Matrix-oriented implementation for the numerical solution of the partial differential equations governing flows and transport in porous media

Handle URI:
http://hdl.handle.net/10754/562300
Title:
Matrix-oriented implementation for the numerical solution of the partial differential equations governing flows and transport in porous media
Authors:
Sun, Shuyu ( 0000-0002-3078-864X ) ; Salama, Amgad ( 0000-0002-4463-1010 ) ; El-Amin, Mohamed ( 0000-0002-1099-2299 )
Abstract:
In this paper we introduce a new technique for the numerical solution of the various partial differential equations governing flow and transport phenomena in porous media. This method is proposed to be used in high level programming languages like MATLAB, Python, etc., which show to be more efficient for certain mathematical operations than for others. The proposed technique utilizes those operations in which these programming languages are efficient the most and keeps away as much as possible from those inefficient, time-consuming operations. In particular, this technique is based on the minimization of using multiple indices looping operations by reshaping the unknown variables into one-dimensional column vectors and performing the numerical operations using shifting matrices. The cell-centered information as well as the face-centered information are shifted to the adjacent face-center and cell-center, respectively. This enables the difference equations to be done for all the cells at once using matrix operations rather than within loops. Furthermore, for results post-processing, the face-center information can further be mapped to the physical grid nodes for contour plotting and stream lines constructions. In this work we apply this technique to flow and transport phenomena in porous media. © 2012 Elsevier Ltd.
KAUST Department:
Computational Transport Phenomena Lab; Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program; Earth Science and Engineering Program
Publisher:
Elsevier BV
Journal:
Computers & Fluids
Issue Date:
Sep-2012
DOI:
10.1016/j.compfluid.2012.07.027
Type:
Article
ISSN:
00457930
Appears in Collections:
Articles; Environmental Science and Engineering Program; Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program; Computational Transport Phenomena Lab

Full metadata record

DC FieldValue Language
dc.contributor.authorSun, Shuyuen
dc.contributor.authorSalama, Amgaden
dc.contributor.authorEl-Amin, Mohameden
dc.date.accessioned2015-08-03T09:59:58Zen
dc.date.available2015-08-03T09:59:58Zen
dc.date.issued2012-09en
dc.identifier.issn00457930en
dc.identifier.doi10.1016/j.compfluid.2012.07.027en
dc.identifier.urihttp://hdl.handle.net/10754/562300en
dc.description.abstractIn this paper we introduce a new technique for the numerical solution of the various partial differential equations governing flow and transport phenomena in porous media. This method is proposed to be used in high level programming languages like MATLAB, Python, etc., which show to be more efficient for certain mathematical operations than for others. The proposed technique utilizes those operations in which these programming languages are efficient the most and keeps away as much as possible from those inefficient, time-consuming operations. In particular, this technique is based on the minimization of using multiple indices looping operations by reshaping the unknown variables into one-dimensional column vectors and performing the numerical operations using shifting matrices. The cell-centered information as well as the face-centered information are shifted to the adjacent face-center and cell-center, respectively. This enables the difference equations to be done for all the cells at once using matrix operations rather than within loops. Furthermore, for results post-processing, the face-center information can further be mapped to the physical grid nodes for contour plotting and stream lines constructions. In this work we apply this technique to flow and transport phenomena in porous media. © 2012 Elsevier Ltd.en
dc.publisherElsevier BVen
dc.subjectFlow and transporten
dc.subjectMatrix-oriented techniquesen
dc.subjectNumerical methodsen
dc.subjectPorous mediaen
dc.titleMatrix-oriented implementation for the numerical solution of the partial differential equations governing flows and transport in porous mediaen
dc.typeArticleen
dc.contributor.departmentComputational Transport Phenomena Laben
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.contributor.departmentEarth Science and Engineering Programen
dc.identifier.journalComputers & Fluidsen
dc.contributor.institutionXi An Jiao Tong Univ, Ctr Computat Geosci, Xian 710049, Peoples R Chinaen
dc.contributor.institutionAEA, Nucl Res Ctr, Cairo 13759, Egypten
dc.contributor.institutionAswan Univ, Fac Sci, Dept Math, Aswan, Egypten
kaust.authorSun, Shuyuen
kaust.authorSalama, Amgaden
kaust.authorEl-Amin, Mohameden
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