Explicit Discontinuous Galerkin Methods for Linear Hyperbolic Problems

Simple item page
dc.contributor.advisorWarburton, Timothy
dc.contributor.committeeMemberSymes, William W.
dc.contributor.committeeMemberEmbree, Mark
dc.creatorAtcheson, Thomas
dc.date.accessioned2013-11-14T16:40:50Z
dc.date.accessioned2013-11-14T16:40:54Z
dc.date.available2013-11-14T16:40:50Z
dc.date.available2013-11-14T16:40:54Z
dc.date.created2013-12
dc.date.issued2013-11-14
dc.date.submittedDecember 2013
dc.date.updated2013-11-14T16:40:57Z
dc.description.abstractDiscontinuous Galerkin methods have many features which make them a natural candidate for the solution of hyperbolic problems. One feature is flexibility with the order of approximation; a user with knowledge of the solution's regularity can increase the spatial order of approximation by increasing the polynomial order of the discontinuous Galerkin method. A marked increase in time-stepping difficulty, known as stiffness, often accompanies this increase in spatial order however. This thesis analyzes two techniques for reducing the impact of this stiffness on total time of simulation. The first, operator modification, directly modifies the high order method in a way that retains the same formal order of accuracy, but reduces the stiffness. The second, optimal Runge-Kutta methods, adds additional stages to Runge-Kutta methods and modifies them to customize their stability region to the problem. Three operator modification methods are analyzed analytically and numerically, the mapping technique of Kosloff/Tal-Ezer the covolume filtering technique of Warburton/Hagstrom , and the flux filtering technique of Chalmers, et al. . The covolume filtering and flux filtering techniques outperform mapping in that they negligibly impact accuracy but yield a reasonable improvement in efficiency. For optimal Runge-Kutta methods this thesis considers five top performing methods from the literature on hyperbolic problems and applies them to an unmodified method, a flux filtered method, and a covolume filtered method. Gains of up to 80\% are seen for covolume filtered solutions applied with optimal Runge-Kutta methods, showing the potential for efficient high order solutions of unsteady systems.
dc.format.mimetypeapplication/pdf
dc.identifier.citationAtcheson, Thomas. "Explicit Discontinuous Galerkin Methods for Linear Hyperbolic Problems." (2013) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/75120">https://hdl.handle.net/1911/75120</a>.
dc.identifier.slug123456789/ETD-2013-12-584
dc.identifier.urihttps://hdl.handle.net/1911/75120
dc.language.isoeng
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.
dc.subjectDiscontinuous Galerkin
dc.subjectTime-stepping
dc.subjectMathematics
dc.titleExplicit Discontinuous Galerkin Methods for Linear Hyperbolic Problems
dc.typeThesis
dc.type.materialText
thesis.degree.departmentComputational and Applied Mathematics
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelMasters
thesis.degree.nameMaster of Arts
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
ATCHESON-THESIS.pdf
Size:
2.61 MB
Format:
Adobe Portable Document Format
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.61 KB
Format:
Item-specific license agreed upon to submission
Description:
Download
Collections
Rice University Electronic Theses and Dissertations