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PLenary session 15
Sachs, T., Salvatori, R., Salzano, R., Schröder, L., Schön, M., Shevchenko, V., Skov, H., Sonke, J.E., Spolaor, A., Stathopoulos,
V.K., Strahlendorff, M., Thomas, J.L., Vitale, V., Vratolis, S., Barbante, C., Chabrillat, S., Dommergue, A., Eleftheriadis, K.,
Heilimo, J., Law, K.S., Massling, A., Noe, S.M., Paris, J.-D., Prévôt, A.S.H., Riipinen, I., Wehner, B., Xie, Z., Lappalainen, H.K.
2020: Overview: Integrative and Comprehensive Understanding on Polar Environments (iCUPE) – concept and initial
results. Atmospheric Chem. Phys., 20, 8551–8592. https://doi.org/10.5194/ acp-20-8551-2020, 2020.
20. Schmale, J., Arnold, S. R., Law, K. S., Thorp, T., Anenberg, S., Simpson, W. R., Mao, J. and Pratt, K. A., 2018: Local
Arctic air pollution: A neglected but serious problem, Earth’s Futur., doi:10.1029/2018EF000952, 2018.
21. Sokhi, RS, V Singh, X Querol, S Finardi, AC Targino, M de Fatima Andrade, et al., 2021: A global observational
analysis to understand changes in air quality during exceptionally low anthropogenic emission conditions, Environment
international, 157, 106818.
22. Varentsov, M., Konstantinov, P., Baklanov, A., Esau, I., Miles, V., and Davy, R., 2018: Anthropogenic and natural
drivers of a strong winter urban heat island in a typical Arctic city, Atmos. Chem. Phys., 18, 17573– 17587, https://doi.org/
10.5194/acp-18-17573-2018, 2018.
23. WMO, 2019, 2020: Guidance on Integrated Urban Hydrometeorological, Climate and Environmental Services.
Vol. 1: Concept and Methodology. Volume 2: Demonstration Cities. WMO-No. 1234.
On numerical methods for solving direct problems in the mechanics of composite structures
1,2 1,3 1,2 1 1,2 1
L. S. Bryndin , S. K. Golushko , V. A. Belyaev , A. G. Gorynin , V. P. Shapeev , E. V. Amelina
1Novosibirsk State University
2Khristianovich Institute of Theoretical and Applied Mechanics SB RAS
3Federal Research Center for Information and Computational Technologies
Email: l.bryndin@g.nsu.ru
DOI 10.24412/9999-017A-2021-1-00-09
Solving direct problems of calculating strength of composite structures and analyzing their stress-strain
state (SSS) necessitates solving boundary value problems for systems of differential equations. In this report,
numerical methods of linear algebra and the least-squares collocation method in combination with modern algo-
rithms of an iterative process acceleration are applied to modelling and simulation of composite beams bending
[1]. The quasi-static loading process with repeated solution of systems of nonlinear algebraic equations and
boundary value problems for ordinary differential equations is considered to analyze beams SSS [1, 2].
This work was supported by the Russian Foundation for Basic Research (project no. 18-29-18029).
References
1. Golushko S. K., Shapeev V. P., Belyaev V. A., Bryndin L. S., Boltaev A. I., Gorynin A. G. The least-squares collocation
method in the mechanics of deformable solids // J. of Physics: Conf. Ser. 2021. V. 1715, N. 012029. P. 1-10.
2. Shapeev V. P., Belyaev V. A., Golushko S. K., Idimeshev S. V. New possibilities and applications of the least squares
collocation method // EPJ Web of Conferences. 2018. V. 173, N. 01012. P. 1-8.
Conservative-characteristic algorithms for systems of conservation laws of hyperbolic type. Achievements
and challenges
V. M. Goloviznin
Lomonosov Moscow State University
Email: gol@ibrae.ac.ru
DOI 10.24412/9999-017A-2021-1-01-24
Conservative-characteristic (CH) computational algorithms combine the advantages of conservative dif-
ference schemes with automatic trapping of strong discontinuities and the method of characteristics in the
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16 Plenary session
domains of solution smoothness. A characteristic feature of these algorithms is the use of two types of u n-
known quantities - conservative variables related to the centers of the computational cells, and flow variables
related to the faces of the computational cells. In this case, flux variables are expressed not only in terms of
conservative values in adjacent cells, but also depend on flux variables from the previous time layer.
The conservative-characteristic algorithms are based on the finite volume method, and the flows on the
faces of the computational cells are calculated using the characteristic form of the equations. In each compu-
tational cell, local Riemann invariants are constructed, the values of which on a new layer in time are calculat-
ed by extrapolation or interpolation. Extrapolation algorithms include the CABARET scheme.
Conservative-characteristic algorithms have the second order of approximation on irregular computation-
al grids, which transforms into the first in the vicinity of strong discontinuities. The monotonicity of the sol u-
tion is achieved by nonlinear correction of fluxes based on the maximum principle, which does not depend on
any tuning parameters. As applied to the equations of gas dynamics, CH schemes make it possible to calculate
both shock-wave processes of any intensity and turbulent flows with incomplete resolution of the spectrum of
turbulent pulsations without tuning parameters, in particular, the generation of sound by turbulent jet and its
propagation in the near and middle zones.
The report will provide a brief overview of the use of CH algorithms in the problems of aeroacoustics, hy-
drogen safety and computational oceanology.
On preconditioning of grid SLAEs using graph transformations
1,2,3 1,2 1,3 1
V. P. Il'in , G. A. Omarova , D. V. Perevozkin , A. V. Petukhov
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Novosibirsk State University
3Novosibirsk State Technical University
Email: ilin@sscc.ru
DOI 10.24412/9999-017A-2021-1-00-19
The general principles and some specific implementations of the co nstruction of graph preconditioners
[1, 4] for iterative methods in Krylov subspaces [2] are considered, focused on the fast solution of systems of
linear algebraic equations (SLAE) with sparse matrices of large orders that arise when approximating multidi-
mensional boundary value problems of mathematical modeling by the methods of finite differences, finite vol-
umes, finite elements and discontinuous Galerkin [6] algorithms of various orders of accuracy on unstructured
grids. Approaches to the construction of spanning trees for multidimensional weighted connected graphs are
investigated, a reduction algorithm for fast solution of grid equations on graphs is described, as well as issues
of parallelization of the proposed preconditioned iterative processes in Krylov subspaces. Variants of domain
decomposition and multigrid methods [3, 5] are considered as special cases of the proposed approach. The
results of numerical experiments are discussed that demonstrate the effectiveness of these algorithms on a
representative series of typical methodological examples.
References
1. Pravin M. Vaidya. Solving linear equations with symmetric diagonally dominant matrices by constructing good
preconditioners. Unpublished manuscript. A talk based on the manuscript was presented at the IMA Workshop on Graph
Theory and Sparse Matrix Computation, October 1991, Minneapolis.
2. Saad, Y. Iterative methods for sparse linear systems. Society for Industrial and Applied Mathematics, 2003.
3. A. Napov and Y. Notay, An efficient multigrid method for graph laplacian system II: robust aggregation, SIAM J. SCI.
COMPUT., 39 (2017), No. 5, pp. S379-S403.
