Skochko V. Special geometrical models of processes which develop in continuum

Thesis is devoted to discrete geometric simulation of static and dynamic processes which develop in continuum and can be described by the differential equations with partial derivatives. As a case in point are investigated the heat-mass exchange processes, which arise from drying or warming-up of wet capillary-porous materials, and the deformation processes of the elastic solids under the outside forces influence. A new method to describe continuum by discrete geometrical models is founded. These models allow taking into consideration heterogeneity of the continuum and perception of outside forces which affect on gravity centers of the elementary fragments of investigated solids. The model of continuum can be presented by two types of nets: 1) central net, 2) supplementary net. The nodes of supplementary net coincide with vertexes of elementary fragments which make up the whole area of continuum. The nodes of central net must correspond with gravity centers of the elementary fragments. The modeling process assumes ascertainment of interdependence between nodes of both nets taking into account starting and edge conditions. It is developed the method of complex modeling of following physical fields, which arise from drying of wet materials with using of direct current: electric field intensity; temperature field; humidity field; displacement field of fluid in interstice. The method of geometrical modeling of stressedly-deformed mode of elastic solids is developed. The modeling is based on generalized statico-geometric method, finite difference method and finite element method. The results of researches are included in practice of engineering calculations and the teaching process of KNUCA. Keywords: discreet geometric modeling, mathematical method of numerical modeling, heat-mass exchange, stressedly-deformed mode.