RESEARCH OF STATIONARY PLANE FIELDS BY MEANS OF COMPLEX POTENTIAL

Abstract

Some of the most frequently encountered and generic types of plane vector fields with singular points at the origin of the coordinate system have been studied using complex variable theory methods combined with complex potential methods and field theory methods. The basic concepts of field theory and vector analysis, which are used to study vector fields and the main numerical characteristics of these fields, have been considered.

The study of the most frequently encountered vector fields with singular points of four types, namely the generator, the vortical point, the eddy source, the dipole, have been conducted. The application of the complex potential for finding the main characteristics of the vector fields of the considered types, namely their divergence and rotor, has been shown. Equipotential lines and streamlines of the considered vector fields have been obtained and graphically constructed using the method of complex potential. Studied using the vector analysis methods and the methods of the theory of complex variable functions (complex potential) characteristics of vector fields can be used for mathematical modeling of various problems, arising during the study of layers, namely soil and water reservoir filtration problems, as well as in studying the flow of fluid or gas in layers problems.

The developed and considered mathematical models of flat vector fields and the found numerical characteristics of these fields can be used to solve other problems of the oil and gas complex, which require studies of the flow of liquids or gases in gas- or oil-bearing beds.