CC BY
8A combined analytical and numerical approach to solve spatial bending problems of composite beams
S. K. Golushko1,3, G. L. Gorynin2, A. G. Gorynin1
1Novosibirsk State University
2Surgut State University
3Federal Research Center for Information and Computational Technologies
Email: s.k.golushko@gmail.com
DOI 10.24412/cl-35065-2021-1-00-15
The spatial problem of the theory of elasticity with small parameter is solved in application to the bending
of composite beams. Using the asymptotic splitting method [1, 2] the problem is reduced to consecutive solv-
ing of two and one-dimensional problems, where two-dimensional problems are defined on the cross-section
of the beam and one-dimensional problem is defined along beams length. In the general case of complex
cross-section geometry, numerical solutions are obtained using the least-squares collocation method [3] and
finite-element method.
This work was supported by the Russian Foundation for Basic Research (project no. 18-29- 18029).
References
1. Gorynin G. L., Nemirovsky Y. V. Deformation of Laminated Anisotropic Bars in the Three-dimensional Statement 1.
Transverse-longitudinal Bending and Edge Compatibility Condition // Mechanics of Composite Materials. 2009. V. 45, N.
3, P. 257-280.
2. Golushko S. K., Gorynin G. L., Gorynin A. G. Method of Asymptotic Splitting in Dynamical Problems of the Spatial
Theory of Elasticity // Itogi Nauki i Tekhniki. Seriya" Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory".
2020. V. 188, P. 43-53.
3. Shapeev V., Belyaev V., Golushko S., Idimeshev S. New Possibilities and Applications of the Least Squares
Collocation Method // EPJ Web of Conferences. � EDP Sciences, 2018. V. 173 (01012).
Modelling of burning coke sediment at catalyst grain
I. M. Gubaidullin1, E. E. Peskova2, O. S. Yazovtseva2
1Ufa State Petroleum Technological University
2National Research Ogarev Mordovia State University, Saransk
Email: kurinaos@gmail.com
DOI 10.24412/cl-35065-2021-1-00-16
Recovery of the catalyst activity is an essential part for industrial catalytic processes. One of the least cost-
ly regeneration methods is oxidative regeneration � burning out coke sediments from the catalyst grain by ox-
ygen-containing gas [1-3]. The formation of surface complexes on the catalyst grain is observed during oxygen
adsorption [4]. Heat exchange and the exothermic nature of the effect of coke burning inevitably leads to an
increase in the temperature of the grain. One of the undesirable consequences of the oxidative regeneration
process can be overheating of the catalyst layer, leading to its irreversible changes [1, 5]. Another issue requir-
ing special attention is toxic carbon monoxide, which manifests itself during the decomposition of adsorption
complexes. If the permissible limit is exceeded, the using of special procedures to reduce the concentration is
required.
The article is devoted to numerical modelling of the nonlinear regeneration process, which is described by
the partial differential equations system. Modelling results are visualized. Comparison with the experiment
revealed the admissible deviation of the calculated data from the experimental data.
References
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).
