Smirnova V. Mathematical modeling and numerical analysis of not isothermal modes of natural gas transport in pipeline

The subject of inquiry is the physical processes in not isothermal mode of natural gas transport in pipeline. The subject of investigation is the mathematical models of not isothermal modes of natural gas transport in pipeline. We used the known methods of modern hydrodynamics, gas dynamics and thermodynamics to construct mathematical models, analytical methods for solving boundary value problems for ordinary differential equations, mathematical methods and functional analysis, methods of mathematical physics to substantiate the proposed method. In computer simulations the finite element method was used. Mathematical models of non-stationary, stationary and subsonic stationary non-isothermal real gas flow in pipeline section as a systems of nonlinear differential equations were formulated. Research of stationary points for dependence of temperature was carried out. Based on two partial solutions of Cauchy problem, function for local approximation of temperature was constructed. New method of Cauchy problem approximate solution for system of two ordinary differential equations in mathematical model of subsonic stationary non-isothermal real gas flow in pipeline was proposed. Form of test function was purpose and analytical equations describing distribution of pressure in pipe were obtained.Scientific results of the thesis can be used to describe a broad class of non-isothermal modes of transmission system parts, for the preparation of specialists in the field of numerical methods.