Characterizing Tradeoffs in Memory, Accuracy, and Speed for Chemistry Tabulation Techniques

ABSTRACT

Chemistry tabulation is a common approach in practical simulations of turbulent combustion at engineering scales. Linear interpolants have traditionally been used for accessing precomputed multidimensional tables but suffer from large memory requirements and discontinuous derivatives. Higher-degree interpolants address some of these restrictions but are similarly limited to relatively low-dimensional tabulation. Artificial neural networks (ANNs) can be used to overcome these limitations but cannot guarantee the same accuracy as interpolants and introduce challenges in reproducibility and reliable training. These challenges are enhanced as the physics complexity to be represented within the tabulation increases. In this manuscript, we assess the efficiency, accuracy, and memory requirements of Lagrange polynomials, tensor product B-splines, and ANNs as tabulation strategies. We analyze results in the context of nonadiabatic flamelet modeling where higher dimension counts are necessary. While ANNs do not require structuring of data, providing benefits for complex physics representation, interpolation approaches often rely on some structuring of the table. Interpolation using structured table inputs that are not directly related to the variables transported in a simulation can incur additional query costs. This is demonstrated in the present implementation of heat losses. We show that ANNs, despite being difficult to train and reproduce, can be advantageous for high-dimensional, unstructured datasets relevant to nonadiabatic flamelet models. We also demonstrate that Lagrange polynomials show significant speedup for similar accuracy compared to B-splines.

KEYWORDS:

• Chemistry tabulation
• artificial neural networks
• interpolation
• nonadiabatic flamelet

Acknowledgments

The authors gratefully acknowledge the support of Sandia National Laboratories. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. SAND Number: SAND2022-0633 J. The authors also thank Robert C. Knaus and Michael A. Hansen from Sandia for their many helpful discussions and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ Total and adiabatic enthalpies are transported from which $\gamma$ is computed.

Additional information

Funding

This work was supported by the Sandia National Laboratories [Contract Purchase Agreement number 2156884].