Geodesic
Features of using iterative successive substitutions methods for calculating phase equilibrium with a capillary jump
Numerical methods and programming, Tome 25 (2024) no. 1, pp. 92-100.

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This article presents modifications of Successive Substitution methods that are used to calculate the phase equilibrium of a multicomponent thermodynamic system. As an example, two methods are considered: the Successive Substitution method and the Quasi-Newton Successive Substitution method. These methods can be used to calculate the equilibrium between gas and liquid phases with a capillary pressure jump. To check the correctness of these methods, the results of calculations of both phase equilibrium at set temperature and pressures in the phases and phase diagrams for different temperatures were compared with each other. A low error in the results was obtained when calculating the phase equilibrium of a multicomponent mixture taking into account the capillary pressure jump for volatile oil.
Keywords: iterative numerical method, nonlinear equations, capillary pressure jump, phase equilibrium. 
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     author = {M. I. Raikovskyi},
     title = {Features of using iterative successive substitutions methods for calculating phase equilibrium with a capillary jump},
     journal = {Numerical methods and programming},
     pages = {92--100},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2024_25_1_a7/}
}
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M. I. Raikovskyi. Features of using iterative successive substitutions methods for calculating phase equilibrium with a capillary jump. Numerical methods and programming, Tome 25 (2024) no. 1, pp. 92-100. http://geodesic.mathdoc.fr/item/VMP_2024_25_1_a7/