Geodesic
Development of a method for calculating flows in a multi-circuit pipeline networks
Matematičeskoe modelirovanie, Tome 33 (2021) no. 12, pp. 103-122.

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This work is devoted to the development of a method for effective calculating the process of non-stationary flow of compressible fluid in pipeline networks based on a system of quasi-one-dimensional (averaged over the cross section of the pipe) equations of mass, energy, and momentum balance in Euler variables. The finite-difference scheme with the corresponding calculation algorithm and the computer program code are constructed. The difference scheme has the property of conservativeness with the fulfillment of grid analogs of the basic conservation laws and meets the criteria of stability and monotonicity of the solution. The proposed solution method consists in reducing the flow calculation in a multi-loop network of pipes with a large number of joints and branches to a set of 3-point successive elimination method carried out independently on each pipe for each Newtonian iteration. The advantage of this method is the ability to parallelize the calculation process. In this regard, the method is promising for use in multiprocessor systems, including systems with hybrid architecture. Examples of numerical calculations showing the efficiency of the developed method are given.
Keywords: mathematical modeling, fully conservative difference scheme, network simulation model, successive elimination method, parallel high-performance computing systems. 
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Yu. A. Poveshchenko; S. B. Popov; E. N. Golovchenko. Development of a method for calculating flows in a multi-circuit pipeline networks. Matematičeskoe modelirovanie, Tome 33 (2021) no. 12, pp. 103-122. http://geodesic.mathdoc.fr/item/MM_2021_33_12_a6/

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