This paper discusses an accurate numerical approach based on complex variables for the computation of the Jacobian matrix of complex chemical reaction mechanisms. The Jacobian matrix is required in the calculation of low dimensional manifolds during kinetic chemical mechanism reduction. The approach is suitable for numerical computations of large-scale problems and is more accurate than the finite difference approach of computing Jacobians. The method is demonstrated via a nonlinear reaction mechanism for the synthesis of Bromide acid and a H2/Air mechanism using a modified CHEMKIN package. The Bromide mechanism consisted of five species participating in six elementary chemical reactions and the H2/Air mechanism consisted of 11 species and 23 reactions. In both cases it is shown that the method is superior to the finite difference approach of computing derivatives with an arbitrary computational step size h.
Computing CHEMKIN Sensitivities Using Complex Variables
Contributed by the Combustion and Fuels Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received by the CF Division March 19, 2001; final revision received by the ASME Headquarters November 1, 2001. Associate Editor: S. Gollahalli.
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Butuk , N., and Pemba , J. (August 15, 2003). "Computing CHEMKIN Sensitivities Using Complex Variables ." ASME. J. Eng. Gas Turbines Power. July 2003; 125(3): 854–858. https://doi.org/10.1115/1.1469006
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