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732 Mini.symposium
Multiscale Finite Element Method, where we construct a multiscale space using solution of the local spectral
problems on the snapshot space related to the coarse grid edges.We present numerical results for the Helmholtz
problem in perforated domain with Dirichlet boundary condition on perforations. Proposed method are
studied for a different wave numbers and numbers of the edge multiscale basis functions.
Embeddeddiscrete fracture model on structured grids
D. Y. Nikiforov
M. K. Ammosov North.Eastern FederalUniversity, Yakutsk
Email: dju92@mail.com
DOI 10.24412/cl.35065.2021.1.02.82
An approximation of the embedded discrete fracture model EDFM by the finite element method is considered.
The paper proposes to use exponential functions instead of the Dirac delta function [1]. With this approach,
instead of a separate computational mesh for fractures, a mesh for a porous medium can be used. The
results of numerical experiments demonstrate the efficiency of the proposed approach.
This work was supported by the Ministry of science and higher education of the Russian Federation, supplementary
agreement N075.02.2020.1542/1, April 29, 2020.
References
1. Nikiforov D. Y., Stepanov S. P. Numerical simulation of the embedded discrete fractures by the finite element
method //J. of Physics: Conference Series.�IOP Publishing, 2019.Vol. 1158. No. 3. P. 032038.
Multiscale finite element technique for mathematical modelling of multi.physics processes
in the near.wellbore region
E. P. Shurina1,2, N. B. Itkina1,3, D. A. Arhipov1,2, D. V. Dobrolubova1,2, A. Yu. Kutishcheva1,2, S. I. Markov1,2,
N. V. Shtabel1,2, E. I. Shtanko1,2
1The Trofimuk Institute of Petroleum Geology and Geophysics SB RAS
2Novosibirsk State Technical University
3Institute of Computational Technologies SBRAS
Email: shurina@online.sinor.ru
DOI 10.24412/cl.35065.2021.1.00.56
In borehole physic, the results of the direct mathematical modelling of multi.physical phenomena are
used to controldrilling and well operation. Electromagnetic and acoustic measurements are the most accessible
indirect methods for determining the thermal, transport and mechanical properties of rock samples in the
near.wellbore zone.Mathematical modelling is one of the technologies used for solving multi.physical problems.
A multi.physical problem is formulated as a system of partialdifferential equations with special interface
conditions coupling mathematical models of physical processes. The near.wellbore region is characterized by a
multi.scale geometric structure,high contrast and anisotropy of physical parameters. The discretization method
should take into account the specifics of the problem and preserve the global regularity of mathematical
models at a discrete level. The paper presents modified variational formulations of multiscale non.conforming
finite element methods for mathematical modelling of electromagnetic and acoustic fields in fluid.saturated
media at various temperatures and mechanical loads. To solve the discretized mathematical models, special
multilevel solvers are developed. The results of three.dimensional mathematical modelling using model rock
samples from the near.wellbore zone are presented.
