Modeling chemically reacting flow systems—i. A comparison of finite difference and finite element methods for one-dimensional reactive diffusion
| Autor: | Norman Loren Schryer, D. Edelson |
|---|---|
| Rok vydání: | 1978 |
| Předmět: |
Mathematical optimization
Partial differential equation General Chemical Engineering Computation Finite difference Finite difference coefficient Mixed finite element method Applied Microbiology and Biotechnology Finite element method Flow (mathematics) Applied mathematics Biotechnology Sparse matrix Mathematics |
| Zdroj: | Computers & Chemistry. 2:71-74 |
| ISSN: | 0097-8485 |
| DOI: | 10.1016/0097-8485(78)87004-1 |
| Popis: | Two different computer programs for solving partial differential equations, finite-differences and finite-elements, have been tested on a representative problem in reactive flow in one spatial dimension. Results are reported for several different spatial discretizations, and the run times, core requirements and total computation costs are compared. It is found that both programs cost approximately the same for the small problem considered here (four chemical species), but that the finite-element procedure gives somewhat better accuracy. The present experience is used to extrapolate to the expenditure required to solve “real” problems involving considerably larger numbers of chemical species and it is shown that this will rapidly become unmanageable. However, examination of the sparsity of the coupling matrix for such a typical large problem leads to the conclusion that the use of sparse matrix techniques can effect order-of-magnitude economies in the finite-element method, whereas the attainability of equivalent savings with the finite-difference technique is uncertain. |
| Databáze: | OpenAIRE |
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