Boyarska Y. Mathematical modeling and numerical analysis of nonstationary nonisothermal modes of the gas transport systems

The оbject of research - nonstationary nonisothermal operation modes of the gas transport system of complex structure with of multi-line linear sections and compressor stations. Goal of research - the development of mathematical models and numerical methods of calculation nonstationary nonisothermal operation modes of the gas transport system of complex structure with of multi-line linear sections and compressor stations to compute and predict the standard and emergency modes of the gas transport system, and the effects of emergencies. Research methods - difference methods for solving systems of differential equations and numerical methods for solving systems of linear and nonlinear algebraic equations. Hardware - Personal computer. The theoretical and practical research results - the mathematical models and methods nonstationary nonisothermal operation modes of the gas transport system of complex structure with a given accuracy can simulate transient regimes of the gas transport system; control, plan, describe and predict the modes of the gas transport system; conduct a detailed comprehensive analysis of the pre-crash or emergency and, on this basis, to provide advice on the control action. Scientific novelty - the mathematical model of nonstationary nonisothermal flow mode of gas through the pipeline section has been improved. The model takes into account in the energy equation of the Joule -Thomson's effect. This allowed more adequately describe the thermal and hydraulic modes of transport of gas through the section of the pipeline, as well as throughout the gas transport system; the existing mathematical models of nonstationary nonisothermal operation modes of the gas transport system have been improved. To the model have been entered functional equations, which describe modes of compressor stations. This model has allowed to simulate the control action on the operation modes of the gas transport system and more adequately describe the technological schemes and operation modes of the gas transport system; first proposed a numerical method for the calculation of nonstationary nonisothermal operation modes of the gas transport system of complex structure with of multi-line linear sections and compressor stations. The method different from the known method of accounting functional equations that describe the modes of compressor stations, in solving nonlinear equations, as well as a way of solving a linear system of equations obtained at each step of the Newton method. This has reduced the dimension of the linear system and conduct joint calculation of modes of compressor stations and pipeline segments; the mathematical model for unsteady nonstationary nonisothermal operation modes of the gas transport system has been improved by introducing the boundary conditions at the intermediate nodes of the network graph (outputs compressor units), which describes the structure of the gas transport system, allowing to take into account the work of automatic control of compressor shops. Proposed a numerical method for solving the resulting system of equations. The results of the thesis are used in the manufacturing process on the branch of "Scientific Research and Design Institute for Gas Transportation" (R&D Institute for Gas Transportation) "Ukrtransgas". The research results are used in educational and research processes at the Department of Applied Mathematics, Kharkov National University of Radio and Electronics when reading the course "Mathematical modeling of systems with distributed parameters" as well as course and degree design.