An efficient semi-implicit numerical method is developed for solving the detailed chemical kinetic source terms in internal combustion (IC) engine simulations. The detailed chemistry system forms a group of coupled stiff ordinary differential equations (ODEs), which presents a very stringent time-step limitation when solved by standard explicit methods, and is computationally expensive when solved by iterative implicit methods. The present numerical solver uses a stiffly stable noniterative semi-implicit method. The formulation of numerical integration exploits the physical requirement that the species density and specific internal energy in the computational cells must be non-negative, so that the Lipschitz time-step constraint is not present and the computation time step can be orders of magnitude larger than that possible in standard explicit methods. The solver exploits the characteristics of the stiffness of the ODEs by using a sequential sort algorithm that ranks an approximation to the dominant eigenvalues of the system to achieve maximum accuracy. Subcycling within the chemistry solver routine is applied for each computational cell in engine simulations, where the subcycle time step is dynamically determined by monitoring the rate of change of concentration of key species, which have short characteristic time scales and are also important to the chemical heat release. The chemistry solver is applied in the KIVA-3V code to diesel engine simulations. Results are compared to those using the CHEMKIN package, which uses the VODE implicit solver. Good agreement was achieved for a wide range of engine operating conditions, and $40-70%$ CPU time savings were achieved by the present solver compared to the standard CHEMKIN.

1.
Reitz
,
R. D.
, 1980, “
Computations of Laminar Flame Propagation Using an Explicit Numerical Method
,”
18th Symposium (International) on Combustion
, Combust. Inst., Pittsburgh, PA, pp.
433
442
.
2.
Roberts
,
C. E.
, 1979,
Ordinary Differential Equations: A Computational Approach
,
Prentice-Hall
, Englewood Cliffs, NJ.
3.
Kee
,
R. J.
,
Rupley
,
F. M.
, and
Miller
,
J. A.
, 1989, “
CHEMKIN-II: A FORTRAN Chemical Kinetics Package for the Analyses of Gas Phase Chemical Kinetics
,” Sandia Report, No. SAND 89-8009.
4.
Brown
,
P. N.
,
Byrne
,
G. D.
, and
Hindmarsh
,
A. C.
, 1989,
“VODE, A Variable-Coefficient ODE Solver
,”
SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput.
0196-5204,
10
, pp.
1038
1051
.
5.
Kong
,
S.-C.
, and
Reitz
,
R. D.
, 2002, “
Application of Detailed Chemistry and CFD for Predicting Direct Injection HCCI Engine Combustion and Emissions
,”
Proc. Combust. Inst.
29
, pp.
663
669
.
6.
Kong
,
S.-C.
,
Han
,
Z.
, and
Reitz
,
R. D.
, 1995, “
The Development and Application of a Diesel Ignition and Combustion Model for Multidimensional Engine Simulation
,” SAE Paper No. 950278.
7.
Senecal
,
P. K.
, and
Reitz
,
R. D.
, 2000, “
Simultaneous Reduction of Engine Emissions and Fuel Consumption Using Genetic Algorithms and Multi-Dimensional Spray and Combustion Modeling
,” SAE Paper No. 2000-01-1890.
8.
Amsden
,
A. A.
,
O’Rourke
,
P. J.
, and
Butler
,
T. D.
, 1989, “
KIVA-II: A Computer Program for Chemically Reactive Flows with Sprays
,” Los Alamos National Labs, LA-11560-MS.
9.
Golovitchev
,
V. I.
, 2000, http:∕∕www.tfd.chalmers.se∕∼valeri∕MECH.html, Chalmers Univ. of Tech, Gothenburg, Sweden.
10.
Patel
,
A.
,
Kong
,
S.-C.
, and
Reitz
,
R. D.
, 2004, “
Development and Validation of a Reduced Reaction Mechanism for HCCI Engine Simulations
,” SAE Paper No. 2004-01-0558.
11.
Tanaka
,
S.
,
Ayala
,
F.
, and
Keck
,
J. C.
, 2003, “
A Reduced Chemical Kinetic Model for HCCI Combustion of Primary Reference Fuels in a Rapid Compression Machine
,”
Combust. Flame
0010-2180,
133
, pp.
467
481
.
12.
Turns
,
S. R.
, 2000,
An Introduction to Combustion: Concepts and Applications
,
McGraw-Hill
, New York.
13.
Klingbeil
,
A. E.
, 2002, “
Particulate and NOx Reduction in a Heavy-Duty Diesel Engine Using High Levels of Exhaust Gas Recirculation and Very Early and Very Late Injection
,” MS thesis, University of Wisconsin-Madison.