porous media; phase transitions; Stefan problem; multiphase flows; asymptotic solutions; interface; stability; geothermal systems; gas hydrates; permafrost; ground water.
Subject:
The main objective of the study is to construct the new mathematical models of the transport processes with phase transition in porous media. The models were formulated as generalizations of the classical Stefan problem and are based upon fundamental conservation laws and relations of equilibrium thermodynamics. It was shown that phase transition moving boundary can be presented as a jump of saturation functions. This fact allowed apply the theory of discontinuity to obtain the boundary conditions at unknown moving boundaries for wide class of various processes in porous media. The semi-analytical asyptotic method using both similarity solutions and numerical calculation was developed. This approach was applied to investigate the phase transitions problems in the field of soil science (freezing, thawing and evaporation in soils), geothermal reservoir modelling and mathematical modelling of gas hydrate decomposition in strata and marine sediments.
Biography
Graduated from Faculty of Mathematics and Machanics of M. V. Lomonosov Moscow State University (MSU) in 1976 (department of hydromechanics). Ph.D. thesis was defended in 1982. D.Sci. thesis was defended in 1995. A list of my work contains about 70 titles.
Main publications:
Tsypkin G. G., Brevdo L. A phenomenological model of the increase of solute concentration in ground water due to the evaporation // Transport in porous media, 1999, 37, 129–151.
Tsypkin G. G. Mathematical models of gas hydrates dissociation in porous media // Annals of the New York Academy of Sciences, 2000, 912, 428–436.
G. G. Tsypkin, “Formation of the region of phase transformations in the case of the conversion of CH$_4$ hydrate into CO$_2$ hydrate in a porous medium”, TMF, 224:3 (2025), 659–670; Theoret. and Math. Phys., 224:3 (2025), 1671–1680
2.
K. R. Zhitnikov, G. G. Tsypkin, “Time dependence of stability of the water-vapor phase transition front in high-temperature rocks”, Zh. Vychisl. Mat. Mat. Fiz., 65:5 (2025), 752–764; Comput. Math. Math. Phys., 65:5 (2025), 1090–1102
2023
3.
G. G. Tsypkin, “Mathematical Model of Replacing Methane in Hydrate with Carbon Dioxide When It Is Injected into a Reservoir Saturated with a Mixture of Hydrate, Methane, and Water”, Trudy Mat. Inst. Steklova, 322 (2023), 233–240; Proc. Steklov Inst. Math., 322 (2023), 224–231
G. G. Tsypkin, “Investigation of the transition to instability of the water boiling front during injection into a geothermal reservoir”, TMF, 211:2 (2022), 347–357; Theoret. and Math. Phys., 211:2 (2022), 735–743
G. G. Tsypkin, A. T. Il'ichev, “Superheating of water and morphological instability of the boiling front moving in the low-permeability rock”, Int. J. Heat Mass Transfer, 167 (2021), 120820–8
G. G. Tsypkin, A. T. Il'ichev, “Comparative Analysis of the Occurrence of Water Superheating and Instability of the Boiling Front in a Porous Medium”, Doklady RAN. Fiz. Tekhn. Nauki, 494:1 (2020), 64–68; Dokl. Phys., 65:9 (2020), 333–337
2018
7.
G. G. Tsypkin, “Instability of the phase transition front during water injection into high-temperature rock”, Trudy Mat. Inst. Steklova, 300 (2018), 197–204; Proc. Steklov Inst. Math., 300 (2018), 189–195
A. T. Il'ichev, G. G. Tsypkin, “Evolution of a condensation surface in a porous medium near the instability threshold”, Trudy Mat. Inst. Steklova, 300 (2018), 86–94; Proc. Steklov Inst. Math., 300 (2018), 78–85
2017
9.
G. G. Tsypkin, “A mathematical model of freezing of unsaturated soils in the presence of capillary pressure”, Mathematical notes of NEFU, 24:2 (2017), 96–107
2016
10.
G. G. Tsypkin, A. T. Il'ichev, “Dynamical instability of the evaporation front in low-permeability geothermal reservoirs”, Dokl. Akad. Nauk, 468:6 (2016), 644–647; Dokl. Phys., 61:6 (2016), 297–300
11.
A. T. Il'ichev, G. G. Tsypkin, “Morphological instability of an evaporation front moving in a geothermal reservoir”, Izv. Ross. Akad. Nauk Mekh. Zhidk. Gaza, 2016, no. 6, 65–71; Fluid Dynamics, 51:6 (2016), 776–783
Andrej T. Il'ichev, George G. Tsypkin, “Geothermal energy and hydrodynamic instability of phase flows”, Energy Science and Technology, 2015, 214–241
13.
