Analysis and solution of key problems of analytical theory of potentials applied to models of air distribution in coal mines

Abstract

Introduction. This study is devoted to an in-depth examination and resolution of key issues in analytical potential theory related to the modeling of air distribution processes in a coal mine. Research methods. The study is based on the methodological principles of the analytical theory of three-dimensional problems. The main approaches rely on the application of two key concepts: the concept of reduction and the concept of reversibility of a direct solution. The specific features of the analysis of each specific model are determined by the possibility of transforming the original problems into corresponding algebraic problems. Research results and discussion. Approaches to the formalization of schemes for the automatic derivation of analytical formulas for the direct problem, the analysis of the structure of external fields, and the automatic resolution of uniqueness and equivalence issues are considered. Conclusions. The problems of automating the theoretical analysis of specific models extend beyond diffusion modeling methods and remain relevant (and new) in the general context of air distribution processes in mines. A radical solution is automation–an approach that allows solving analytical problems of complex multiparameter models, when traditional analysis methods require a huge amount of calculations, prohibitive for manual processing. A unified solution to key issues in the analytical theory of specific models should be based on identifying common characteristics of various models and analysis technologies. The infrastructure of the air distribution process system should reflect this approach: the theoretical analysis block will be formed not by separate, specialized algorithms for individual models, but by software packages focused on solutions for efficient air distribution management in coal mines. Developing specialized tools based on the proposed system will improve control accuracy, optimize energy consumption, and reduce environmental impacts through accurate air flow modeling and measurement analysis.