Advanced search options

Advanced Search Options 🞨

Browse by author name (“Author name starts with…”).

Find ETDs with:

in
/  
in
/  
in
/  
in

Written in Published in Earliest date Latest date

Sorted by

Results per page:

You searched for subject:(Arbogast Tao element). One record found.

Search Limiters

Last 2 Years | English Only

No search limiters apply to these results.

▼ Search Limiters


University of Texas – Austin

1. -5063-5889. Numerical analysis of multiphase flows in porous media on non-rectangular geometry.

Degree: PhD, Computational Science, Engineering, and Mathematics, 2017, University of Texas – Austin

Fluid flow through porous media is a subject of common interest in many branches of engineering as well as applied natural science. In this work, we investigate the behavior and numerical treatment of multiphase flow in porous media. To be more specific, we take the sequestration of CO₂ in geological media as an example. Mathematical modeling and numerical study of carbon sequestration helps to predict both short and long-term behavior of CO₂ storage in geological media, which can be a benefit in many ways. This work aims at developing accurate and efficient numerical treatment for problems in porous media on non-rectangular geometries. Numerical treatment of Darcy flow and transport have been developed for many years on rectangular and simplical meshes. However, extra effort is required to extend them to general non-rectangular meshes. In this dissertation work, for flow simulation, we develop new H(div)- conforming mixed finite elements (AT and AT [superscript red] ) which are accurate on cuboidal hexahedra. We also develop the new direct serendipity finite element (DS [subscript r] ), which is H¹ -conforming and accurate on quadrilaterals and a special family of hexahedra called truncated cubes. The use of the direct serendipity finite element reduces the number of degrees of freedom significantly and therefore accelerates numerical simulations. For transport, we use the newly developed direct serendipity elements in an enriched Galerkin method (EG), which is locally conservative. The entropy viscosity stabilization is applied to eliminate spurious oscillations. We test the EG-DS [subscript r] method on problems with diffusion, transport, and coupled flow and transport. Finally, we study two-phase flow in heterogeneous porous media with capillary pressure. We work on a new formulation of the problem and force the continuity of the capillary flux with a modification to conquer the degeneracy. The numerical simulation of two-phase flow is conducted on non-rectangular grids and uses the new elements. Advisors/Committee Members: Arbogast, Todd James, 1957- (advisor), Wheeler, Mary F (committee member), Ghattas, Omar (committee member), Demkowicz, Leszek F (committee member), Hesse, Marc A (committee member).

Subjects/Keywords: Multiphase flow; Porous media; Mixed finite element; H(div)-approximation; Arbogast-Tao element; Arbogast-Correa element; Direct serendipity element; Serendipity element; Enriched Galerkin method; Entropy viscosity stabilization; Capillary flux reconstruction; Heterogeneous capillary pressure; Two-phase flow

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

-5063-5889. (2017). Numerical analysis of multiphase flows in porous media on non-rectangular geometry. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/68171

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Chicago Manual of Style (16th Edition):

-5063-5889. “Numerical analysis of multiphase flows in porous media on non-rectangular geometry.” 2017. Doctoral Dissertation, University of Texas – Austin. Accessed April 10, 2021. http://hdl.handle.net/2152/68171.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7th Edition):

-5063-5889. “Numerical analysis of multiphase flows in porous media on non-rectangular geometry.” 2017. Web. 10 Apr 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-5063-5889. Numerical analysis of multiphase flows in porous media on non-rectangular geometry. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2017. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/2152/68171.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-5063-5889. Numerical analysis of multiphase flows in porous media on non-rectangular geometry. [Doctoral Dissertation]. University of Texas – Austin; 2017. Available from: http://hdl.handle.net/2152/68171

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

.