Geodesic
On the numerical solution to the problem of air shock wave propagation in mine workings
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 64 (2020), pp. 108-120

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Coal mines are hazardous production facilities, where various accidents are possible. The most destructive accidents are gas and dust explosions. They lead to enormous financial and often human losses. Since 2004, an industry methodology has been used to calculate the parameters of the air shock waves and impact areas. The methodology is based on a system of unsteady gasdynamic equations in a one- and three-dimensional formulation. The main source of data is a spatial network of mine workings. An approach is developed to apply the method for solving the problems of the propagation of shock waves in an extensive network of mine workings with allowance for arbitrary angles of their linking. The approach is based on the use of the Godunov method and the selection of entities: “computational cell”, “cell face”, and “boundary between cells”. The calculations are performed for the following test topologies: circle, square, and “crosscut”. The implementation of the laws of conservation of mass and energy is verified. The symmetry is observed in the circle and square topologies.
Keywords: network of mine workings, methane explosion, air shock waves, mathematical model
Mots-clés : solution technique. 
@article{VTGU_2020_64_a7,
     author = {E. E. Mazepa and P. I. Kusainov and O. Yu. Lukashov and A. Yu. Krainov},
     title = {On the numerical solution to the problem of air shock wave propagation in mine workings},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {108--120},
     publisher = {mathdoc},
     number = {64},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2020_64_a7/}
}
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E. E. Mazepa; P. I. Kusainov; O. Yu. Lukashov; A. Yu. Krainov. On the numerical solution to the problem of air shock wave propagation in mine workings. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 64 (2020), pp. 108-120. http://geodesic.mathdoc.fr/item/VTGU_2020_64_a7/