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Geometric multigrid methods for Darcy-Forchheimer flow in fractured porous media [article]

Andrés Arrarás, Francisco J. Gaspar, Laura Portero, Carmen Rodrigo
2018 arXiv   pre-print
In this paper, we present a monolithic multigrid method for the efficient solution of flow problems in fractured porous media.  ...  Specifically, we consider a mixed-dimensional model which couples Darcy flow in the porous matrix with Forchheimer flow within the fractures.  ...  In this work, we propose a monolithic multigrid method for solving the Darcy-Forchheimer flow in a fractured porous media.  ... 
arXiv:1811.02988v1 fatcat:3n3bigcijjfzpklrfrfyd445qq

Mixed-Dimensional Geometric Multigrid Methods for Single-Phase Flow in Fractured Porous Media

Andrés Arrarás, Francisco J. Gaspar, Laura Portero, Carmen Rodrigo
2019 SIAM Journal on Scientific Computing  
This paper deals with the efficient numerical solution of single-phase flow problems in fractured porous media.  ...  \bfK \bfe \bfy \bfw \bfo \bfr \bfd \bfs . fracture network, fractured porous media, monolithic multigrid method, singlephase flow, Vanka smoother \bfA \bfM \bfS \bfs \bfu \bfb \bfj \bfe \bfc \bft \bfc  ...  Monolithic multigrid methods for mixed-dimensional elliptic problems. In this work, we propose an efficient monolithic geometric multigrid solver for flow in fractured porous media.  ... 
doi:10.1137/18m1224751 fatcat:kf35pzetebf2doy2cmprpppbqe

Monolithic mixed-dimensional multigrid methods for single-phase flow in fractured porous media [article]

Andrés Arrarás, Francisco J. Gaspar, Laura Portero, Carmen Rodrigo
2018 arXiv   pre-print
This paper deals with the efficient numerical solution of single-phase flow problems in fractured porous media.  ...  A monolithic multigrid method is proposed for solving two-dimensional arbitrary fracture networks with vertical and/or horizontal possibly intersecting fractures.  ...  Monolithic multigrid methods for mixed-dimensional elliptic problemsIn this work, we propose an efficient monolithic multigrid solver for flow in fractured porous media.  ... 
arXiv:1811.01264v1 fatcat:ff7si4k6ebdifearg4qtzlqawy

Flow Mechanism and Simulation Approaches for Shale Gas Reservoirs: A Review

Tao Zhang, Shuyu Sun, Hongqing Song
2018 Transport in Porous Media  
In mechanism, it is found that gas adsorption process can be concluded into different isotherm models for various reservoir basins.  ...  Flow mechanism and equations vary with different Knudsen number, which could be figured out in two ways: Molecular Dynamics (MD) and Lattice Boltzmann Method (LBM).  ...  Conway, "Beyond beta factors: A complete model for 637 darcy, forchheimer, and trans-forchheimer flow in porous media," 2004. 638 [13] T. Babadagli, S. Raza, X. Ren, and K.  ... 
doi:10.1007/s11242-018-1148-5 fatcat:cxlfsk4jabhgxekpg7sygploii

Meshless techniques for anisotropic diffusion

Annamaria Mazzia, Giorgio Pini, Flavio Sartoretto
2014 Applied Mathematics and Computation  
Moreover, it would be good for the methods to be of high order accuracy.  ...  A good numerical method would be locally mass conservative, produce no or minimal over/under-shoots, produce minimal numerical diffusion, and require no CFL time-step limit for stability.  ...  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

Reactive Flows in Deformable, Complex Media

Margot Gerritsen, Jan Martin Nordbotten, Iuliu Sorin Pop, Barbara Wohlmuth
2014 Oberwolfach Reports  
Such kind of problems are encountered as mathematical models in the subsurface, material science, or biological systems.The emerging mathematical models account for various processes at different scales  ...  Many processes of highest actuality in the real life are described through systems of equations posed in complex domains.  ...  Talbot) The miscible flow in porous media problem.  ... 
doi:10.4171/owr/2014/43 fatcat:cxkazxwlwnaqnmxamofkkhdnru

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

Mary F. Wheeler, Małgorzata Peszyńska
2002 Advances in Water Resources  
In the CES tools area, we discuss a few representative programming tools and technologies.  ...  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.  ...  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

A brief introduction to homogenization and miscellaneous applications

Grégoire Allaire
2012 ESAIM: Proceedings and Surveys  
Several applications of the method are given: derivation of Darcy's law for flows in porous media, derivation of the porosity model and long time behavior of a diffusion equation.  ...  Plusieurs applications de la méthode sont données: dérivation de la loi de Darcy pour desécoulements en milieux poreux, dérivation du modèle de double porosité et comportement en temps grand d'uneéquation  ...  Homogenization of diffusion equations Double Permeability This subsection is devoted to the derivation of the so-called double porosity model for describing single-phase flows in fractured porous media  ... 
doi:10.1051/proc/201237001 fatcat:tusxh7trpncfxc6oftguuji5si

