Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations

Handle URI:
http://hdl.handle.net/10754/617606
Title:
Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations
Authors:
Alzahrani, Hasnaa H. ( 0000-0003-1786-7121 )
Abstract:
A tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly together with explicit treatment of diffusion. The second-order Runge-Kutta- Chebyshev (RKC) scheme is adjusted to integrate diffusion. Spatial operator is de- scretised by second-order finite differences on a uniform grid. The overall solution is advanced over S fractional stiff integrations, where S corresponds to the number of RKC stages. The behavior of the scheme is analyzed by applying it to three simple problems. The results show that it achieves second-order accuracy, thus, preserving the formal accuracy of the original RKC. The presented development sets the stage for future extensions, particularly, to multidimensional reacting flows with detailed chemistry.
Advisors:
Knio, Omar M.
Committee Member:
Gomes, Diogo; Laleg-Kirati, Taous-Meriem ( 0000-0001-5944-0121 ) ; Parsani, Matteo ( 0000-0001-7300-1280 )
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Applied Mathematics and Computational Science
Issue Date:
26-Jul-2016
Type:
Thesis
Appears in Collections:
Theses

Full metadata record

DC FieldValue Language
dc.contributor.advisorKnio, Omar M.en
dc.contributor.authorAlzahrani, Hasnaa H.en
dc.date.accessioned2016-07-27T06:05:11Z-
dc.date.available2016-07-27T06:05:11Z-
dc.date.issued2016-07-26-
dc.identifier.urihttp://hdl.handle.net/10754/617606-
dc.description.abstractA tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly together with explicit treatment of diffusion. The second-order Runge-Kutta- Chebyshev (RKC) scheme is adjusted to integrate diffusion. Spatial operator is de- scretised by second-order finite differences on a uniform grid. The overall solution is advanced over S fractional stiff integrations, where S corresponds to the number of RKC stages. The behavior of the scheme is analyzed by applying it to three simple problems. The results show that it achieves second-order accuracy, thus, preserving the formal accuracy of the original RKC. The presented development sets the stage for future extensions, particularly, to multidimensional reacting flows with detailed chemistry.en
dc.language.isoenen
dc.subjectstiffnessen
dc.subjectlow mach numberen
dc.subjectnumerical integrationen
dc.subjectrunge-kutta-chebysheven
dc.subjectnon-split schemeen
dc.titleMixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equationsen
dc.typeThesisen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen_GB
dc.contributor.committeememberGomes, Diogoen
dc.contributor.committeememberLaleg-Kirati, Taous-Meriemen
dc.contributor.committeememberParsani, Matteoen
thesis.degree.disciplineApplied Mathematics and Computational Scienceen
thesis.degree.nameMaster of Scienceen
dc.person.id134122en
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