Modeling low Mach number reacting flow with detailed chemistry and transport

H. N. Najm*, O. M. Knio

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


An efficient projection scheme is developed for the simulation of reacting flow with detailed kinetics and transport. The scheme is based on a zero-Mach-number formulation of the compressible conservation equations for an ideal gas mixture. It relies on Strang splitting of the discrete evolution equations, where diffusion is integrated in two half steps that are symmetrically distributed around a single stiff step for the reaction source terms. The diffusive half-step is integrated using an explicit single-step, multistage, Runge-Kutta-Chebyshev (RKC) method. The resulting construction is second-order convergent, and has superior efficiency due to the extended real-stability region of the RKC scheme. Two additional efficiency-enhancements are also explored, based on an extrapolation procedure for the transport coefficients and on the use of approximate Jacobian data evaluated on a coarse mesh. We demonstrate the construction in 1D and 2D flames, and examine consequences of splitting errors. By including the above enhancements, performance tests using 2D computations with a detailed C1C 2 methane-air mechanism and a mixture-averaged transport model indicate that speedup factors of about 15 are achieved over the starting split-stiff scheme.

Original languageEnglish (US)
Pages (from-to)263-287
Number of pages25
JournalJournal of Scientific Computing
Issue number1
StatePublished - Oct 2005
Externally publishedYes


  • Operator splitting
  • Reacting flow
  • Runge-Kutta-Chebyschev
  • Stiffness
  • Time integration

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • General Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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