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Mixed Multiscale Finite Volume Methods for Elliptic Problems in Two-Phase Flow Simulations

Lijian Jiang, Ilya D. Mishev
2012 Communications in Computational Physics  
AbstractWe develop a framework for constructing mixed multiscale finite volume methods for elliptic equations with multiple scales arising from flows in porous media.  ...  This method uses novel multiscale velocity basis functions that are suited for using global information, which is often needed to improve the accuracy of the multiscale simulations in the case of continuum  ...  Jiang acknowledges the support from the ExxonMobil Upstream Research Company for the research.  ... 
doi:10.4208/cicp.170910.180311a fatcat:jzupqx3ayfa6jh6cfqbx7fbwba

A Multiscale Method for Modeling Transport in Porous Media on Unstructured Corner-Point Grids

Jørg E. Aarnes, Yalchin Efendiev
2008 Journal of Algorithms & Computational Technology  
Multiscale solution methods are currently under active investigation for the simulation of subsurface flow in heterogeneous formations.  ...  In this paper we propose a multiscale method for solving transport equations on a coarse grid.  ...  In Section 3 we present the multiscale mixed finite element method (MsMFEM) [3] that is used to compute flow velocities.  ... 
doi:10.1260/174830108784646616 fatcat:3wyaogepkfhgbkiioqnk76t34e

Multiscale Methods for Model Order Reduction of Non Linear Multiphase Flow Problems [article]

Gurpreet Singh, Wingtat Leung, Mary F. Wheeler
2018 arXiv   pre-print
An expanded mixed finite element formulation is used to separate the spatial scales between non-linear, flow and transport problems.  ...  Numerical simulations for flow and transport in subsurface porous media often prove computationally prohibitive due to property data availability at multiple spatial scales that can vary by orders of magnitude  ...  Generalized mixed multiscale method In this subsection, we will present a numerical result of the generalized mixed multiscale method for black oil equation.  ... 
arXiv:1803.03721v1 fatcat:z2xtzt7xx5caxepbzpb6g2xywm

Multiscale Computations for Flow and Transport in Heterogeneous Media [chapter]

Yalchin Efendiev, Thomas Yizhao Hou
2008 Lecture notes in mathematics  
The purpose of this lecture note is to review some recent advances in developing multiscale finite element (volume) methods for flow and transport in strongly heterogeneous porous media.  ...  In part 2, I will review some recent developments of multiscale finite element (volume) methods.  ...  Mixed finite element methods with limited global information One can carry out the analysis of mixed multiscale finite element method with limited global information.  ... 
doi:10.1007/978-3-540-79574-2_4 fatcat:wcihalffjvfobppsdjxjrlywva

Multiscale Computations for Flow and Transport in Porous Media [chapter]

Thomas Y. Hou
2009 Series in Contemporary Applied Mathematics  
This paper reviews some of the recent advances in developing systematic multiscale methods with particular emphasis on multiscale finite element methods with applications to flow and transport in heterogeneous  ...  This manuscript is not intended to be a general survey paper on this topic. The discussion is limited by the scope of the lectures and expertise of the author.  ...  Mixed finite element methods with limited global information One can carry out the analysis of mixed multiscale finite element method with limited global information.  ... 
doi:10.1142/9789814273268_0003 fatcat:c2otu3os5vd43neqiopwbpfkqy

Meshless techniques for anisotropic diffusion

Annamaria Mazzia, Giorgio Pini, Flavio Sartoretto
2014 Applied Mathematics and Computation  
The latter would allow better use of parallel computers, since time-stepping is essentially a serial process. Moreover, it would be good for the methods to be of high order accuracy.  ...  Transport processes are common in geoscience applications, and find their way into models of, e.g., the atmosphere, oceans, shallow water, subsurface, seismic inversion, and deep earth.  ...  We present complex scenarios of multicomponent reactive transport in 2-D and in 3-D. These scenarios are further developments of the setting given by the MoMaS benchmark.  ... 
doi:10.1016/j.amc.2014.03.032 fatcat:c527226gyfgbffnq4p67qxd7wi

Locally conservative, stabilized finite element methods for variably saturated flow

C.E. Kees, M.W. Farthing, C.N. Dawson
2008 Computer Methods in Applied Mechanics and Engineering  
Standard Galerkin finite element methods for variably saturated groundwater flow have several deficiencies.  ...  Here, we consider conforming finite element discretizations based on a multiscale formulation along with recently developed, local postprocessing schemes.  ...  As a point of reference, we also considered a locally conservative nonconforming finite element approximation that coincides with a mixed hybrid finite element approximations in many cases.  ... 
doi:10.1016/j.cma.2008.06.005 fatcat:r2p7kyyz3zg4zpnpq3cqu6kdta

Adaptive generalized multiscale approximation of a mixed finite element method with velocity elimination [article]

Zhengkang He, Eric T. Chung, Jie Chen, Zhangxin Chen
2020 arXiv   pre-print
In this paper, we propose offline and online adaptive enrichment algorithms for the generalized multiscale approximation of a mixed finite element method with velocity elimination to solve the subsurface  ...  The numerical results also show that with a suitable initial multiscale space that includes all offline basis functions corresponding to relative smaller eigenvalues of local spectral decompositions in  ...  Recently, a generalized multiscale approximation of a mixed finite element method (MFEM) with velocity elimination has been developed in [27] for the subsurface flow problem, which also follows the GMsFEM  ... 
arXiv:2007.08934v1 fatcat:kfilpurzyvfszn53c4yntmob3u

