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:(mesh restrictions). One record found.

Search Limiters

Last 2 Years | English Only

No search limiters apply to these results.

▼ Search Limiters


University of Houston

1. -2158-7723. On Enforcing Maximum Principles and Element-Wise Species Balance for Advective-Diffusive-Reactive Systems.

Degree: Civil and Environmental Engineering, Department of, 2015, University of Houston

This dissertation aims at developing robust numerical methodologies to solve advective-diffusive-reactive systems that provide accurate and physical solutions for a wide range of input data (e.g., Péclet and Damköhler numbers) and for complicated geometries. It is well-known that physical quantities like concentration of chemical species and the absolute temperature naturally attain non-negative values. Moreover, the governing equations of an advective-diffusive-reactive system are either elliptic (in the case of steady-state response) or parabolic (in the case of transient response) partial differential equations, which possess important mathematical properties like comparison principles, maximum-minimum principles, non-negativity, and monotonicity of the solution. It is desirable and in many situations necessary for a predictive numerical solver to meet important physical constraints. For example, a negative value for the concentration in a numerical simulation of reactive-transport will result in an algorithmic failure. The objective of this dissertation is two fold. First, we show that many existing popular numerical formulations, open source scientific software packages, and commercial packages do not inherit or mimic fundamental properties of continuous advective-diffusive-reactive systems. For instance, the popular standard single-field Galerkin formulation produces negative values and spurious node-to-node oscillations for the primary variables in advection-dominated and reaction-dominated diffusion-type equations. Furthermore, the violation is not mere numerical noise and cannot be neglected. Second, we shall provide various numerical methodologies to overcome such difficulties. We critically evaluate their performance and computational cost for a wide range of Péclet and Damköhler numbers. We first derive necessary and sufficient conditions on the finite element matrices to satisfy discrete comparison principle, discrete maximum principle, and non-negative constraint. Based on these conditions, we obtain restrictions on the computational mesh and generate physics-compatible meshes that satisfy discrete properties using open source mesh generators. We then show that imposing restrictions on computational grids may not always be a viable approach to achieve physically meaningful non-negative solutions for complex geometries and highly anisotropic media. We therefore develop a novel structure-preserving numerical methodology for advective-diffusive reactive systems that satisfies local and global species balance, comparison principles, maximum principles, and the non-negative constraint on coarse computational grids. This methodology can handle complex geometries and highly anisotropic media. The proposed framework can be an ideal candidate for predictive simulations in groundwater modeling, reactive transport, environmental fluid mechanics, and modeling of degradation of materials. The framework can also be utilized to numerically obtain scaling laws for complicated problems with non-trivial initial and… Advisors/Committee Members: Nakshatrala, Kalyana Babu (advisor), Willam, Kaspar J. (committee member), Vipulanandan, Cumaraswamy (committee member), Wang, Keh-Han (committee member), Kulkarni, Yashashree (committee member), Lim, Gino J. (committee member).

Subjects/Keywords: Advection-diffusion-reaction equations; non-self-adjoint operators; comparison principles; maximum principles; non-negative constraint; monotone property; monotonicity; local and global species balance; oscillatory chemical reactions; chaotic mixing; mesh restrictions; anisotropic M-uniform meshes; angle conditions; least-squares mixed formulations; convex optimization; Pao's method; Picard's method; Newton-Raphson methods.

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

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

APA (6th Edition):

-2158-7723. (2015). On Enforcing Maximum Principles and Element-Wise Species Balance for Advective-Diffusive-Reactive Systems. (Thesis). University of Houston. Retrieved from http://hdl.handle.net/10657/2001

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

-2158-7723. “On Enforcing Maximum Principles and Element-Wise Species Balance for Advective-Diffusive-Reactive Systems.” 2015. Thesis, University of Houston. Accessed November 20, 2019. http://hdl.handle.net/10657/2001.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

-2158-7723. “On Enforcing Maximum Principles and Element-Wise Species Balance for Advective-Diffusive-Reactive Systems.” 2015. Web. 20 Nov 2019.

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

Vancouver:

-2158-7723. On Enforcing Maximum Principles and Element-Wise Species Balance for Advective-Diffusive-Reactive Systems. [Internet] [Thesis]. University of Houston; 2015. [cited 2019 Nov 20]. Available from: http://hdl.handle.net/10657/2001.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

-2158-7723. On Enforcing Maximum Principles and Element-Wise Species Balance for Advective-Diffusive-Reactive Systems. [Thesis]. University of Houston; 2015. Available from: http://hdl.handle.net/10657/2001

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Not specified: Masters Thesis or Doctoral Dissertation

.