# An efficient chemical kinetics solver using high dimensional model representation

## Abstract

A high dimensional model representation (HDMR) technique is introduced to capture the input-output behavior of chemical kinetic models. The HDMR expresses the output chemical species concentrations as a rapidly convergent hierarchical correlated function expansion in the input variables. In this paper, the input variables are taken as the species concentrations at time t{sub i} and the output is the concentrations at time t{sub i} + {delta}, where {delta} can be much larger than conventional integration time steps. A specially designed set of model runs is performed to determine the correlated functions making up the HDMR. The resultant HDMR can be used to (1) identify the key input variables acting independently or cooperatively on the output, and (2) create a high speed fully equivalent operational model (FEOM) serving to replace the original kinetic model and its differential equation solver. A demonstration of the HDMR technique is presented for stratospheric chemical kinetics. The FEOM proved to give accurate and stable chemical concentrations out to long times of many years. In addition, the FEOM was found to be orders of magnitude faster than a conventional stiff equation solver. This computational acceleration should have significance in many chemical kinetic applications.

- Authors:

- Publication Date:

- Research Org.:
- Mission Research Corp., Nashua, NH (US)

- Sponsoring Org.:
- USDOE; National Aeronautics and Space Administration

- OSTI Identifier:
- 20000051

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Physical Chemistry A: Molecules, Spectroscopy, Kinetics, Environment, amp General Theory

- Additional Journal Information:
- Journal Volume: 103; Journal Issue: 36; Other Information: PBD: 9 Sep 1999; Journal ID: ISSN 1089-5639

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 40 CHEMISTRY; MATHEMATICAL MODELS; KINETICS; ABUNDANCE; CONVERGENCE; EQUATIONS; CHEMISTRY; THEORETICAL DATA

### Citation Formats

```
Shorter, J.A., Ip, P.C., and Rabitz, H.A.
```*An efficient chemical kinetics solver using high dimensional model representation*. United States: N. p., 1999.
Web. doi:10.1021/jp9843398.

```
Shorter, J.A., Ip, P.C., & Rabitz, H.A.
```*An efficient chemical kinetics solver using high dimensional model representation*. United States. doi:10.1021/jp9843398.

```
Shorter, J.A., Ip, P.C., and Rabitz, H.A. Thu .
"An efficient chemical kinetics solver using high dimensional model representation". United States. doi:10.1021/jp9843398.
```

```
@article{osti_20000051,
```

title = {An efficient chemical kinetics solver using high dimensional model representation},

author = {Shorter, J.A. and Ip, P.C. and Rabitz, H.A.},

abstractNote = {A high dimensional model representation (HDMR) technique is introduced to capture the input-output behavior of chemical kinetic models. The HDMR expresses the output chemical species concentrations as a rapidly convergent hierarchical correlated function expansion in the input variables. In this paper, the input variables are taken as the species concentrations at time t{sub i} and the output is the concentrations at time t{sub i} + {delta}, where {delta} can be much larger than conventional integration time steps. A specially designed set of model runs is performed to determine the correlated functions making up the HDMR. The resultant HDMR can be used to (1) identify the key input variables acting independently or cooperatively on the output, and (2) create a high speed fully equivalent operational model (FEOM) serving to replace the original kinetic model and its differential equation solver. A demonstration of the HDMR technique is presented for stratospheric chemical kinetics. The FEOM proved to give accurate and stable chemical concentrations out to long times of many years. In addition, the FEOM was found to be orders of magnitude faster than a conventional stiff equation solver. This computational acceleration should have significance in many chemical kinetic applications.},

doi = {10.1021/jp9843398},

journal = {Journal of Physical Chemistry A: Molecules, Spectroscopy, Kinetics, Environment, amp General Theory},

issn = {1089-5639},

number = 36,

volume = 103,

place = {United States},

year = {1999},

month = {9}

}