FINITE-ELEMENT ANALYSIS OF TIME-DEPENDENT CONVECTION DIFFUSION EQUATIONS (PETROV-GALERKIN).

Persistent Link:
http://hdl.handle.net/10150/183930
Title:
FINITE-ELEMENT ANALYSIS OF TIME-DEPENDENT CONVECTION DIFFUSION EQUATIONS (PETROV-GALERKIN).
Author:
YU, CHUNG-CHYI.
Issue Date:
1986
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Petrov-Galerkin finite element methods based on time-space elements are developed for the time-dependent multi-dimensional linear convection-diffusion equation. The methods introduce two parameters in conjunction with perturbed weighting functions. These parameters are determined locally using truncation error analysis techniques. In the one-dimensional case, the new algorithms are thoroughly analyzed for convergence and stability properties. Numerical schemes that are second order in time, third order in space and stable when the Courant number is less than or equal to one are produced. Extensions of the algorithm to nonlinear Navier-Stokes equations are investigated. In this case, it is found more efficient to use a Petrov-Galerkin method based on a one parameter perturbation and a semi-discrete Petrov-Galerkin formulation with a generalized Newmark algorithm in time. The algorithm is applied to the two-dimensional simulation of natural convection in a horizontal circular cylinder when the Boussinesq approximation is valid. New results are obtained for this problem which show the development of three flow regimes as the Rayleigh number increases. Detailed calculations for the fluid flow and heat transfer in the cylinder for the different regimes as the Rayleigh number increases are presented.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Heat -- Convection -- Mathematical models.; Diffusion -- Mathematical models.; Fluid mechanics -- Mathematical models.; Finite element method.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Aerospace and Mechanical Engineering; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Heinrich, Juan C.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleFINITE-ELEMENT ANALYSIS OF TIME-DEPENDENT CONVECTION DIFFUSION EQUATIONS (PETROV-GALERKIN).en_US
dc.creatorYU, CHUNG-CHYI.en_US
dc.contributor.authorYU, CHUNG-CHYI.en_US
dc.date.issued1986en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractPetrov-Galerkin finite element methods based on time-space elements are developed for the time-dependent multi-dimensional linear convection-diffusion equation. The methods introduce two parameters in conjunction with perturbed weighting functions. These parameters are determined locally using truncation error analysis techniques. In the one-dimensional case, the new algorithms are thoroughly analyzed for convergence and stability properties. Numerical schemes that are second order in time, third order in space and stable when the Courant number is less than or equal to one are produced. Extensions of the algorithm to nonlinear Navier-Stokes equations are investigated. In this case, it is found more efficient to use a Petrov-Galerkin method based on a one parameter perturbation and a semi-discrete Petrov-Galerkin formulation with a generalized Newmark algorithm in time. The algorithm is applied to the two-dimensional simulation of natural convection in a horizontal circular cylinder when the Boussinesq approximation is valid. New results are obtained for this problem which show the development of three flow regimes as the Rayleigh number increases. Detailed calculations for the fluid flow and heat transfer in the cylinder for the different regimes as the Rayleigh number increases are presented.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectHeat -- Convection -- Mathematical models.en_US
dc.subjectDiffusion -- Mathematical models.en_US
dc.subjectFluid mechanics -- Mathematical models.en_US
dc.subjectFinite element method.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineAerospace and Mechanical Engineeringen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorHeinrich, Juan C.en_US
dc.contributor.committeememberPearlstein, Arne J.en_US
dc.contributor.committeememberChen, C. F.en_US
dc.identifier.proquest8702358en_US
dc.identifier.oclc697842025en_US
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