An efficient semi-implicit time-integration scheme for stiff chemical source terms

Y. Xuan, B. Savard, B. Bobbitt, G. Blanquart

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, a semi-implicit iterative time-integration scheme for stiff chemical source terms is proposed, specifically designed for the numerical simulations of unsteady reacting flows with finite-rate chemistry using detailed chemical kinetic mechanisms. This scheme eliminates the expense of inverting the full chemical source Jacobian matrix at each location and time step of a numerical simulation. This is achieved by approximating the chemical source Jacobian matrix by a diagonal matrix, based on the intrinsic relations between the chemical source terms and the species mass fractions. Second order temporal accuracy of this scheme is achieved by using an iterative procedure within each time step. This scheme also possesses better stability characteristics than its explicit counterpart. Furthermore, the convection, diffusion, and chemistry are all integrated simultaneously, which makes this scheme free of lagging errors. The performance of the proposed time-integration scheme is assessed first on a one-dimensional laminar premixed flame. Numerical results show that the new semi-implicit iterative scheme allows for a stable time step size more than 500 times larger than that for the explicit scheme, with almost the same computational cost within each time step. This scheme is also shown to be more efficient computationally than the DASSL solver. This scheme is further applied to the direct numerical simulation of a three-dimensional turbulent premixed flame of n-heptane at a high Karlovitz number.

Original languageEnglish (US)
Title of host publicationWestern States Section of the Combustion Institute Spring Technical Meeting 2014
PublisherWestern States Section/Combustion Institute
Pages38-57
Number of pages20
ISBN (Electronic)9781632665218
StatePublished - 2014
EventWestern States Section of the Combustion Institute Spring Technical Meeting 2014 - Pasadena, United States
Duration: Mar 24 2014Mar 25 2014

Publication series

NameWestern States Section of the Combustion Institute Spring Technical Meeting 2014

Other

OtherWestern States Section of the Combustion Institute Spring Technical Meeting 2014
CountryUnited States
CityPasadena
Period3/24/143/25/14

All Science Journal Classification (ASJC) codes

  • Chemical Engineering(all)
  • Physical and Theoretical Chemistry
  • Mechanical Engineering

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