2 research outputs found
Mixed GMsFEM for linear poroelasticity problems in heterogeneous porous media
Accurate numerical simulations of interaction between fluid and solid play an
important role in applications. The task is challenging in practical scenarios
as the media are usually highly heterogeneous with very large contrast. To
overcome this computational challenge, various multiscale methods are
developed. In this paper, we consider a class of linear poroelasticity problems
in high contrast heterogeneous porous media, and develop a mixed generalized
multiscale finite element method (GMsFEM) to obtain a fast computational
method. Our aim is to develop a multiscale method that is robust with respect
to the heterogeneities and contrast of the media, and gives a mass conservative
fluid velocity field. We will construct decoupled multiscale basis functions
for the elastic displacement as well as fluid velocity. Our multiscale basis
functions are local. The construction is based on some suitable choices of
local snapshot spaces and local spectral decomposition, with the goal of
extracting dominant modes of the solutions. For the pressure, we will use
piecewise constant approximation. We will present several numerical examples to
illustrate the performance of our method. Our results indicate that the
proposed method is able to give accurate numerical solutions with a small
degree of freedoms
A comparison of mixed multiscale finite element methods for multiphase transport in highly heterogeneous media
In this paper, we systemically review and compare two mixed multiscale finite
element methods (MMsFEM) for multiphase transport in highly heterogeneous
media. In particular, we will consider the mixed multiscale finite element
method using limited global information, simply denoted by MMsFEM, and the
mixed generalized multiscale finite element method (MGMsFEM) with residual
driven online multiscale basis functions. Both methods are under the framework
of mixed multiscale finite element methods, where the pressure equation is
solved in the coarse grid with carefully constructed multiscale basis functions
for the velocity. The multiscale basis functions in both methods include local
and global media information. In terms of MsFEM using limited global
information, only one multiscale basis function is utilized in each local
neighborhood while multiple basis are used in MGMsFEM. We will test and compare
these two methods using the benchmark three-dimensional SPE10 model. A range of
coarse grid sizes and different combinations of basis functions (offline and
online) will be considered with CPU time reported for each case. In our
numerical experiments, we observe good accuracy by the two above methods.
Finally, we will discuss and compare the advantages and disadvantages of the
two methods in terms of accuracy and computational costs.Comment: 25 page