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    A hybrid, non-split, stiff/RKC, solver for advection–diffusion–reaction equations and its application to low-Mach number combustion

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    Type
    Article
    Authors
    Lucchesi, Marco
    Alzahrani, Hasnaa H. cc
    Safta, C.
    Knio, Omar
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    Date
    2019-04-05
    Permanent link to this record
    http://hdl.handle.net/10754/631846
    
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    Abstract
    We present a new strategy to couple, in a non-split fashion, stiff integration schemes with explicit, extended-stability predictor-corrector methods. The approach is illustrated through the construction of a mixed scheme incorporating a stabilised second-order, Runge-Kutta-Chebyshev method and the CVODE stiff solver. The scheme is first applied to an idealised stiff reaction-diffusion problem that admits an analytical solution. Analysis of the computations reveals that as expected the scheme exhibits a second-order in time convergence, and that, compared to an operator-split construction, time integration errors are substantially reduced. The non-split scheme is then applied to model the transient evolution of a freely-propagating, 1D methane-air flame. A low-mach-number, detailed kinetics, combustion model, discretised in space using fourth-order differences, is used for this purpose. To assess the performance of the scheme, self-convergence tests are conducted, and the results are contrasted with computations performed using a Strang-split construction. Whereas both the split and non-split approaches exhibit second-order in time behaviour, it is seen that for the same value of the time step, the non-split approach exhibits significantly smaller time integration errors. On the other hand, the results also indicate that the application of the present non-split construction becomes attractive when large integration steps are used, due to numerical overhead.
    Citation
    Lucchesi M, Alzahrani HH, Safta C, Knio OM (2019) A hybrid, non-split, stiff/RKC, solver for advection–diffusion–reaction equations and its application to low-Mach number combustion. Combustion Theory and Modelling: 1–21. Available: http://dx.doi.org/10.1080/13647830.2019.1600723.
    Sponsors
    Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525. The views expressed in this paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.
    Publisher
    Informa UK Limited
    Journal
    Combustion Theory and Modelling
    DOI
    10.1080/13647830.2019.1600723
    Additional Links
    https://www.tandfonline.com/doi/full/10.1080/13647830.2019.1600723
    ae974a485f413a2113503eed53cd6c53
    10.1080/13647830.2019.1600723
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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