Journal article
A nonnegativity preserved efficient algorithm for atmospheric chemical kinetic equations
Applied mathematics and computation, Vol.271, pp.519-531
11/15/2015
DOI: 10.1016/j.amc.2015.09.033
Abstract
Air pollution models plays a critical role in atmospheric environment research. Chemical kinetic equations is an important component of air pollution models. The chemical equations is numerically sticky because of its stiffness, nonlinearity, coupling and nonnegativity of the exact solutions. Over the past decades, numerous papers about chemical equation solvers have been published. However, these solvers cannot preserve the nonnegativity of the exact solutions. Therefore, in the calculation, the negative numerical concentration values are usually set to zero artificially, which may cause simulation errors. To obtain real nonnegative numerical concentration values, very small step-size has to be adopted. Then enormous amount of CPU time is consumed to solve the chemical equations. In this paper, we revisit this topic and derive a new algorithm. Our algorithm Modified-Backward-Euler (MBE) Method can unconditionally preserve the nonnegativity of the exact solutions. MBE is a simple, robust and efficient solver. It is much faster and more precise than the traditional solvers such as LSODE and QSSA. The numerical results and parameter suggestions are shown at the end of the paper. MBE is based on the P-L structure of the chemical equations and a deeper view into the nature of Euler Methods. It cannot only be used to solve chemical equations, but can also be applied to conquer ordinary differential equations (ODEs) with similar P-L structure.
Details
- Title: Subtitle
- A nonnegativity preserved efficient algorithm for atmospheric chemical kinetic equations
- Creators
- Fan Feng - Chinese Academy of SciencesZifa Wang - Chinese Academy of SciencesJie Li - Chinese Academy of SciencesGregory R Carmichael - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Applied mathematics and computation, Vol.271, pp.519-531
- Publisher
- Elsevier Inc
- DOI
- 10.1016/j.amc.2015.09.033
- ISSN
- 0096-3003
- eISSN
- 1873-5649
- Grant note
- DOI: 10.13039/501100002367, name: Chinese Academy of Sciences, award: XDB05030200
- Language
- English
- Date published
- 11/15/2015
- Academic Unit
- Civil and Environmental Engineering; Nursing; Chemical and Biochemical Engineering
- Record Identifier
- 9984185370002771
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