CC BY
5This work was supported by the Russian Science Foundation under grant � 20-11-20189.
References
1. Chesnokov A., Liapidevskii V. Hyperbolic model of internal solitary waves in a three-layer stratified fluid // Eur.
Phys. J. Plus. 2020. V. 135. 590.
2. Liapidevskii V., Turbin M., Khrapchenkov F., Yaroshchuk I. Nonlinear internal waves in multilayer shallow water //
J. Appl. Mech. Tech. Phys. 2020. V. 61. P. 45�53.
Particle filters in data assimilation problems for chemical kinetics models
P. M. Golenko
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Email: p.golenko@g.nsu.ru
DOI 10.24412/cl-35065-2021-1-01-23
Methods of data assimilation based on the particle filter [1, 2] are quite a new and promising direction.
The advantage of the algorithms is that they allow us to estimate not only the value of the model state func-
tion based on measurement data, but also the density of the probability distribution of its values. Particle fil-
ters are well parallelized and require only an algorithm for solving a direct problem for their calculation. We
are actively working on the development of particle filters for multidimensional nonlinear problems of geo-
physics with an emphasis on atmospheric and oceanic applications. The paper considers the application of
methods based on a particle filter in nonlinear problems of assimilation of chemical kinetics data [3]. The effi-
ciency of the algorithm is numerically investigated.
References
1. Peter Jan van Leeuwen, Particle filters for high-dimensional geoscience applications: A review � Quarterly Journal
of the Royal Meteorological Society, 21 May 2019.
2. Alban Farchi and Marc Bocquet, Review article:Comparison of local particle filters and new implementations �
EGU, 12 November 2018.
3. Willem Hundsdorfer, Jan Verwer, Numerical Solution of Time-Dependent Advection-Diffusion Reaction
Equations � Originally published by Springer-Verlag Berlin Heidelberg New York in 2003.
Hyperbolized �soft cover� model for calculating stratified flows with a free boundary in a non-hydrostatic
approximation
V. M. Goloviznin1, Pavel A. Maiorov2, Petr A. Maiorov2, A. V. Solovjov2
1Lomonosov Moscow State University
2Nuclear Safety Institute RAS, Moscow
Email: gol@ibrae.ac.ru; pavel.a.mayorov@gmail.com; maiorov.peter@gmail.com solovjev@ibrae.ac.ru
DOI 10.24412/cl-35065-2021-1-01-25
The original system of equations describing the dynamics of a stratified fluid with a free surface in the
Boussinesq approximation, presented in terms of density and pressure variations is elliptic and it is necessary
to solve the Poisson difference equation in its numerical implementation. With a large number of computa-
tional nodes, this procedure requires significant computational resources and complicates the algorithm paral-
lelization on multiprocessor computers.
The hyperbolization of the problem based on the weak compressibility approximation is an alternative op-
tion. In this approach, an equation of state establishes a linear dependence of pressure on the parameter ..
This parameter characterizes the degree of volume deviation of the Lagrangian particle from the initial state:
.P = c2(.
� .0), .0 = 1. Even though its change is described by the continuity equation this parameter does not
coincide with the density. Parameter c is an artificial sound speed. It is determined by the condition that the
parameter . does not deviate from the initial value by more than one percent. The density equation is a
transport type.
The pressure force acting on the free surface returning it to the state of static equilibrium. It can be called
"soft cover" mechanism. This pressure depends on the magnitude of deviation of the free surface from the
equilibrium position. A standard kinematic condition is also set at the liquid boundary.
The explicit-implicit CABARET scheme is used to solve the hyperbolized system, explicit in horizontal direc-
tions and implicit in depth. It makes it possible to use large time steps on grids with thinning of layers to a free
surface. The proposed non-hydrostatic model is verified by laboratory experiments, in which the formation
and propagation of internal bottom waves formed during the rapid extraction of a lock gate separating a dens-
er part of the liquid with a controlled vertical salinity distribution from a homogeneous liquid in a long channel
are investigated. The results are compared with laboratory measurements and calculations using a hydrostatic
model.
Validation of the CABARET-MFSH hydrostatic model for modeling the flows of stratified fluids with a free
surface in laboratory experiments
V. M. Goloviznin1, Pavel A. Maiorov1,2, Petr A. Maiorov1, A. V. Solovjov2
1Lomonosov Moscow State University
2Nuclear Safety Institute, Moscow
Email: gol@ibrae.ac.ru, pavel.a.mayorov@gmail.com, maiorov.peter@gmail.com, solovjev@ibrae.ac.ru
DOI 10.24412/cl-35065-2021-1-01-26
This paper is devoted to the results of validation on two series of laboratory experiments of the new low-
dissipative multilayer hydrostatic model CABARET-MFSH, which describes the dynamics of a fluid with variable
density and a free surface. The computational algorithm of the new model is based on representing a multi-
layer environment as separate layers interacting across interfaces. We call this method hyperbolic decomposi-
tion. An explicit CABARET scheme is used to solve the system of hyperbolic equations in each layer. The
scheme has a second order of approximation and is time reversible. To regularize the multilayer hydrostatic
model, mass and momentum exchange between the layers and the filtration of flux variables are used. The
filtration parameters are determined empirically from the condition of the stability of the algorithm and the
minimality of the scheme viscosity.
In laboratory experiments, the emergence and propagation of bottom internal waves is investigated. They
are formed when the gate is quickly pulled out between a liquid with a controlled vertical salinity distribution
and a homogeneous liquid.
The calculation results are in good agreement with the experimental data.
Changes in the state of the Siberian Arctic seas in the last two decades
E. N. Golubeva, M. V. Kraineva, G. A. Platov, D. F. Yakshina
The Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Email: elen@ommfao.sscc.ru
DOI 10.24412/cl-35065-2021-1-01-27
This report discusses issues related to climatic changes in the ice and water state of the shelf seas of the
Siberian sector of the Arctic. The research is based on analyzing observational data and modeling results using
