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An Arbitrary-Order Scheme on Generic Meshes for Miscible Displacements in Porous Media

Daniel Anderson, Jérôme Droniou
<span title="">2018</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wbdvoluxebgjhn3wq3qsnldey4" style="color: black;">SIAM Journal on Scientific Computing</a> </i> &nbsp;
We design, analyse and implement an arbitrary order scheme applicable to generic meshes for a coupled elliptic-parabolic PDE system describing miscible displacement in porous media.  ...  The discretisation is based on several adaptations of the Hybrid-High-Order (HHO) method due to Di Pietro et al. [Computational Methods in Applied Mathematics, 14(4), (2014)].  ...  The authors would like to thank Daniele Di Pietro and Matteo Cicuttin for giving us access to the hho software platform, 1 which served as an invaluable starting point for our implementation.  ... 
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Page 2820 of Mathematical Reviews Vol. , Issue 99d [page]

<span title="">1991</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The FEM for a model of compressible miscible displacement in porous media is studied. The model includes molecular diffu- sion and mechanical dispersion.  ...  (Q)) norm of FEM for a model for compressible miscible displacement in porous media. (English summary) Numer. Math. J. Chinese Univ. (English Ser.) 4 (1995), no. 2, 222-236.  ... 
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Page 1160 of Mathematical Reviews Vol. , Issue 84c [page]

<span title="">1984</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
in porous media.  ...  We derive stability and convergence results for a second-order semi-implicit scheme and for the leapfrog scheme.” Eilbeck, J.  ... 
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A numerical study of two-phase miscible flow through porous media with a Lagrangian model

M Jalal Ahammad, Jahrul M Alam
<span title="2017-04-30">2017</span> <i title="SAGE Publications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jmkeqlquhjddzprz5xbqx74xka" style="color: black;">The Journal of Computational Multiphase Flows</a> </i> &nbsp;
The multiphase flow mechanism in miscible displacement through porous media is an important topic in various applications, such as petroleum engineering, low Reynolds number suspension flows, dusty gas  ...  In this work, a streamline-based Lagrangian methodology is extended for an efficient numerical approach to handle dispersion and diffusion of solvent saturation during a miscible flow.  ...  a miscible displacement For a fluid flow through an isotropic porous media, the dispersion depends largely on the velocity field [52, 53] .  ... 
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Analytical and variational numerical methods for unstable miscible displacement flows in porous media

Guglielmo Scovazzi, Mary F. Wheeler, Andro Mikelić, Sanghyun Lee
<span title="">2017</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/f7kkigxhzjakref5b42jt4uoya" style="color: black;">Journal of Computational Physics</a> </i> &nbsp;
The miscible displacement of one fluid by another in a porous medium has received considerable attention in subsurface, environmental and petroleum engineering applications.  ...  Jim Douglas Jr., for his seminal contributions to miscible displacement and variational numerical methods.  ...  More recent work [268, 269] featured higher-order DG methods for miscible displacement viscous fingering problems in heterogeneous porous media.  ... 
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Dynamics of a Highly Viscous Circular Blob in Homogeneous Porous Media

Vandita Sharma, Satyajit Pramanik, Manoranjan Mishra
<span title="2017-06-11">2017</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5bqnhgw7njc53i7otzqblwexk4" style="color: black;">Fluids</a> </i> &nbsp;
Viscous fingering is ubiquitous in miscible displacements in porous media, in particular, oil recovery, contaminant transport in aquifers, chromatography separation, and geological CO 2 sequestration.  ...  We use the finite element method (FEM)-based COMSOL Multiphysics simulator to simulate miscible displacements in homogeneous porous media with very large viscosity contrasts.  ...  Acknowledgments: Vandita Sharma acknowledges Srikant Shekhar Padhee, Indian Institute of Technology Ropar for various fruitful discussions on finite element method.  ... 
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Numerical solutions of the incompressible miscible displacement equations in heterogeneous media

