List of Suggested Benchmarks
With reference to the specified guidelines, we suggest in the two main areas of interest, each involving both homogeneous and non-homogeneous systems, the following benchmark problems:
a) a chain-branching model proposed in [F.A.Williams, Combustion Theory, (1985), 2nd ed., App. B. 2.5.3, page 520]; this model has an hyperbolic fixed point, features explosive behavior, and is nonlinear at infinity ( ODE MODEL FORM );
b) the Lindemann model proposed in [K.J.Laidler, Theories of Chemical Reaction Rates, (1969)]; this model has a non-hyperbolic fixed point, and features a slow manifold with a region of weaker attractivity ( ODE MODEL FORM );
c) the Semenov model in an open system proposed in [Uppal, et al. Chemical Engineering Science. 1974, Vol. 29. pp. 967-985]; this model can develop oscillatory (limit cycle, chaotic) behavior ( ODE MODEL FORM , PDE MODEL FORM ).
a) propane-air chemistry using the detailed Natural Gas mechanism based on [E.L. Petersen, D.M. Kalitan, S. Simmons, G. Bourque, H.J. Curran, J.M. Simmie, Methane/Propane Oxidation at High Pressures: Experimental and Detailed Chemical Kinetic Modeling, Proc. Comb. Inst., vol. 31, April, 2006] ; two problems are suggested, namely:
> the auto-ignition process of an homogeneous system;
b) the detailed mechanism for CO-H2 mixtures analyzed in [R.B.Brad et al., The application of chemical reduction methods to a combustion system exhibiting complex dynamics, Proc. Comb. Inst. (2006), doi:10.1016/j.proci.2006.07.026 ], in the oscillatory regime of a CSTR system.
With reference to the above specified benchmark problems, the contributors might provide the following kinds of outputs:
1) description of the model reduction technique;
2) diagnostics of the detailed model (e.g. identification of time scales, major and minor species, relevant manifolds, stretch rates, Liapunov numbers, whenever applicable ...) ;
3) accuracy and computational efficiency of the reduced vs. the full model.
Small nonlinear model problems
Problems with detailed chemical kinetics