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| Titel: |
Efficient Formation of Numerical Jacobian Used in Flame Codes |
| Auteur: |
Olsson, Jim O. Lindgren, Ove Andersson, Owe |
| Verschenen in: |
Combustion science and technology |
| Paginering: | Jaargang 77 (1991) nr. 4-6 pagina's 319-327 |
| Jaar: |
1991-06-01 |
| Inhoud: |
An efficient method for the formation of the numerical Jacobian in combustion codes has been applied to premixed laminar and counterflow diffusion flames. The improvements are portable to similar codes for treating ignition, two-dimensional flames and the general class of reactive-diffusive processes. Execution times were reduced by a factor of seven with no decrease in accuracy, for a mechanism containing 46 species and 213 reactions, when compared with the starting form of the premixed flame code developed at Sandia Laboratories (Smooke, 1982). The most important new feature is the efficient formation of the numerical Jacobian, reducing the CPU-time spent on computing chemical kinetics, thermodynamic and transport properties among the N unknowns (temperature, species mass fractions, and mass flow) in the system. Normally, the Jacobian is i formed in 3N + I full vector function evaluations requiring 90-95% of the computing time (Smooke, 1982). Every variable is perturbed simultaneously at every third node and the numerical derivatives are formed at the corresponding nodes. The process is repeated for the two other groups of nodes. In the present work, the formation of the Jacobian is improved in three different ways, none of which decreases the accuracy of the solution, nor adversely affects the rate of convergence. First, the temperature dependent parameters which have no concentration dependence are computed with only the temperature variable perturbed. This applies to the properties related to an individual species — thermal conductivity, specific heat, and enthalpy — as well as to the rate constants. Second, the mixture averaged/related properties — diffusion, thermal conductivity, specfic heat and enthalpy — are evaluated only at the perturbed node for the change in the perturbed variable. Third, the chemical kinetics rates, depending on the species variables, are only recalculated if a species variable is perturbed at that node. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 4 van 11 gevonden artikelen
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