Geodesic
Difference schemes based on the support operator method for fluids dynamics problems in a collector containing gas hydrates
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 8, pp. 1341-1355

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Difference schemes based on the support operator method are considered as applied to fluid dynamics in underground collectors containing gas hydrate deposits. A system of mass and energy balances describing fluid dynamics in a porous medium containing gas hydrate deposits is given. A dissipative hydrate equation is derived that determines the thermodynamic evolution of the parameters of the system. It is shown that the jumps in specific volumes and internal energy occurring in phase transitions play a crucial role in the stability of the evolution of the system in the dissipation thermodynamic module of the system. A family of rotation-invariant difference schemes of the support operator method on unstructured meshes is constructed for numerical computations. The schemes are tested on a series of model problems. Their numerical solutions are presented. 
@article{ZVMMF_2015_55_8_a6,
     author = {V. A. Gasilov and I. V. Gasilova and L. V. Klochkova and Yu. A. Poveshchenko and V. F. Tishkin},
     title = {Difference schemes based on the support operator method for fluids dynamics problems in a collector containing gas hydrates},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1341--1355},
     publisher = {mathdoc},
     volume = {55},
     number = {8},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_8_a6/}
}
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V. A. Gasilov; I. V. Gasilova; L. V. Klochkova; Yu. A. Poveshchenko; V. F. Tishkin. Difference schemes based on the support operator method for fluids dynamics problems in a collector containing gas hydrates. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 8, pp. 1341-1355. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_8_a6/