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5References
1. Masagutov R. M., Morozov B. F., Kutepov B. I. Regeneration of catalysts in oil processing and petrochemistry.
M.: Himiya, 1987. 144 p.
2. Gubaydullin I. M. Mathematical modelling of dynamic modes of oxidative regeneration of catalysts in motionless
layer]: dis.... kand. fiz.-mat. nauk / Institut Neftekhimii i kataliza AN RB. Ufa, 1996. 109 p.
3. Gubaydullin I.M., Yazovtseva O.S. Investigation of the averaged model of coked catalyst oxidative regeneration //
Computer Research and Modeling, 2021, V. 13, no. 1, pp. 149-161.
4. Kuryatnikov V. V. Role of the surface properties of dispersed carbon in its inflammation] // Combustion, Explosion,
and Shock Waves. 1983. V. 19. No 5. P. 18-21.
5. Gubaydullin I. M. Stability of high temperature zones in a motionless catalyst layer // Tez.dokl. II Vsesoyuz. konf.
molodyh uchenyh po fizkhimii. Moskva, 1983. P. 232-233.
On conjugate residual methods for solving non-symmetric SLAEs
V. P. Il'in1,2, D. I. Kozlov1, A. V. Petukhov1
1Institute of Computational Mathematics and Mathematical Geophysics SBRAS
2Novosibirsk State University
Email: ilin@sscc.ru
DOI 10.24412/cl-35065-2021-1-00-17
The aim of this work is to develop and study iterative methods in Krylov subspaces for solving systems of
linear algebraic equations (SLAEs) with non-symmetric sparse matrices of high orders arising in the approxima-
tion of multidimensional boundary value problems on the unstructured grids and which are also relevant in
many applications, including diffusion-convective equations. The considered algorithms are based on the con-
struction ATA � orthogonal direction vectors calculated using short recursions and providing global minimiza-
tion of the residual at each iteration. Methods based on Lanczos orthogonalization, AT � preconditioned conju-
gate residuals algorithm, as well as left Gaussian transformation for the original SLAE are implemented. In ad-
dition, the efficiency of these iterative processes was investigated when solving algebraic systems precondi-
tioned using an approximate factorization of the original matrix in the Eisenstat modification. The results of a
set of computational experiments for various grids and values of convective coefficients are presented, which
demonstrate a sufficiently high efficiency of the approaches under consideration.
Algorithm for the numerical solution of the pure Neumann problem in fractured porous media
M. I. Ivanov1, I. A. Kremer1,2, Yu. M. Laevsky1,2
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Novosibirsk State University
Email:ivanov@sscc.ru, kremer@sscc.ru, laev@labchem.sscc.ru
DOI 10.24412/cl-35065-2021-1-00-20
The paper considers some variants of boundary value problems for the pressures and filtration rates of a
liquid in fractured porous media [1]. For non-flow conditions at the external reservoir boundaries, the pres-
sures inside the media are determined ambiguously. A variant of the pure Neumann problem arises [2]. For
such a problem, the condition of unique solvability is derived. Classical and mixed generalized problem state-
ments that include the constraint on the pressures explicitly are investigated. An algorithm for numerical solu-
tion of the problem using the mixed finite element method is presented. The properties of the proposed algo-
rithm are discussed on the examples of numerical solutions of model problems.
This work was supported by the RSF (grant 19-11-00048).
References
1. Ivanov M.I., Kremer I.A., Laevsky Yu.M. A computational model of fluid filtration in fractured porous media //
Siberian J. Num. Math. 2021. V. 24, N. 2. P. 145-166.
2. Ivanov, M.I., Kremer, I.A., Urev, M.V. Solving the Pure Neumann Problem by a Finite Element Method // Numer.
Analys. Appl. 2019. V. 12, N. 4. P. 359�371. https://doi.org/10.1134/S1995423919040049.
Schemes for solving filtration problem of a heat-conducting two-phase liquid in a porous medium
M. I. Ivanov1, I. A. Kremer1,2, Yu. M. Laevsky1,2
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Novosibirsk State University
Email:ivanov@sscc.ru, kremer@sscc.ru, laev@labchem.sscc.ru
DOI 10.24412/cl-35065-2021-1-00-22
This work is a continuation of the study of the problem of the motion of a two-phase liquid in a porous
medium [1]. In addition, the dependence of the oil viscosity on the temperature is determined, and the energy
equation is included in the system of equations. In the framework of the single-temperature model, the energy
equation is reduced to the heat equation, which describes the conductive mechanism of heat propagation in a
in a porous structure and in a heat-conducting liquid, as well as the convective heat transfer by the filtration
flow. The heat equation is written in a mixed generalized formulation. By analogy with the IMPES scheme, the
convective term is considered on the explicit time layer, and the integration of the conductive term is carried
out using the implicit scheme. This approach to the numerical solution of the heat equation allows to save the
value of the integration step and reuse previously developed codes for filtration problems. The representation
of phase velocities in the form of components co-directed with the total flow, and oppositely directed compo-
nents [2] provides a strict balance of heat in the grid elements. The properties of the proposed algorithm are
discussed on the examples of numerical solutions of model problems.
This work was supported by the RSF (grant 19-11-00048).
References
1. Ivanov M. I., Kremer I. A., Laevsky Yu. M. On the streamline upwind scheme of solution to the filtration problem //
Siberian Electronic Mathematical Reports. 2019. V. 16. P. 757-776. DOI:10.33048/semi.2019.16.051.
2. Ivanov M.I., Kremer I.A., Laevsky Yu. M. Numerical model of gravity segregation of two-phase fluid in porous
media based on hybrid upwinding // Russian J. of Numerical Analysis and Mathematical Modelling. 2021. V. 36, N 1.
P. 17-32. DOI: https://doi.org/10.1515/rnam-2021-0002.
Simulation of heat transfer with considering permafrost thawing in 3D media
D. A. Karavaev
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Email: kda@opg.sscc.ru
DOI 10.24412/cl-35065-2021-1-00-23
An approach to mathematical modeling of heat transfer with permafrost algorithm [1, 2] in 3D based on
the idea of localizing the phase transition area is considered. The paper presents a problem statement for a
non-stationary heat transfer and a description of a numerical method based on a predictor-corrector scheme.
For a better understanding of the proposed splitting method the approximation accuracy was studied taking
into account inhomogeneous right-hand side. The phase changes in the numerical implementation of perma-
frost thawing is considered in the temperature range and requires recalculation of coefficients values of heat
