2019, Rahimly, P. I., Podryga, V. O., Rahimly, O. R., Ritus, I. V., Poveshchenko, Y. A., Повещенко, Юрий Андреевич

© 2019, Pleiades Publishing, Ltd. Abstract: This paper considers a thermodynamically equilibrium coupled discrete model of two-component (H 2 O, CH 4 ) three-phase (water, gas, hydrate) filtration fluid dynamics and two-phase processes in a melt zone with no gas hydrates, for which splitting into physical processes is performed. The purpose of the study is to construct a joint family of two-layer completely conservative difference schemes of the support operator method with space-time temporal scales in accordance with the proposed algorithm for splitting the equilibrium model into physical processes both in the melt zone and in a medium with gas-hydrate inclusions. The direct use of the studied system for determining the dynamics of variables and for constructing an implicit difference scheme required for the calculation of filtration processes with large time steps would present serious difficulties.

2019, Rahimly, P., Podryga, V., Rahimly, O., Poveshchenko, Y., Повещенко, Юрий Андреевич

© 2019, Springer Nature Switzerland AG.In the paper the thermodynamically equilibrium joint discrete model of a two-component three-phase (water, methane, hydrate) filtration fluid dynamics and two-phase processes in a melted zone with absence of gas hydrates is considered, for which the splitting by physical processes is performed. In the numerical calculations the direct unsplit using of the system being studied is difficult. Thus the splitting by physical processes is important for the purposes of determining the dynamics of variables and constructing the implicit difference scheme required for calculations of filtering processes with large steps in time is difficult.

2019, Rahimly, P. I., Gasilova, I. V., Kazakevich, G. I., Sharova, Y. S., Poveshchenko, Y. A., Повещенко, Юрий Андреевич

© 2019, Springer Nature Switzerland AG.In this paper, the calculations of water saturation, thermal expansion hydrate thaw and thermodynamic parameters (pressure and temperature) were made using the proposed two-block mathematical model of the dissociation of gas hydrates in a porous medium. The numerical model allows discretizing the task in a one-dimensional case and implementing unconditionally stable difference scheme. The obtained results demonstrate the applicability of the proposed model for the solution of typical problems of gas hydrate fluid dynamics, including the studies of the complex dynamics of water and hydrate saturations of the formation in respect to adiabatic expansion of the gas in the collector space. This model will help in the research and modeling of the problems of the phase transformations of gas hydrate inclusions in the porous media.

2019, Rahimly, P. I., Rahimly, O. R., Podryga, V. O., Gasilova, I. V., Poveshchenko, Y. A., Повещенко, Юрий Андреевич

© 2019, Pleiades Publishing, Ltd.Abstract: The article describes a model, algorithm, and structure of an applied software complex (code) intended for the simulation of flows in a porous medium containing compounds of natural gases (methane, etc.) with water or gas hydrates. The HYDRAT1D code makes it possible to solve fluid dynamics equations in the thawed zone and the piezoconductive medium taking into account phase transitions. The HYDRAT1D code is implemented in JavaScript and operates within the client–server computer architecture.

2019, Sharova, Y. S., Smirnova, N. S., Podryga, V. O., Poveshchenko, Y. A., Gasilov, V. A., Повещенко, Юрий Андреевич, Гасилов, Владимир Анатольевич

© 2019, Springer Nature Switzerland AG.The supercompression of matter caused by gravitational coupling or self-gravitational forces leads to density growth by several orders in magnitude. Keeping in mind the importance of self-gravitation in astrophysical processes like supernovae star evolution we consider it reasonable to develop a numerical technique based on the consistent approximation to the terms describing gravitational energy transfer into the kinetic energy of a matter in the star along its life cycle. The so-called completely conservative gas-dynamics difference schemes including the gravitation effects are the proper numerical technique able to simulate correctly the problems concerning gravitational coupling effects. The accounting for gravitational forces in the construction of completely conservative difference schemes is a significant complication. In the paper, we propose an integrally-consistent difference scheme that utilizes the method of support difference operators thus providing a possibility to conform the balance between kinetic and gravitational energy increments or losses. According to this method, we use the result of the total gravitational energy varying and construct the symmetrized strain rate tensor as the base operator. The result of varying the gravitational energy of the system is a discrete convolution of the Newton gravitational tensor in the difference media under study, which exhaustively answers all the gravitational processes unfolding against the background of the hydrodynamic motion of matter. The symmetrized strain tensor governs the kinematic motion in a considered system. The conjugate operator related to the convolution of these tensors automatically gives the approximation to the gravitational forces acting in the interior of the balance volume of the difference model built via the support operator approach.

2019, Popov, I. V., Poveshchenko, Y. A., Polyakov, S. V., Попов, Игорь Викторович, Повещенко, Юрий Андреевич, Поляков, Сергей Владимирович

© 2019, Springer Nature Switzerland AG.The method of adaptive artificial viscosity is used to model the process of one-dimensional nonlinear convection-diffusion equation. For this purpose, a finite difference scheme (FDS) of the second order of time and space approximation has been developed. The scheme was tested using a numerical solution of the problem on formation of a gradient catastrophe. The process of two-phase filtration was analyzed with the help of constructed FDS. Numerical calculations showed that the proposed method, and in this case reliably tracks the discontinuities of the solution.

