The ODEs describing a chemical kinetics system can be very stiff and are the most computationally costly part of most reactive flow simulations. Research areas ranging from combustion to climate modeling are often limited by their ability to solve these chemical ODE systems both accurately and efficiently. These problems are commonly treated with an implicit numerical method due to the stiffness that is usually present. The implicit solution technique introduces a large amount of computational overhead necessary to solve the nonlinear algebraic system derived from the implicit time-stepping method. In this paper, a code is presented that avoids much of the usual overhead by preconditioning the implicit method with an iterative technique. This results in a class of time-stepping method that is explicit and very stable for chemical kinetics problems. (Source:

References in zbMATH (referenced in 11 articles , 1 standard article )

Showing results 1 to 11 of 11.
Sorted by year (citations)

  1. Khalsaraei, Mohammad Mehdizadeh; Shokri, Ali; Molayi, Maryam: The new class of multistep multiderivative hybrid methods for the numerical solution of chemical stiff systems of first order IVPs (2020)
  2. Feng, Fan; Chi, Xuebin; Wang, Zifa; Li, Jie; Jiang, Jinrong; Yang, Wenyi: A nonnegativity preserved efficient chemical solver applied to the air pollution forecast (2017)
  3. Feng, Fan; Wang, Zifa; Li, Jie; Carmichael, Gregory R.: A nonnegativity preserved efficient algorithm for atmospheric chemical kinetic equations (2015)
  4. Falati, M.; Hojjati, G.: Integration of chemical stiff ODEs using exponential propagation method (2011)
  5. Kim, Seong-Lyong; Choi, Jeong-Yeol; Jeung, In-Seuck; Park, Yang-Ho: Application of approximate chemical Jacobians for constant volume reaction and shock-induced combustion (2001)
  6. Pinhão, Nuno R.: PLASMAKIN: a chemical kinetics library for plasma physics modeling (2001)
  7. Mott, David R.; Oran, Elaine S.; van Leer, Bram: A quasi-steady-state solver for the stiff ordinary differential equations of reaction kinetics (2000)
  8. Knio, Omar M.; Najm, Habib N.; Wyckoff, Peter S.: A semi-implicit numerical scheme for reacting flow. II: Stiff, operator-split formulation (1999)
  9. Najm, Habib N.; Wyckoff, Peter S.; Knio, Omar M.: A semi-implicit numerical scheme for reacting flow. I: Stiff chemistry (1998)
  10. Aro, Colin J.: CHEMSODE: A stiff ODE solver for the equations of chemical kinetics (1996)
  11. Aro, Colin J.: A stiff ODE preconditioner based on Newton linearization (1996)