteristics of porous media are analyzed and predictive estimates of behavior of the spread and distribution of pollutants in them are received. Appropriate software is developed.