2019, Podryga, V. O., Popov, S. B., Rahimly, P. I., Kazakevich, G. I., Poveshchenko, Y. A., Popov, I. V., Повещенко, Юрий Андреевич, Попов, Игорь Викторович

© 2019, Kazan Federal University. All rights reserved.The paper deals with some typical problems of gas hydrates dissociation in a porous medium, which in the first approximation can be reduced to one-dimensional. The research aims to study the mutual effects of underground gas hydrates and climate change, as well as some important technological and ecological problems of the flow in the well or fault area in the presence of hydrate-containing formations. New conservative difference schemes were developed for this class of problems. They are based on the splitting of gas-hydrodynamic processes. The advantage of these schemes is the phased solution of parabolic and hyperbolic equations. This approach greatly simplifies the solution procedure and at the same time increases its stability. Notably, within the framework of the approach, an algorithm was proposed to jointly solve the systems of equations describing the processes in various fields characterized by their own set of coexisting phases. The coordination of computational schemes for them is not a trivial and automatic process. Numerical calculations using mathematical modeling for the joint description of the gas hydrate zone and the zone with no gas hydrates were carried out. The results of calculations showed the applicability of the developed methods for solving the problems under study.

2019, Podryga, V., Rahimly, P., Poveshchenko, Y., Повещенко, Юрий Андреевич

© 2019, Springer Nature Switzerland AG.The paper deals with the thermodynamically equilibrium model of the splitting by physical processes of a two-component three-phase filtration fluid dynamics with gas hydrate inclusions, for which a family of two-layer completely conservative difference schemes based on support operators method with space-time temporal scales is constructed.

2019, Sharova, Yu. S., Podryga, V. O., Poveshchenko, Y. A., Gasilov, V. A., Повещенко, Юрий Андреевич, Гасилов, Владимир Анатольевич

© 2019 Author(s).The supercompression of matter caused by gravitational coupling, or self-gravitational forces, leads to density growth by several orders in magnitude. Keeping in mind the importance of self-gravitation in astrophysical processes like supernovae star evolution we consider it reasonable to develop a numerical technique based on the consistent approximation to the terms describing gravitational energy transfer into the kinetic energy of a matter in the star along its life cycle. In the paper, we propose an integrally-consistent difference scheme that utilizes the method of support difference operators thus providing a possibility to conform the balance between kinetic and gravitational energy increments or losses. According to this method, we use the result of the total gravitational energy varying and construct the symmetrized strain rate tensor as the base operator. The result of varying the gravitational energy of the system is a discrete convolution of the Newton gravitational tensor in the difference media under study, which exhaustively answers all the gravitational processes unfolding against the background of the hydrodynamic motion of matter. The symmetrized strain tensor governs the kinematic motion in a considered system. The conjugate operator related to the convolution of these tensors automatically gives the approximation to the gravitational forces acting in the interior of the balance volume of the difference model built via the support operator approach.

2019, Tsygvintsev, I. P., Krukovskiy, A. Y., Poveshchenko, Y. A., Gasilov, V. A., Повещенко, Юрий Андреевич, Гасилов, Владимир Анатольевич

Finite-di (R) erence approximations of elastic forces on the staggered moving grid were constructed. For the displacement vectors at the irregular grids in which topological and geometrical structures are subjected to minimal reasonable restrictions, with regard to the nitedi (R) erence schemes of the elasticity theory problems, approximations of the vector analysis operators in plane and cylindrical geometries were constructed. Taking into account the energy balance of the medium, the families of integral consistent approximations of the vector analysis operators, which are su +/- cient for the discrete modeling of these processes considering the space curvature caused by the cylindrical geometry of the system, were built. The schemes, both using a stress tensor in the full form and dividing it into volumetric and deviator components, were studied. This separation is used to construct homogeneous equations that are applicable for solid body and vaporized phase. The linear theory of elasticity was used. The resulting expressions for the elastic forces were presented in the explicit form for two-dimensional degrees at and axisymmetric geometries for a mesh consisting of triangular and quadrangular cells. Generalization of the method for other cases (non-linear strain tensor, non-Hookean relation between strain and stress, full 3D geometry, etc.) can be performed by analogy, but this was not a subject of the current paper. Using the model problem, comparison between di (R) erent temporal discretizations for the obtained ordinary di (R) erential equations system was carried out. In particular, we considered fully implicit approximation, conservative implicit approximation (Crank Nicolson method), and explicit approximation, which is similar to the \leap-frog" method. The analysis of full energy imbalance and calculation costs showed that the latter is more advantageous. The analysis of the e (R) ectiveness of various temporal approximations was performed via numerical experiments.