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Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization

Sanghyun Lee, Mary F. Wheeler
2017 Journal of Computational Physics  
We present a novel approach to the simulation of miscible displacement by employing adaptive enriched Galerkin finite element methods (EG) coupled with entropy residual stabilization for transport.  ...  In particular, numerical simulations of viscous fingering instabilities in heterogeneous porous media and Hele-Shaw cells are illustrated.  ...  Wheeler was partially supported by a DOE grant DE-FG02-04ER25617, a Statoil grant STNO-4502931834, and an Aramco grant UTA 11-000320.  ... 
doi:10.1016/j.jcp.2016.10.072 fatcat:2f6pc3rxqnas5ciyez4mxwnifu

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.  ...  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.  ... 
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  
Many processes of highest actuality in the real life are described through systems of equations posed in complex domains.  ...  The focus in this workshop was on novel techniques and ideas in the mathematical modelling, analysis, the numerical discretization and the upscaling of problems as described above.  ...  Also to keep an accurate solution with less triangles, we are investigating the use of a higher order hybridizable discontinuous Galerkin technique, the HHO method [18] , combined with a posteriori error  ... 
doi:10.4171/owr/2014/43 fatcat:cxkazxwlwnaqnmxamofkkhdnru

Models for non-isothermal compositional gas-liquid flow and transport in porous media [article]

Holger Class, Universität Stuttgart, Universität Stuttgart
2009
A large chapter presents example applications that illustrate the basic processes and phenomena by simulation results.  ...  This work deals in particular with the numerical modeling of gas-liquid flow in porous media, thereby considering non-isothermal and compositional effects.  ...  Fingering effects occur when a less-viscous fluid displaces a more-viscous resident fluid.  ... 
doi:10.18419/opus-299 fatcat:toazzx5gq5fc3ddwdnq35ymgom

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

Bernd Flemisch, Universität Stuttgart, Universität Stuttgart
2013
Part C "Open-Source Porous-Media Simulation" deals with the idea of developing such a computer code by means of open-source development techniques.  ...  It is divided into three parts: Part A "Model Coupling" deals with uncoupled and coupled porous-media models in general and describes some of these models in detail.  ...  In order to overcome this deficiency, an algebraic multigrid solver for non-overlapping grids is currently developed within DUNE and will be available for parallel simulations with DuMu x in the future  ... 
doi:10.18419/opus-499 fatcat:ut2pc2ag7bhmvovcmluc5izgmu