Mass Conservative Domain Decomposition for Porous Media Flow [chapter]

Jan M., Eirik Keilegavlen, Andreas Sandvi
2012 Finite Volume Method - Powerful Means of Engineering Design  
The governing equations for subsurface flow are a set of non-linear partial differential equations of mixed elliptichyperbolic type, and the parameter fields are highly heterogeneous with characteristic  ...  Introduction Understanding flow in subsurface porous media is of great importance for society due to applications such as energy extraction and waste disposal.  ... 
doi:10.5772/38700 fatcat:sq4x7m6invhjverdywpo6cfgoy

A hybrid HDMR for mixed multiscale finite element method with application for flows in random porous media [article]

Lijian Jiang, J. David Moulton, Jia Wei
2013 arXiv   pre-print
To treat the heterogeneity, we use a mixed multiscale finite element method (MMsFEM) to simulate each of derived stochastic models.  ...  A few numerical experiments are carried out for two-phase flows in random porous media and support the efficiency and accuracy of the MMsFEM based on the hybrid HDMR.  ...  Mixed multiscale finite element method.  ... 
arXiv:1211.6510v2 fatcat:qlahhxu3hjggncjbiwqelod7iq

A multiscale multilevel mimetic (M3) method for well-driven flows in porous media

Konstantin Lipnikov, J. David Moulton, Daniil Svyatskiy
2010 Procedia Computer Science  
The multiscale multilevel mimetic (M 3 ) method was designed in [13] for the accurate modeling of two-phase flows in highly heterogeneous porous media on general polygonal meshes.  ...  In this article, it is extended to well-driven flows in porous media. We demonstrate its ability to treat accurately non-orthogonal locally-refined meshes and tensorial material properties.  ...  A similar elimination procedure is often used in mixed-hybrid finite element methods.  ... 
doi:10.1016/j.procs.2010.04.083 fatcat:jbseksm44rehtfkragksduuyha

A Multilevel Multiscale Mimetic (M3) Method for an Anisotropic Infiltration Problem [chapter]

Konstantin Lipnikov, David Moulton, Daniil Svyatskiy
2009 Lecture Notes in Computer Science  
We demonstrate that with an efficient temporal updating strategy for the coarsening parameters, fine-scale accuracy of prominent features in the flow is maintained by the M 3 method.  ...  Recently, a hierarchical approach dubbed the Multilevel Multiscale Mimetic (M 3 ) method, was developed to simulate two-phase flow in porous media.  ...  The authors thank George Zyvoloski (LANL) for suggestions and fruitful discussions relating to the numerical experiment.  ... 
doi:10.1007/978-3-642-01970-8_68 fatcat:ugpkxbswvrdt3garglauurak4m

A multilevel multiscale mimetic (M3) method for two-phase flows in porous media

K. Lipnikov, J.D. Moulton, D. Svyatskiy
2008 Journal of Computational Physics  
We describe a multilevel multiscale mimetic (M 3 ) method for solving twophase flow (water and oil) in a heterogeneous reservoir.  ...  Specifically, with this advance the M 3 method can handle full permeability tensors and general coarsening strategies, which may generate polygonal meshes on the coarse grid.  ...  materials [3, 27] , they were introduced to the subsurface flow modeling community through the Galerkin Multiscale Finite Element Method (MsFEM) [18] .  ... 
doi:10.1016/j.jcp.2008.03.029 fatcat:vwipd6xgwfht7ah5twmbevw72i

Open-source MATLAB implementation of consistent discretisations on complex grids

Knut–Andreas Lie, Stein Krogstad, Ingeborg Skjelkvåle Ligaarden, Jostein Roald Natvig, Halvor Møll Nilsen, Bård Skaflestad
2011 Computational Geosciences  
The grid representation for polyhedral grids in turn affects the efficient implementation of numerical methods for subsurface flow simulations.  ...  Herein, we show examples of multiscale methods and adjoint methods for use in optimisation of rates and placement of wells.  ...  Acknowledgements The research was funded in part by the Research Council of Norway through grants no. 158908, 174551, 175962, 178013 and 186935.  ... 
doi:10.1007/s10596-011-9244-4 fatcat:xv7sbejn7jat7bqwfkjmt3haza

Computational engineering and science methodologies for modeling and simulation of subsurface applications

Mary F. Wheeler, Małgorzata Peszyńska
2002 Advances in Water Resources  
We present several simulation examples which reflect the experiences of the research group at the Center for Subsurface Modeling at The University of Texas at Austin.  ...  We discuss computational engineering and science (CES) methodologies and tools applicable to a variety of subsurface models and their couplings.  ...  Acknowledgements We would like to thank several colleagues affiliated with Center for Subsurface Modeling. Beatrice Rivi e ere  ... 
doi:10.1016/s0309-1708(02)00105-7 fatcat:per2wqssenaltickcykqmnt6mi
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