Asymptotic preserving space-time discontinuous Galerkin methods for a class of relaxation systems

dc.contributor.advisor James A. Rossmanith
dc.contributor.author Lischke, Anna
dc.contributor.department Mathematics
dc.date 2018-08-11T08:30:09.000
dc.date.accessioned 2020-06-30T02:57:08Z
dc.date.available 2020-06-30T02:57:08Z
dc.date.copyright Thu Jan 01 00:00:00 UTC 2015
dc.date.embargo 2001-01-01
dc.date.issued 2015-01-01
dc.description.abstract <p>Various models derived from the Boltzmann equation can be used to model heat conduction, neutron transport, and gas dynamics. These models arise when one expands the distribution function for the Boltzmann equation in spherical harmonics, which results in singularly perturbed hyperbolic systems scaled by a diffusive relaxation parameter epsilon. In the diffusive limit, the perturbed equations limit to parabolic-type systems such as the heat equation and the advection-diffusion equation. Much work has been done in developing numerical schemes that are useful in the rarefied regime and that preserve the diffusive limit at the discrete level. A method that does this successfully is called asymptotic preserving (AP).</p> <p>One difficulty in using standard numerical methods for these models is that they have a very restrictive CFL condition on time-step size which vanishes in the diffusive limit. Some attempts to overcome this hurdle have used implicit time-integration schemes, but this requires computing the solution to very large linear systems at each time step.</p> <p>Our strategy is to develop a space-time discontinuous Galerkin method that will admit a less restrictive limit on the time-step size and will maintain its order of accuracy as the diffusive relaxation parameter becomes very small.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/etd/14498/
dc.identifier.articleid 5505
dc.identifier.contextkey 7986464
dc.identifier.doi https://doi.org/10.31274/etd-180810-4049
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath etd/14498
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/28683
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/etd/14498/Lischke_iastate_0097M_14910.pdf|||Fri Jan 14 20:21:07 UTC 2022
dc.subject.disciplines Applied Mathematics
dc.subject.keywords Applied Mathematics
dc.subject.keywords discontinuous Galerkin
dc.subject.keywords Finite element method
dc.subject.keywords Scientific computing
dc.title Asymptotic preserving space-time discontinuous Galerkin methods for a class of relaxation systems
dc.type article
dc.type.genre thesis
dspace.entity.type Publication
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
thesis.degree.level thesis
thesis.degree.name Master of Science
File
Original bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
Lischke_iastate_0097M_14910.pdf
Size:
507.31 KB
Format:
Adobe Portable Document Format
Description: