### Abstract

A comprehensive mathematical model incorporating multicomponent molecular diffusion, complex chemistry, and heterogeneous processes was developed to investigate a variety of chemically reacting flow problems which emphasize the elementary chemical and physical processes rather than complex flow geometry. The goal here is not only to calculate chemical species profiles, temperature profiles, and mass flow rates, but also to obtain sensitivity information. The timedependent, one-dimensional partial differential equations resulting from the mathematical model formulation were discretized by the Galerkin Finite Element Method and then integrated over time by backward differentiation formulas (the implicit Gear algorithm). The sensitivity equations were decoupled from the model equations and integrated one time step behind the integration of the model equations. Stiff changes in the first- and second-order spatial gradients were lessened by continuously moving nodes in a non-stiff manner. The grid system resulting from each time step is tested for further node refinements. The Jacobian matrices were evaluated analytically rather than numerically to eliminate unnecessary computational efforts and to accelerate convergence rates of the Newton iteration. The use of analytical Jacobian matrices also enhances the accuracy of sensitivity coefficients which are calculated together with model solutions. The mathematical model developed here has been successfully applied to combustion of liquid droplets, oxidation of carbon particles, and chemically facilitated vaporization of boron oxide droplets. All the computations presented here were performed using currently available workstations with only a few hours of CPU time.

Original language | English (US) |
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Pages (from-to) | 160-179 |

Number of pages | 20 |

Journal | Journal of Computational Physics |

Volume | 102 |

Issue number | 1 |

DOIs | |

State | Published - Sep 1992 |

### All Science Journal Classification (ASJC) codes

- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics

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## Cite this

*Journal of Computational Physics*,

*102*(1), 160-179. https://doi.org/10.1016/S0021-9991(05)80013-0