CC BY
21The research was supported by RSF Project No. 20-71-00134 (coupled heat and mass transfer), Project No. 0266-
2019-0007 (hydrodynamics and acoustics), Project No. 0331-2019-0015 (electromagnetism).
Analysis of ionospheric irregularities based on multi-instrumental data
D. Sidorov1,2, Yu. Yasukevuch1, E. Astafyeva3, A. Garashenko1, A. Yasyukevich1, A. Oinats1, A. Vesnin1
1Institute of Solar-Terrestrial Physics SB RAS
2Institute of Energy Systems SB RAS
3Universite de Paris, Institut de Physique du Globe de Paris, CNRS UMR 7154, France
Email: contact.dns@gmail.com
DOI 10.24412/cl-35065-2021-1-03-06
The most complex ionospheric phenomena occur in the areas of auroral ovals. These areas are character-
ised by intense small-scale ionospheric inhomogeneities that exist in both calm and disturbed geomagnetic
conditions. Such irregularities could result in radio wave scattering, GNSS (global navigation satellite system)
positioning quality deterioration, failures in radio communication, etc. GNSS ROTI (rate of total electron con-
tent index) datasets along with other datasets are available to study complex dynamics of ionospheric irregu-
larities. This report analyses the auroral oval dynamics datasets, based on GNSS global network, coherent ra-
dars data, and satellite data. The SIMuRG system (https://simurg.iszf.irk.ru/) is employed. The auroral oval re-
gions corresponds to high values of ROTI, therefore it is possible to separate their location from mid-latitude
data. Coherent scatter radars record signal scattering from the oval boundary. The SuperDARN-like radars lo-
cated in Russia were employed. Satellite data shows sharp variations in field-aligned currents. During magnetic
storms the oval expands equatorward, and small-scale irregularities shifts to mid-latitudes. All the data show
close positions of the oval boundary. The latter makes it possible to use the datasets of different modalities to
estimate the oval boundary. Some advance was achieved by computer vision techniques to find the auroral
oval boundary in the Northern hemisphere. The techniques implemented mathematical morphology to ex-
pand data and decrease data gaps, Otsu techniques and K-means to cluster image data.
This work was supported by the Russian Science Foundation (project RSF 17-77-20005).
Mixed generalized multiscale finite element method for flow problem in thin domains
D. A. Spiridonov1, M. V. Vasilyeva1,2, Ya. Efendiev3, E. Chung4, M. Wang 5
1M. K. Ammosov North-Eastern Federal University, Yakutsk
2Institute for Scientific Computation, Texas A&M University
3Department of Mathematics & Institute for Scientific Computation (ISC), Texas A&M University, College
Station, Texas, USA
4Department of Mathematics, The Chinese University of Hong Kong (CUHK), Hong Kong SAR
5Duke University (Durham), USA
Email: d.stalnov@mail.ru
DOI 10.24412/cl-35065-2021-1-02-83
In this work, we consider the construction of the Mixed Generalized Multiscale Finite Element Method
approximation on a coarse grid for an elliptic problem in thin two-dimensional domains. We consider the ellip-
tic equation with homogeneous boundary conditions on the domain walls. For reference solution of the prob-
lem, we use a Mixed Finite Element Method on a fine grid that resolves complex geometry on the grid level. To
construct a lower dimensional model, we use the Mixed Generalized Multiscale Finite Element Method, where
we present the construction of the multiscale basis functions for velocity fields. The construction is based on
the definition of the local snapshot space that takes all possible flows on the interface between coarse cells
into account. In order to reduce the size of the snapshot space, we solve a local spectral problem. We present
a convergence analysis of the presented multiscale method. Numerical results are presented for two-
dimensional problems in three testing geometries along with the errors associated to different number of the
multiscale basis functions used for velocity field. Numerical investigations are conducted for problems with
homogeneous and heterogeneous properties respectively.
Multiscale mathematical modeling of the seepage into the soil under cryolithozone conditions
S. Stepanov, D. Nikiforov and Al. Grigorev
M. K. Ammosov North-Eastern Federal University, Yakutsk
Email: cepe2a@inbox.ru
DOI 10.24412/cl-35065-2021-1-02-84
In this work, the numerical modelling of fluid seepage in the presence of permafrost in heterogeneous
soils is considered. The multiphysics model consists of the coupled Richards� equation and the Stefan problem.
These problems often contain heterogeneities due to variations of soil properties. In the paper, we design a
multiscale simulation method based on Generalized Multiscale Finite Element Method (GMsFEM). For this rea-
son, we design coarse-grid spaces for this multiphysics problem and design algorithms for solving the overall
problem. Numerical simulations are carried out on two-dimensional and three-dimensional model problems.
For the case of a three-dimensional, somewhat realistic geometry with a complex surface structure is consid-
ered. We demonstrate the efficiency and accuracy of the proposed method using several representative nu-
merical results.
This work was (partially) supported by the Foundation mega-grant of the Russian 230 Federation Government
N14.Y26.31.0013.
Generalized Multiscale Finite Element Method for the poroelasticity problem in multicontinuum media
A. A. Tyrylgin1, M. V. Vasilyeva2, D. A. Spiridonov1, E. T. Chung3
1 M. K. Ammosov North-Eastern Federal University, Yakutsk
2Institute for Scientific Computation, Texas A&M University, College Station, TX 77843-3368 & Department of
Computational Technologies
3Department of Mathematics, The Chinese University of Hong Kong (CUHK), Hong Kong SAR
Email: aa.tyrylgin@mail.ru
DOI 10.24412/cl-35065-2021-1-02-85
In this paper, we consider a poroelasticity problem in heterogeneous multicontinuum media that is widely
used in simulations of the unconventional hydrocarbon reservoirs and geothermal fields. Mathematical model
contains a coupled system of equations for pressures in each continuum and effective equation for displace-
ment with volume force sources that are proportional to the sum of the pressure gradients for each continu-
um. To illustrate the idea of our approach, we consider a dual continuum background model with discrete
fracture networks that can be generalized to a multicontinuum model for poroelasticity problem in complex
heterogeneous media. We present a fine grid approximation based on the finite element method and Discrete
Fracture Model (DFM) approach for two and three-dimensional formulations. The coarse grid approximation is
constructed using the Generalized Multiscale Finite Element Method (GMsFEM), where we solve local spectral
problems for construction of the multiscale basis functions for displacement and pressures in multicontinuum
media. We present numerical results for the two and three dimensional model problems in heterogeneous
