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5Section 2
NUMERICAL STATISTICAL MODELING AND MONTE CARLO METHODS
Stochastic model of the joint spatio-temporal field of precipitation and wind speed in the southern part
of the Lake Baikal region
M. S. Akenteva1, V. A. Ogorodnikov1,2, N. A. Kargapolova1,2
1Novosibirsk State University
2Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Email: nkargapolova@gmail.com
DOI 10.24412/cl-35065-2021-1-00-69
The report presents a numerical stochastic model of the joint spatio-temporal field of the wind speed with
a three-hour resolution and semidiurnal precipitation. The model proposed is constructed on the basis of long-
term observation data at an irregular network of meteorological stations positioned in the area of Lake Baikal.
The model is developed under the assumption of the daily non-stationarity of the real joint meteorological
field and its spatial heterogeneity, induced by the physical and geographical features of the considered terrain.
The quality of interpolation of the simulated precipitation field on a regular spatial grid and the possibility of
using the model proposed to study extreme precipitation regimes in the river basins located in the southern
part of the Lake Baikal region are discussed.
The work was supported by the Ministry of Science and Higher Education of the Russian Federation (grant No. 075-
15-2020-787 for implementation of large scientific project "Fundamentals, methods and technologies for digital monitor-
ing and forecasting of the environmental situation on the Baikal natural territory").
Setting unsteady inflow boundary conditions of a stochastic turbulence with the desired autocorrelation
A. V. Alexandrov1, L. W. Dorodnicyn2, A. P. Duben1, D. R. Kolyukhin3
1Keldysh Institute of Applied Mathematics RAS, Moscow
2 Lomonosov Moscow State University
3Trofimuk Institute of Petroleum Geology and Geophysics SB RAS
Email: dorodn@cs.msu.ru
DOI 10.24412/cl-35065-2021-1-00-70
In computational fluid dynamics, synthetic turbulent velocity fields are commonly used for the imposition
of inflow boundary conditions for the LES zone. The inflow artificial turbulent field should be unsteady and
have the same properties, such as autocorrelation, as real turbulent fields. In the work presented, the artificial
turbulent fields are generated with the help of Randomized Spectral Method [1, 2] as the sum of stochastic
Fourier modes, with the time dependence at the boundary using random frequencies, following [3]. An appro-
priate model has been chosen on the base of time correlation analysis�both theoretical and numerical, given
by test LES computations of turbulence in the cube. For comparison, the results for a time filtering method are
also presented.
This work was partially supported by RFBR (Grant 19-51-80001 BRICS_t) and IPGG SB RAS (Project AAAA-A16-
116122810045-9).
References
1. Sabelfeld K. K. Monte Carlo methods in boundary value problems. Springer, Heidelberg�Berlin�New York, 1991.
2. Aleksandrov A. V., Dorodnitsyn L. V., Duben A.P. Generation of three-dimensional homogeneous isotropic
turbulent velocity fields using the Randomized Spectral Method // Mathematical Models and Computer Simulations.
2020. V. 12, N. 3. P. 388�396.
3. Sabelfeld K. K., Kurbanmuradov O. Stochastic Lagrangian models for two-particle motion in turbulent flows //
Monte Carlo Methods Appl. 1997. V. 3, N. 1. P. 53�72.
Application of an economic algorithm for modeling of random variables for simulation of a Poisson point
process
T. A. Averina
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Novosibirsk State University
Email: ata@osmf.sscc.ru
DOI 10.24412/cl-35065-2021-1-00-71
Statistical solution of the problems of analysis, synthesis and filtration for systems of the diffusion-
discontinuous type, requires simulation of inhomogeneous Poisson point process [1]. In order to simulate the
latter, sometimes an algorithm based on the ordinariness property of the process is used. In this article, a
modification of the algorithm is being constructed by using an economic method for modeling of random vari-
ables [2�4]. The developed method is verified by solving test problems
This work was carried out under state contract with ICMMG SB RAS (0251-2021-0002).
References
1. Averina T.A., Rybakov K.A. Using maximum cross section method for filtering jump-diffusion random processes //
Russian Journal of Numerical Analysis and Mathematical Modelling. 2020. V. 35. N. 2. P. 55-67.
2. Mikhailov G.A. Construction of economic Algorithms for the Simulation of Random Variables // U.S.S.R. Computa-
tional Mathematics and Mathematical Physics. 1966. V. 6. N. 6, P. 269--273.
3. Mikhailov G.A. and Voitishek A.V. Chislennoe statisticheskoe modelirovanie. Metody Monte-Karlo (Numerical Sta-
tistical Simulation: Monte Carlo Methods). Moscow: Izd. Tsentr �Akademiya�. 2006. [in Russian]
4. Averina, T.A. New Algorithms for the Statistical Modeling of Inhomogeneous Poisson Ensembles // Computational
Mathematics and Mathematical Physics. 2010. V. 50. N 1. P. 16�23.
Double randomization method for estimating the moments of solution to the coagulation equation
A. V. Burmistrov1,2, M. A. Korotchenko1
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Novosibirsk State University
Email: burm@osmf.sscc.ru, kmaria@osmf.sscc.ru
DOI 10.24412/cl-35065-2021-1-00-72
The problem of estimating the probability moments of linear functionals from the solution to the Smolu-
chowski equation with random coagulation coefficients is considered. For this purpose, we modify the algo-
rithms previously proposed by the authors for solving kinetic problems [1, 2] using the double randomization
method. In addition, a splitting method is proposed to reduce the computational costs of the algorithms [3].
This work was created under the state contract with ICMMG SB RAS (0315-2019-0002).
