Zhukovskyi V. Mathematical and computer modeling of saline solutions mass transfer in catalytic and dispersed particles media of microporous structure

The dissertation is devoted to the updating of existing and the construction of new nonlinear one-and two-dimensional mathematical models of pollutants migration in the soil mass in the catalytic particles of a microporous structure presence, i.e. taking into account the influence of the mass transfer in porous micro- and nanosorbents to the overall kinetics of the process. The given mathematical models with the account of nonisothermal conditions, nonlinear dependence of diffusion and filtration coefficients on concentration, diffusion influence in the soil skeleton have been improved. Finite-difference methods for solvind numerical solutions of the corresponding nonlinear boundary value problems in one-dimensional and two-dimensional cases have been developed. On the basis of developed algorithms a software complex NanoSurface was created using parallel computing in a cloud environment. Verification of NanoSurface code and its comparison with other software complexes of modeling processes of underground hydromechanics has been carried out. A series of numerical experiments was conducted and their analysis. The influence of micro and nanoparticles sorbent, temperature, nonlinear dependences of filtration rate and diffusion coefficients on the filtration of saline solutions in saturated media is shown.