A hybrid, non-split, stiff/RKC, solver for advection–diffusion–reaction equations and its application to low-Mach number combustion
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Permanent link to this recordhttp://hdl.handle.net/10754/631846
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AbstractWe 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.
CitationLucchesi 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.
SponsorsSandia 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.
PublisherInforma UK Limited
JournalCombustion Theory and Modelling