DEVELOPMENT OF A METHOD FOR CONSTRUCTING IRREGULAR MESHES BASED ON THE DIFFERENTIAL POISSON EQUATION
Ключові слова:non-uniform structured discrete models, mesh thickening, parameters of control functions, mesh orthogonality, Poisson equation
Mathematical modeling of real processes in structures consisting of a large number of components and connections between them has certain difficulties. This is due to the complexity of the geometric shape of the respective areas. Methods for generating discrete models of geometric objects, the finite elements of which are condensed in places of stress concentration and in places with a special shape of the structure, have been developed. This is an urgent task, for example, to study the strength and durability of engineering structures. The mathematical device for construction of non-uniform structured discrete models (grids) by differential methods with the set parameters of condensation and a guarantee of quality of model is developed. Coordinate transformation was used for the curvilinear computational domain when constructing the grid, which allows the curvilinear physical domain to be translated into a rectangular computational domain. The transformation from the physical domain to the calculated one was obtained by the differential method by solving the Poisson equation. The influence of parameters of control functions, by means of which it is possible to perform thickening to straight lines (vertical and horizontal), on grid quality, namely its orthogonality (grid cell angles should be close to straight lines) is considered. The value of the maximum angle of each element of non-uniform structured discrete models is determined. Visualization of orthogonality research is carried out by means of coloring of elements of discrete model in gradations of gray color according to change of value of the maximum angle of each element of a grid. An empirical method has established the relationship between the values of the variables of the computational and physical areas. The generation of non-uniform structured discrete models by the elliptical method and the visualization of the data obtained during the study were performed using a freely distributable software package Scilab.
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