V. A. Shargatov, A. T. Il'ichev, G. G. Tsypkin, “Dynamics and stability of moving fronts of water evaporation in a porous medium”, Int. J. Heat Mass Transfer, 83 (2015), 552–561
A. T. Ilichev, G. G. Tsypkin, “Interaction of stabilizing and destabilizing factors and bifurcations of phase transition fronts”, Engineering Journal: Science and Innovation, 2013, no. 2, 44–13
15.
A. T. Il'ichev, G. G. Tsypkin, “Classification of the types of instability of vertical flows in geothermal systems”, Trudy Mat. Inst. Steklova, 281 (2013), 188–198; Proc. Steklov Inst. Math., 281 (2013), 179–188
2012
16.
A. T. Il'ichev, G. G. Tsypkin, “Stability of water-vapor phase transition in geothermal systems”, Izv. Ross. Akad. Nauk Mekh. Zhidk. Gaza, 2012, no. 4, 82–92; Fluid Dyn., 47:4 (2012), 501–510
G. G. Tsypkin, C. Calore, M. Marcolini, “Mathematical modeling of cold water injection into a depleted high-temperature geothermal reservoir”, TVT, 44:3 (2006), 453–459; High Temperature, 44:3 (2006), 450–457
G. G. Tsypkin, A. T. Il'ichev, “Устойчивость стационарного фронта фазовых переходов вода-пар в гидротермальных системах”, Dokl. Akad. Nauk, 378:2 (2001), 197
A. A. Barmin, G. G. Tsypkin, “On the movement of a phase-transition front during the injection of water into a geothermal vapor-saturated stratum”, Dokl. Akad. Nauk, 350:2 (1996), 195–197
1995
20.
V. I. Vasiliev, A. M. Maksimov, E. E. Petrov, G. G. Tsypkin, “Mathematical model of the freezing-thawing of saline frozen soil”, Prikl. Mekh. Tekh. Fiz., 36:5 (1995), 57–66; J. Appl. Mech. Tech. Phys., 36:5 (1995), 689–696
G. G. Tsypkin, “Formation of two moving boundaries of phase transitions during steam
production from hot-water hydrothermal reservoir”, Dokl. Akad. Nauk, 337:6 (1994), 748–751
1992
22.
G. G. Tsypkin, “The formation of two moving boundaries of phase transitions during
dissociation of gas hydrates in strata”, Dokl. Akad. Nauk, 323:1 (1992), 52–57; Dokl. Math., 37:3 (1992), 126–128
1991
23.
A. M. Maksimov, G. G. Tsypkin, “Formulation of problems with moving phase-transition boundaries in hydrothermal strata”, Prikl. Mekh. Tekh. Fiz., 32:5 (1991), 98–102; J. Appl. Mech. Tech. Phys., 32:5 (1991), 744–749
1989
24.
È. A. Bondarev, A. M. Maksimov, G. G. Tsypkin, “On the simulation of gas hydrate dissociation”, Dokl. Akad. Nauk SSSR, 308:3 (1989), 575–578
A. M. Maksimov, G. G. Tsypkin, “A mathematical model for the freezing of a water-saturated porous medium”, Zh. Vychisl. Mat. Mat. Fiz., 26:11 (1986), 1743–1747; U.S.S.R. Comput. Math. Math. Phys., 26:6 (1986), 91–95
N. I. Kidin, G. G. Tsypkin, “On Riemann waves in electrohydrodynamics”, Dokl. Akad. Nauk SSSR, 260:4 (1981), 818–821
1979
27.
N. I. Kidin, G. G. Tsypkin, “Nonlinear and linear wave processes in electrohydrodynamics taking account of charge diffusion”, Prikl. Mekh. Tekh. Fiz., 20:1 (1979), 105–113; J. Appl. Mech. Tech. Phys., 20:1 (1979), 80–85
Течения с фазовыми переходами в пористых средах G. G. Tsypkin All-Russian conference "Modern Problems of Continuum Mechanics" devoted to 110 anniversary of L. I. Sedov November 14, 2017 11:40
6.
Задачи с фазовыми переходами в теории фильтрации G. G. Tsypkin International conference "Contemporary Problems of Mechanics" dedicated to the 80th anniversary of academician A. G. Kulikovskii March 18, 2013 16:40
