The monography offers a detailed analysis of the methods for constructing mathematical models of transient non-isothermal flows of gas mixtures, multicomponent fluids, and gas - liquid fluids through systems of long branched pipelines including annular sections. To enhance the presentation clarity, the proposed methods are extended to the modeling of flows of heat-conducting multicomponent liquids through long branched open channels.
Together with the model construction methods, the strategies of their numerical analysis are discussed in detail, with the use of various classes of finite-difference schemes, including completely conservative spline schemes of high approximation order. Special emphasis is placed on expounding the method of Lagrangian particles as applied to the analysis of heat-conducting multicomponent liquids transmitted through open channels and to the study of complex flows in linear and annular pipeline networks.
The methods for constructing mathematical models for functioning of trunklines and gas distribution systems operated in gas industry are also discussed in detail. They involve the strategies for prognostic optimization of costs covering the full range of natural gas transmission modes, failure-preventing algorithms (e.g., in case of pipeline ruptures or surge in compressor house networks), and new methods for identifying sources of unrecovery and automated tuning of model parameters to the characteristics of actual pipeline networks. All the described methods for constructing mathematical models and their analysis have been developed within a unique modeling framework, which considerably simplifies their study and practical application. During the last decade, the reliability and efficiency of these methods have been confirmed in practice, in solving industrial problems.

The monography can be useful to researchers, postgraduate students, and educators dealing with mathematical modeling, software application development, and working on computational and analytic problems for the needs of pipeline transmission, engineering industries, power industry, and environmental organizations. The presentation is accessible to undergraduate students of engineering.