Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Multiscale Finite Element method for multicontinua
  unsaturated flow problems in fractured porous media   In this paper, we present a multiscale method for simulations of the
multicontinua unsaturated flow problems in heterogeneous fractured porous
media. The mathematical model is described by the system of Richards equations
for each continuum that coupled by the specific transfer term. To illustrate
the idea of our approach, we consider a dual continua background model with
discrete fractures networks that generalized as a multicontinua model for
unsaturated fluid flow in the complex heterogeneous porous media. We present
fine grid approximation based on the finite element method and Discrete
Fracture Model approach. In this model, we construct an unstructured fine grid
that take into account a complex fracture geometries for two and three
dimensional formulations. Due to construction of the unstructured grid, the
fine grid approximation leads to the very large system of equations. For
reduction of the discrete system size, we develop a multiscale method for
coarse grid approximation of the coupled problem using Generalized Multiscale
Finite Element Method. In this method, we construct a coupled multiscale basis
functions that used to construct highly accurate coarse grid approximation. The
multiscale method allowed us to capture detailed interactions between multiple
continua. We investigate accuracy of the proposed method for the several test
problems in two and three dimensional formulations. We present a comparison of
the relative error for different number of basis functions and for adaptive
approach. Numerical results illustrate that the presented method provide
accurate solution of the unsaturated multicontinua problem on the coarse grid
with huge reduction of the discrete system size.

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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
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The categories of this paper are: econ
29
The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an