Persistent Link:
http://hdl.handle.net/10150/185688
Title:
Numerical transport in diffusive regimes
Author:
Jin, Shi.
Issue Date:
1991
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:
In highly scattering regimes, the transport equation with anisotropic boundary conditions has a limit in which the leading behavior of its solution is determined by the solution of a diffusion equation with associated boundary conditions. In order for a numerical scheme to be effective in these regimes, it must have both a correct interior diffusion limit and a correct boundary condition limit. The behavior of several numerical methods are studied in these limits and formulas for the resulting diffusion equations and its boundary conditions are derived. Theoretic and numerical results show that with correct diffusion limits, the numerical methods will give promising results with coarse grids throughout the domain, even if the boundary layers are not resolved. We also prove that with correct diffusion limits, the numerical solutions will converge to the transport solution uniformly in ε, although the collision operators have a ε⁻¹ contribution to the truncation error that generally gives rise to a nonuniform consistency with the transport equation for small ε. In last part of this dissertation we study numerical methods for the hyperbolic systems with long time parabolic behavior. In this regime the lower order terms of the hyperbolic systems break the conservation law and the systems become parabolic. Most of the numerical methods for conservation laws fail to capture this long time behavior, as shown in our analysis. We will solve the general Riemann problem of the shallow water equations and use it to modified higher order Godunov schemes in order to capture the long time behavior of the nonlinear river equations.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Dissertations, Academic; Civil engineering
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Levermore, C. David

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleNumerical transport in diffusive regimesen_US
dc.creatorJin, Shi.en_US
dc.contributor.authorJin, Shi.en_US
dc.date.issued1991en_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.abstractIn highly scattering regimes, the transport equation with anisotropic boundary conditions has a limit in which the leading behavior of its solution is determined by the solution of a diffusion equation with associated boundary conditions. In order for a numerical scheme to be effective in these regimes, it must have both a correct interior diffusion limit and a correct boundary condition limit. The behavior of several numerical methods are studied in these limits and formulas for the resulting diffusion equations and its boundary conditions are derived. Theoretic and numerical results show that with correct diffusion limits, the numerical methods will give promising results with coarse grids throughout the domain, even if the boundary layers are not resolved. We also prove that with correct diffusion limits, the numerical solutions will converge to the transport solution uniformly in ε, although the collision operators have a ε⁻¹ contribution to the truncation error that generally gives rise to a nonuniform consistency with the transport equation for small ε. In last part of this dissertation we study numerical methods for the hyperbolic systems with long time parabolic behavior. In this regime the lower order terms of the hyperbolic systems break the conservation law and the systems become parabolic. Most of the numerical methods for conservation laws fail to capture this long time behavior, as shown in our analysis. We will solve the general Riemann problem of the shallow water equations and use it to modified higher order Godunov schemes in order to capture the long time behavior of the nonlinear river equations.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectDissertations, Academicen_US
dc.subjectCivil engineeringen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorLevermore, C. Daviden_US
dc.contributor.committeememberHyman, Macen_US
dc.contributor.committeememberBrio, Moyseyen_US
dc.contributor.committeememberBayly, Bruce J.en_US
dc.identifier.proquest9210295en_US
dc.identifier.oclc712064839en_US
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