An efficient semi-implicit numerical method is developed for solving the detailed chemical kinetic source terms in I.C. engine simulations. The detailed chemistry system is a group of coupled extremely stiff O.D.E.s, which presents a very stringent timestep 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, in which the numerical solution to the stiff O.D.E.s never blows up for arbitrary large timestep. The formulation of numerical integration exploits the physical requirement that the species density and specific internal energy in the computational cells must be nonnegative, so that the Lipschitz timestep constraint is not present [1,2], and the computation timestep can be orders of magnitude larger than that possible in standard explicit methods and can be formulated to be of high formal order of accuracy. The solver exploits the characteristics of the stiffness of the O.D.E.s 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 timestep 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 with those using the CHEMKIN package which uses the VODE implicit solver. Very 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 CHEMKIN.

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