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

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    Type
    Thesis
    Authors
    Alzahrani, Hasnaa H. cc
    Advisors
    Knio, Omar cc
    Committee members
    Gomes, Diogo A. cc
    Laleg-Kirati, Taous-Meriem cc
    Parsani, Matteo cc
    Program
    Applied Mathematics and Computational Science
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2016-07-26
    Permanent link to this record
    http://hdl.handle.net/10754/617606
    
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    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.
    Citation
    Alzahrani, H. H. (2016). Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations. KAUST Research Repository. https://doi.org/10.25781/KAUST-070XM
    DOI
    10.25781/KAUST-070XM
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-070XM
    Scopus Count
    Collections
    Applied Mathematics and Computational Science Program; Theses; Theses; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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