Gavryluk V. Mathematical modeling of quasi-ideal processes with aftereffect in free boundary domains.

The thesis is devoted to development of new mathematical models of filtration processes with free boundary domains taking into account interaction process and medium characteristics, parameters optimization, control, anisotropic perturbation and numerical techniques of quasiconformal mappings development for solving nonlinear boundary value problem. First respective algorithms combined with dummy boundary methods were applied for calculation of filtration suffusion interaction in soil dam, drainage contractions and other hydraulics. First the integrated approach to modeling processes of filtration in the free boundary domains and algorithm of solving corresponding boundary value problems with respect to different constructive parameters of hydraulics were firstly developed. The mathematical model of shaft filtration is made in order to predict the process of distraction caused by suffusion appearance. The new programming system for calculation of free surface seepage flow in the dam provided by fast rise of the water level in front of it and calculation of the hydrodynamic mesh and other characteristics of the process was developed.