Fluid flow in porous media : A combined numerical and experimental approach

Philipp Eichheimer
For this reason it is of major importance for several geoscience disciplines, including Hydrogeology, Petrophysics and Volcanology to investigate fluid flow and its related processes on various scales.  ...  Until now the distribution and total amount of water in Earth's mantle is under debate and estimates for water storage in the deeper mantle range from 0.25 - 4 ocean masses.  ...  We thank Kirill Gerke and an anonymous reviewer for their constructive comments that helped to improve the manuscript considerably.  ... 
doi:10.15495/epub_ubt_00004865 fatcat:mjdjb4h6fjfc3pq6o63vbg5ire

Numerical coupling of Navier-Stokes and Darcy flow for soil-water evaporation [article]

Christoph Grüninger, Universität Stuttgart, Universität Stuttgart
The objective of this work is to develop algorithms and provide a framework for an efficient coupling of free flow and porous-medium flow to simulate porous-medium-soil-water evaporation.  ...  As the pressure has different orders in the free-flow and porous-medium-flow subdomains, the coupling is not straightforward.  ...  The convergence of these geometric multigrid methods is faster, but the implementation needs access to the grid management.  ... 
doi:10.18419/opus-9657 fatcat:pur4gklhorhexfhsoqijirgnie

Discrete fracture modeling of multi-phase flow and deformation in fractured poroelastic media [article]

Dennis Gläser, Universität Stuttgart
In dieser Arbeit werden verschiedene Modellkonzepte und Diskretisierungsverfahren zur numerischen Simulation von Mehrphasenströmungen in deformierbaren und geklüfteten porösen Medien präsentiert und vergleichend  ...  Figure 3 . 1 - 31 Model concept for flow in fractured porous media.  ...  Mathematical models for flow and deformation in fractured porous media This chapter is devoted to extending the concepts of the previous chapter to fractured porous media.  ... 
doi:10.18419/opus-11040 fatcat:6pv26zd4ena45pvva26tlfiynu

Tackling coupled problems in porous media : development of numerical models and an open source simulator [article]

Bernd Flemisch, Universität Stuttgart, Universität Stuttgart
"Locally Conservative Discretization Methods," as treated in Part B, are a fundamental ingredient of reasonable numerical models for porous media flow and transport processes.  ...  Flow and transport processes in porous media are the governing processes in a large variety of geological, technical and biological systems.  ...  just called it a new formulation for two-phase flow in porous media.  ... 
doi:10.18419/opus-499 fatcat:ut2pc2ag7bhmvovcmluc5izgmu

Domain decomposition methods for multiphysics problems

Tommaso Vanzan, Martin Jakob Gander
We then consider the Stokes-Darcy coupling which is a mathematical model to describe the flow of a Newtonian fluid which interacts with a porous medium.  ...  We then introduce discrete fracture networks, which are advanced mathematical models to simulate flows in a fractured medium, and we provide a theoretical analysis of the scalability of the optimized Schwarz  ...  Scalability analysis for Discrete Fracture Network Discrete fracture networks (DFNs) are advanced mathematical models to study flows in fractured media.  ... 
doi:10.13097/archive-ouverte/unige:143037 fatcat:n4hfmpes3jbxjkjar5zesgatla

Design of an endoscopic 3-D Particle-Tracking Velocimetry system and its application in flow measurements within a gravel layer

Michael Klar
flow of fluids.  ...  The efforts of a child trying to dam a small stream flowing in the street and his surprise at the strange way the water works its way out has its analog in our attempts over the years to understand the  ...  Flow measurements in/over porous media This section reviews some results of experimental flow measurements in/over porous media.  ... 
doi:10.11588/heidok.00005961 fatcat:6qyahazp3zggppyiubkt7zxjdm

Mixed-dimension models for flow and transport processes in porous media with embedded tubular network systems [article]

Timo Koch, Universität Stuttgart
The method is developed for isotropic, as well as anisotropic porous media. Furthermore, a new mixed-dimension embedded model for tissue perfusion and NMR signal generation is presented.  ...  Conceptually, such systems can be described as porous media with embedded tubular transport networks. We describe numerical methods for the simulation of such systems.  ...  for the description of xylem flow and water and nutrient uptake, see Dunbabin et al. (2013) for a review.  ... 
doi:10.18419/opus-10975 fatcat:vnmu7wfyk5c6ffzoth222qcvjy
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