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, A. T. Il'ichev, “Сравнительный анализ возникновения перегрева воды и неустойчивости фронта кипения в пористой среде”, Doklady RAN. Fiz. Tekhn. Nauki, 494:1 (2020), 64–68
2018
2.
G. G. Tsypkin, “Instability of the phase transition front during water injection into high-temperature rock”, Tr. Mat. Inst. Steklova, 300 (2018), 197–204; Proc. Steklov Inst. Math., 300 (2018), 189–195
3.
A. T. Il'ichev, G. G. Tsypkin, “Evolution of a condensation surface in a porous medium near the instability threshold”, Tr. Mat. Inst. Steklova, 300 (2018), 86–94; Proc. Steklov Inst. Math., 300 (2018), 78–85
2017
4.
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
5.
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
6.
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, 6, 65–71; Fluid Dynamics, 51:6 (2016), 776–783
2015
7.
Andrej T. Il'ichev, George G. Tsypkin, “Geothermal energy and hydrodynamic instability of phase flows”, Energy Science and Technology, 2015, 214–241
8.
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
2013
9.
A. T. Ilichev, G. G. Tsypkin, “Interaction of stabilizing and destabilizing factors and bifurcations of phase transition fronts”, Engineering Journal: Science and Innovation, 2013, 2, 44–13
10.
A. T. Il'ichev, G. G. Tsypkin, “Classification of the types of instability of vertical flows in geothermal systems”, Tr. Mat. Inst. Steklova, 281 (2013), 188–198; Proc. Steklov Inst. Math., 281 (2013), 179–188
2012
11.
A. T. Il'ichev, G. G. Tsypkin, “Stability of water-vapor phase transition in geothermal systems”, Izv. Ross. Akad. Nauk Mekh. Zhidk. Gaza, 2012, 4, 82–92; Fluid Dyn., 47:4 (2012), 501–510
2006
12.
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
2001
13.
G. G. Tsypkin, A. T. Il'ichev, “Устойчивость стационарного фронта фазовых переходов вода-пар в гидротермальных системах”, Dokl. Akad. Nauk, 378:2 (2001), 197
1996
14.
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
1994
15.
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
16.
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
1989
17.
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
1986
18.
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
1981
19.
N. I. Kidin, G. G. Tsypkin, “On Riemann waves in electrohydrodynamics”, Dokl. Akad. Nauk SSSR, 260:4 (1981), 818–821
Presentations in Math-Net.Ru
1.
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
2.
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
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