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5Mini.symposium
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 localspectral 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 mathematicalmodeling of the seepage into the soil under cryolithozone conditions
S. Stepanov, D. Nikiforov and Al. Grigorev
M. K. Ammosov North.Eastern FederalUniversity, 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 reason,
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.dimensionalmodel problems.
For the case of a three.dimensional, somewhat realistic geometry with a complex surface structure is considered.
We demonstrate the efficiency and accuracy of the proposed method using several representative numerical
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 FederalUniversity, Yakutsk
2Institute for Scientific Computation, Texas A&M University, College Station, TX 77843.3368 & Department of
ComputationalTechnologies
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. Mathematicalmodel
contains a coupled system of equations for pressures in each continuum and effective equation for displacement
with volume force sources that are proportional to the sum of the pressure gradients for each continuum.
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 localspectral
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
