A hybrid, non-split, stiff/RKC, solver for advection–diffusion–reaction equations and its application to low-Mach number combustion
Type
ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionApplied Mathematics and Computational Science Program
Date
2019-04-05Permanent link to this record
http://hdl.handle.net/10754/631846
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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 LimitedJournal
Combustion Theory and ModellingAdditional Links
https://www.tandfonline.com/doi/full/10.1080/13647830.2019.1600723ae974a485f413a2113503eed53cd6c53
10.1080/13647830.2019.1600723