scholarly journals Fronts in two‐phase porous media flow problems: The effects of hysteresis and dynamic capillarity

2020 ◽  
Vol 144 (4) ◽  
pp. 449-492
Author(s):  
K. Mitra ◽  
T. Köppl ◽  
I. S. Pop ◽  
C. J. van Duijn ◽  
R. Helmig
Keyword(s):  
Porous Media ◽  
Porous Media Flow ◽  
Two Phase ◽  
Flow Problems ◽  
Dynamic Capillarity

Multiscale estimation with spline wavelets, with application to two-phase porous-media flow

2000 ◽  
Vol 16 (2) ◽  
pp. 315-332 ◽  
Author(s):  
Geir Nævdal ◽  
Trond Mannseth ◽  
Kari Brusdal ◽  
Jan-Erik Nordtvedt
Keyword(s):  
Porous Media ◽  
Porous Media Flow ◽  
Two Phase ◽  
Spline Wavelets

scholarly journals Prediction of Discretization of GMsFEM Using Deep Learning

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 412 ◽  
Author(s):  
Min Wang ◽  
Siu Wun Cheung ◽  
Eric T. Chung ◽  
Yalchin Efendiev ◽  
Wing Tat Leung ◽  
...  
Keyword(s):  
Neural Networks ◽  
Porous Media ◽  
Deep Learning ◽  
Multiscale Model ◽  
Porous Media Flow ◽  
Scale Parameters ◽  
Flow Problems ◽  
Local Problems ◽  
Nonlinear Relation ◽  
Model Reduction Technique

In this paper, we propose a deep-learning-based approach to a class of multiscale problems. The generalized multiscale finite element method (GMsFEM) has been proven successful as a model reduction technique of flow problems in heterogeneous and high-contrast porous media. The key ingredients of GMsFEM include mutlsicale basis functions and coarse-scale parameters, which are obtained from solving local problems in each coarse neighborhood. Given a fixed medium, these quantities are precomputed by solving local problems in an offline stage, and result in a reduced-order model. However, these quantities have to be re-computed in case of varying media (various permeability fields). The objective of our work is to use deep learning techniques to mimic the nonlinear relation between the permeability field and the GMsFEM discretizations, and use neural networks to perform fast computation of GMsFEM ingredients repeatedly for a class of media. We provide numerical experiments to investigate the predictive power of neural networks and the usefulness of the resultant multiscale model in solving channelized porous media flow problems.

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