Kinetic modeling numerical strategies

G. Maria, Expert System for ODE Chemical Kinetic Model Identification by Using a Transfer of Information Numerical Strategy, Comp. Chem. Eng. 17 (1993) 5435-5440. 

The parameter estimation and the kinetic discrimination studies obtained from the numerical simulations are tedious, complex, and time-consuming. Complex softwares are required, and lengthy strategies are used to fit to the data. Moreover. the number of parameters describing the model complicates the interpretation of the experimental results. Simplifying approaches are recommended to make easier the analysis of the chromatographic profiles [371. 

Another common property of multireaction networks is stiffness, that is, the presence of kinetic steps with widely different rate coefficients. This property was pointed out by Curtiss and Hirschfelder (1952), and has had a major impact on the development of numerical solvers such as BASSE (Petzold 1983) and DDAPLUS of Appendix B. Since stiff equations take added computational effort, there is some incentive to reduce the stiffness of a model at the formulation stage this can be done by substituting Eq. (2.5-2b) or (2.5-3) for some of the reaction or production rate expressions. This strategy replaces some differential equations in the reactor model by algebraic ones to expedite numerical computations. 

Independent of the specific modeling strategy, the kinetic equations often exhibit a nonlinear dependence on the species concentrations and a reaction rate rapidly increasing with temperature. In combination with the transport equations for mass, momentum and heat, the resulting numerical problem is usually challenging due to the nonlinearities and the multitude of time scales involved. For this reason, methods are needed to eliminate some of these difficulties and to simplify the numerical structure. 

Abstract Among the noncontinuum-based computational techniques, the lattice Boltzman method (LBM) has received considerable attention recently. In this chapter, we will briefly present the main elements of the LBM, which has evolved as a minimal kinetic method for fluid dynamics, focusing in particular, on multiphase flow modeling. We will then discuss some of its recent developments based on the multiple-relaxation-time formulation and consistent discretizatirai strategies for enhanced numerical stability, high viscosity contrasts, and density ratios for simulation of interfacial instabilities and multiphase flow problems. As examples, numerical investigations of drop collisions, jet break-up, and drop impact on walls will be presented. We will also outline some future directions for further development of the LBM for applications related to interfacial instabilities and sprays. 

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