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


Journal Article

© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group. 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.

Full Text

Cited Authors

  • Lucchesi, M; Alzahrani, HH; Safta, C; Knio, OM

Published Date

  • September 3, 2019

Published In

Volume / Issue

  • 23 / 5

Start / End Page

  • 935 - 955

Electronic International Standard Serial Number (EISSN)

  • 1741-3559

International Standard Serial Number (ISSN)

  • 1364-7830

Digital Object Identifier (DOI)

  • 10.1080/13647830.2019.1600723

Citation Source

  • Scopus