Jizhou Li, Beatrice Riviere
<span title="">2015</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gctv3v6plrgwthusala4ydxxeq" style="color: black;">Computer Methods in Applied Mechanics and Engineering</a> </i> &nbsp;
This paper presents a numerical method based on mixed finite element, discontinuous Galerkin methods in space and high order Runge-Kutta method in time for solving the miscible displacement problem.  ...  The simulation shows robustness of the method for heterogeneous media with highly varying permeabilities.  ...  We propose a new numerical method of arbitrary order for solving the incompressible miscible displacement problem in heterogeneous media.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cma.2014.10.048">doi:10.1016/j.cma.2014.10.048</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ufeaiuhqv5ba3eprdcbbawphue">fatcat:ufeaiuhqv5ba3eprdcbbawphue</a> </span>
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Page 4789 of Mathematical Reviews Vol. , Issue 86j [page]

<span title="">1986</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Numér. 17 (1983), no. 1, 17-33; MR 84f:76047] for approximating the solution of the equations describing miscible displacement in porous media is proposed and analyzed in a periodic setting.  ...  Similar results are briefly discussed for the one-parameter family of completely conservative difference schemes and remarks on the possible generalizations of the obtained results in various directions  ... 
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Page 4372 of Mathematical Reviews Vol. , Issue 2002F [page]

<span title="">2002</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
in porous media.  ...  A new mixed finite element method is discussed for solving a system of nonlinear parabolic equations that governs miscible displacement of one compressible fluid by another in a porous medium.  ... 
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Page 2459 of Mathematical Reviews Vol. , Issue 96d [page]

<span title="">1996</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Summary: “A model for completely compressible miscible dis- placement in porous media is studied.  ...  (E-UPBCE-NM; Barcelona) A general algorithm for compressible and incompressible flow. II. Tests on the explicit form.  ... 
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Page 1312 of Mathematical Reviews Vol. , Issue 99b [page]

<span title="">1991</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Summary: “Numerical approximation by the Galerkin method for equations governing completely compressible miscible displace- ment with molecular diffusion and dispersion in porous media is 76 FLUID MECHANICS  ...  The method generalizes the method of Collins, Collela, and Glaz by providing an explicit-to-implicit switching criterion that is suitable for use on unstructured meshes.  ... 
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Complex Boundary Value Problems of Nonlinear Differential Equations: Theory, Computational Methods, and Applications

Xinguang Zhang, Yong Hong Wu, Dragoş-Pătru Covei, Xinan Hao
<span title="">2013</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dgcr32e3abazpn7i4ocwedp3fa" style="color: black;">Abstract and Applied Analysis</a> </i> &nbsp;
Acknowledgment Here, we would like to thank all the authors and reviewers of the papers for their excellent contributions. Xinguang Zhang Yong Hong Wu Dragos ¸-Pȃtru Covei Xinan Hao  ...  schemes on grids with local refinement in time for two-dimensional compressible miscible displacement flow in porous media.  ...  In the paper titled "A finite difference scheme for compressible miscible displacement flow in porous media on grids with local refinement in time, " the author constructed and studied finite difference  ... 
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Meshless techniques for anisotropic diffusion

Annamaria Mazzia, Giorgio Pini, Flavio Sartoretto
<span title="">2014</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xkk23xlywfez5l246cnmlit4qq" style="color: black;">Applied Mathematics and Computation</a> </i> &nbsp;
Moreover, it would be good for the methods to be of high order accuracy.  ...  Our objective is to simulate transport processes over very long time periods, as needed in, e.g., the simulation of geologic carbon sequestration.  ...  We show how to solve the equations using a global implicit approach in an efficient way, and we present the derived computational results.  ... 
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Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization

Sanghyun Lee, Mary F. Wheeler
<span title="">2017</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/f7kkigxhzjakref5b42jt4uoya" style="color: black;">Journal of Computational Physics</a> </i> &nbsp;
Moreover, EG has fewer degrees of freedom in comparison with discontinuous Galerkin (DG) and an efficient flow solver has been derived which allows for higher order schemes.  ...  Dynamic adaptive mesh refinement is applied in order to save computational cost for large-scale three dimensional applications.  ...  Wheeler was partially supported by a DOE grant DE-FG02-04ER25617, a Statoil grant STNO-4502931834, and an Aramco grant UTA 11-000320.  ... 
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Page 3269 of Mathematical Reviews Vol. , Issue 98E [page]

<span title="">1998</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Summary: “A numerical method is studied for compressible mis- cible displacement in porous media.  ...  Multidimensional upwind schemes for the 3D Euler equations on unstructured tetrahedral meshes.  ... 
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