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6a numerical three-dimensional model of the Arctic Ocean. Changes in the timing of the formation and melting of ice, an increase in heat input into surface sea waters, an increase in the heat content of the seas are ana-lyzed. The extreme rise in surface water temperature in shelf seas can be classified as the existence of marine heatwaves. To identify marine heatwaves, the method described in (1) was applied.
This work was supported by the Russian Science Foundation (19-17-00-154).
References:
1. A.J. Hobday et al. A hierarchical approach to defining marine heatwaves // Progress in Oceanography � 2016. 141. P. 227�238.
Simulation of the interaction of long surface waves with semi-submerged structures with an uneven bilge
O. I. Gusev, G. S. Khakimzyanov, L. B. Chubarov
Federal Research Center for Information and Computational Technologies
Email: gusev_oleg_igor@mail.ru
DOI 10.24412/cl-35065-2021-1-01-28
The study is devoted to the problem of the interaction of long surface waves with semi-submerged fixed structures with an uneven bilge. Numerical algorithms [1] are constructed for one-dimensional nonlinear shal-low water models with and without frequency dispersion [2]. The influence of bilge irregularities on the char-acteristics of the reflected and transmitted waves is investigated. The obtained numerical solutions are com-pared with the results of other authors [3].
References
1. Khakimzyanov G.S., Dutykh D. Long wave interaction with a partially immersed body. Part I: Mathematical models // Communications in Computational Physics. 2020. V. 27, N. 2. P. 321-378.
2. Khakimzyanov G., Dutykh D., Fedotova Z., Gusev O. Dispersive Shallow Water Waves. Theory, Modeling, and Numerical Methods. Lect. Notes in Geosystems Mathematics and Computing. Basel, Birkhauser, 2020.
3. Chang C.-H., Wang K.-H., Hseih P. -C. Fully nonlinear model for simulating solitary waves propagating through a partially immersed rectangular structure // J. of Coastal Research. 2017. V. 33, N. 6. P. 1487-1497.
Some nonlinear models of transport theory
A. V. Kalinin1,2, A. A. Tyukhtina1 A. A. Busalov1, O. A. Izosimova1
1Lobachevsky State University of Nizhny Novgorod
2Institute of Applied Physics RAS
Email: avk@mm.unn.ru
DOI 10.24412/cl-35065-2021-1-01-29
A wide class of problems in physics and engineering leads to the study of integro-differential equations of transport theory. The foundations of mathematical and numerical modeling of particle transport processes were laid in the works [1-4]. We consider stationary and non-stationary problems for nonlinear systems of in-tegro-differential equations of transport theory [5]. The issues of correctness of statements of the correspond-ing mathematical problems, properties of their solutions and algorithms for numerical solution are discussed. The theoretical study of the problems uses the methods of ordered function spaces.
This work was supported by the Scientific and Education Mathematical Center "Mathematics for Future Technolo-gies" (Project No. 075-02-2020-1483/1).
References
1. Marchuk G. I. Methods for nuclear reactor calculations. M.: Gosatomizdat, 1961.
2. Marchuk G. I., Lebedev V. I. Numerical methods of the theory of neutron transport. M. Atomizdat, 1981.
3. Vladimirov V. S. Mathematical problems of the one-velocity theory of particle transport// Trudy Mat. Inst. Steklov. 1961. V. 61. P. 3-158.
4. Sushkevich T. A. Mathematical models of radiation transfer. M.: BINOM, 2006.
5. Kalinin A. V., Morozov S. F. A mixed problem for a nonstationary system of nonlinear inregro-differential equations // Sib. Math. J. 1999. V. 40, N. 5. P. 887-900.
Local ensemble optimal nonlinear filtering algorithm
E. G. Klimova
Federal Research Center for Information and Computational Technologies
Novosibirsk State University
Email: klimova@ict.nsc.ru
DOI 10.24412/cl-35065-2021-1-01-30
A shortcoming of the classical particle filter method is that observation data are used only to calculate the weight coefficients with which the elements (particles) of an ensemble are summed. An approach to solving the nonlinear filtering problem based on a representation of the distribution density as a sum of Gaussian functions has been used. If the distribution density is represented as a sum of Gaussian functions, a sum with weights of estimates obtained in Kalman filters corresponding to Gaussian distribution densities is the optimal estimate. In the report, an approach to solving the nonlinear filtering problem with the distribution density represented as a sum of Gaussian functions is considered. The ensemble .-algorithm, which was proposed earlier by the author, is used to implement the algorithm [1, 2]. The algorithm is local and can be implemented in separate subdomains. This allows its implementation in high-dimensional geophysical models. The results of numerical experiments with a 1-dimensional nonlinear model are presented.
References
1. Klimova, E. A suboptimal data assimilation algorithm based on the ensemble Kalman filter // Quarterly J. of the Royal Meteorological Society. 2012. V.138. P. 2079-2085.
2. Klimova, E.G. The Kalman stochastic ensemble filter with transformation of perturbation ensemble // Numerical Analysis and Applications. 2019. V.12 (1). P. 26�36.
Data assimilation problems for production-destruction models with parameter identification
V. S. Konopleva1,2, A. V. Penenko1
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Novosibirsk State University
Email: v.konopleva@g.nsu.ru
DOI 10.24412/cl-35065-2021-1-01-31
To predict and assess the state of rapidly changing processes, stable data assimilation algorithms are widely used. An example is the process of changing the chemical composition of atmospheric air. To study the dynamics of pollutants in urban conditions, methods of mathematical modeling are used with the assimilation of measurement data of the pollution level obtained at monitoring posts. Data assimilation algorithms restore the missing information about the parameters of the mathematical model in the process of modeling with the input measurement data for the past and current values of the model state functions. We will understand the data assimilation problem as a sequence of related inverse problems [1, 2]. As a basic inverse problem, let us
