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52. A Study Of Terrain-Induced Slugging In Two-Phase Flow Pipelines V. De Henaut and G. D. Raithby Department of
Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3GI (Received 28 April 1994; in revised
form 4 November 1994).
3. Badie S., Hale C.P., Lawrence C.J., Hewitt G.F. Pressure gradient and holdup in horizontal two-phase gas�liquid
flows with low liquid loading. // Int. J. Multiphase Flow 2000. - 26, 1525�1543.
The problem of retrieval the methane profiles in the Earth�s atmosphere from high-resolution IR spectra
P. A. Chistyakov1,2, I. V. Zadvornykh2, K. G. Gribanov2
1Krasovskii Institute of Mathematics and Mechanics UB RAS
2Ural Federal University, Ekaterinburg
Email: pavel.chistyakov@urfu.ru, ilia.zadvornyh@urfu.ru, kgribanov@remotesensing.ru
DOI 10.24412/cl-35065-2021-1-01-21
Here we present some results of modified Levenberg-Marquardt method [1] applicability for solving inverse
problems of greenhouse gases remote sensing in Earth�s atmosphere. The computational experiments were per-
formed to retrieve the vertical profile of the main methane isotopologue from the thermal IR synthetic spectra of
IASI/MetOp spectrometer. The noise parameters were set equivalent to sensor characteristics. The optimal esti-
mation method implemented in FIRE-ARMS software [2] was used for solving the inverse problem. The data of
the retrospective climate analysis CAMS GHG Flux Inversions [3] were used as an initial guess and a statistical set
of profiles. The computational experiment showed convergence and accuracy of the proposed method, which,
however, turned out to be more computationally expensive than Gauss � Newton method.
This work is supported by the Russian Science Foundation grant � 18-11-00024-�.
References
1. Vasin, V.V., Perestoronina, G.Y. �The Levenberg-Marquardt method and its modified versions for solving nonlinear
equations with application to the inverse gravimetry problem�, Proc. Steklov Inst. Math. 280, 174�182 (2013) .
2. Gribanov, K.G., Zakharov, V.I., Tashkun, S.A., Tyuterev, Vl.G., �A New Software Tool for Radiative Transfer
Calculations and its application to IMG/ADEOS data�, JQSRT 68(4), 435-451, (2001).
3. �CAMS Green House Gases Flux Inversions,� https://apps.ecmwf.int/datasets/data/cams-ghg-inversions/
(20 December 2020).
Modelling of internal solitary waves in a multilayer stratified fluid
V. E. Ermishina1,2, V. Yu. Liapidevskii1,2, A. A. Chesnokov1,2
1Lavrentyev Institute of Hydrodynamics
2Novosibirsk State University
Email: eveyrg@gmail.com
DOI 10.24412/cl-35065-2021-1-01-22
We present a hyperbolic model describing the propagation of internal waves in a stratified shallow water
with a non-hydrostatic pressure distribution in two external layers and an arbitrary number of internal hydro-
static layers, which is an extension of the models from [1, 2]. The construction of the hyperbolic model is
based on the use of additional instantaneous variables. This allows the reduction of the dispersive multi-layer
Green�Naghdi model to a first-order system of evolution equations.
Stationary solutions of the motion equations are investigated and conditions for the formation of the soli-
tary waves are formulated. The model was verified by comparison with the results of field observations and
calculations using two-dimensional equations. Numerical simulation of the propagation of non-stationary non-
linear wave packets in a multilayer fluid has been performed.
This 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:
