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dc.contributor.advisorParsani, Matteo
dc.contributor.authorSayyari, Mohammed
dc.date.accessioned2022-05-10T08:48:53Z
dc.date.available2022-05-10T08:48:53Z
dc.date.issued2022-03
dc.identifier.citationSayyari, M. (2022). The capabilities of summation-by-parts and structure-preserving operators for compressible computational fluid dynamics and reaction-diffusion models. KAUST Research Repository. https://doi.org/10.25781/KAUST-1SDB7
dc.identifier.doi10.25781/KAUST-1SDB7
dc.identifier.urihttp://hdl.handle.net/10754/676717
dc.description.abstractWith the algorithm’s suitability for exploiting current petascale and next-generation exascale supercomputers, stable and structure-preserving properties are necessary to develop predictive computational tools. In this dissertation, summation-by-parts (SBP) operators and a new relaxation Runge–Kutta (RRK) scheme are used to construct mimetic and structure-preserving full discretization for non-reactive compressible computational fluid dynamics (CFD) and reaction-diffusion models. In the first chapter, we provide the necessary background and a literature survey that forms the basis of this dissertation. Next, we provide a short overview of entropy stability for general conservation laws. The second chapter covers the analysis of the Eulerian model for compressible and heat-conducting flows. We provide the necessary background of the new system of parabolic partial differential equation (PDE). Then, we present the entropy stability analysis of the model at the continuous level. Subsequently, using the SBP, we construct an entropy-stable discretization of any order for unstructured grids with tensor-product elements. The third chapter discusses the implementation of RRK methods. We start by reviewing the RRK scheme constructed to guarantee conservation or stability with respect to any inner-product norm. Then, we present the extension and generalization of RRK schemes to general convex functionals and their application to compressible fluid flow problems. The final chapter demonstrates the far-reaching capabilities of the SBP operators and RRK schemes presenting the development of a novel fully discrete Lyapunov stable discretization for reaction models with spatial diffusion. Finally, we conclude this dissertation with an overview of our achievements and future research directions.
dc.language.isoen
dc.subjectnonlinear stability
dc.subjectentropy analysis
dc.subjectwall boundary conditions
dc.subjectSBP-SAT operators
dc.subjectrelaxation RK methods
dc.subjectcompressible CFD
dc.subjectcompartmental models
dc.titleThe capabilities of summation-by-parts and structure-preserving operators for compressible computational fluid dynamics and reaction-diffusion models
dc.typeDissertation
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
thesis.degree.grantorKing Abdullah University of Science and Technology
dc.contributor.committeememberGomes, Diogo A.
dc.contributor.committeememberKeyes, David E.
dc.contributor.committeememberZingg, David W.
thesis.degree.disciplineApplied Mathematics and Computational Science
thesis.degree.nameDoctor of Philosophy
dc.identifier.orcidhttps://orcid.org/0000-0003-4967-501X
refterms.dateFOA2022-05-10T08:48:54Z
kaust.request.doiyes
kaust.gpcaida.hoteit@kaust.edu.sa
kaust.availability.selectionRelease the work immediately for public access* on the internet through the KAUST Repository.
kaust.thesis.advisorApprovalRequestedYes, I have already submitted the final approval form to my advisor.


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