Quadrature-based moment methods: High-order realizable schemes and multi-physics applications

dc.contributor.advisor Z J. Wang
dc.contributor.advisor Rodney O. Fox
dc.contributor.author Vikas, Varun
dc.contributor.department Aerospace Engineering
dc.date 2018-08-11T13:27:58.000
dc.date.accessioned 2020-06-30T02:46:16Z
dc.date.available 2020-06-30T02:46:16Z
dc.date.copyright Sun Jan 01 00:00:00 UTC 2012
dc.date.embargo 2013-06-05
dc.date.issued 2012-01-01
dc.description.abstract <p>Kinetic equations occur in mesoscopic models for many physical phenomena. The direct solution of the kinetic equation is prohibitively expensive due to the high dimensionality of the space of independent variables. A viable alternative is to reformulate the problem in terms of the moments of the distribution function. Recently, a suite of quadrature-based moment methods has been developed for approximating solutions to kinetic equations. This suite of quadrature-based moment methods has several desirable properties that makes it more efficient and robust compared to the other moment methods. Despite these desirable properties, there is often a bottleneck associated with these methods. Use of higher than first-order discretization schemes for the convection terms and higher than second-order discretization schemes for the diffusion terms often leads to non-realizable moment sets. A non-realizable moment set does not correspond to a non-negative distribution function. The discretization schemes that can guarantee the non-negativity of the distribution function are called realizable schemes. The standard high-order discretization schemes are non-realizable. As a part of current research study, a set of high-order realizable schemes has been developed for both convection and diffusion terms that guarantee the non-negativity of the distribution function using constraints on the time step size, known as realizability conditions. In addition, the current study also shows the application of quadrature-based moment methods to two multi-physics phenomena - bubble-column flow and radiation transport. The two problems have been formulated and solved using the quadrature-based moment methods with particular attention to realizability.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/etd/12945/
dc.identifier.articleid 3952
dc.identifier.contextkey 4188274
dc.identifier.doi https://doi.org/10.31274/etd-180810-1128
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath etd/12945
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/27134
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/etd/12945/Vikas_iastate_0097E_13074.pdf|||Fri Jan 14 19:33:51 UTC 2022
dc.subject.disciplines Aerospace Engineering
dc.subject.disciplines Applied Mathematics
dc.subject.disciplines Chemical Engineering
dc.subject.keywords Bubble-column
dc.subject.keywords Quadrature-based moment methods
dc.subject.keywords Radiation
dc.subject.keywords Realizable schemes
dc.title Quadrature-based moment methods: High-order realizable schemes and multi-physics applications
dc.type article
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 047b23ca-7bd7-4194-b084-c4181d33d95d
thesis.degree.level dissertation
thesis.degree.name Doctor of Philosophy
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