Data-driven selection of stiff chemistry ODE solver in operator-splitting schemes

Lapointe, Simon; Mondal, Sudeepta; Whitesides, Russell A.

doi:10.1016/j.combustflame.2020.06.033

Data-driven selection of stiff chemistry ODE solver in operator-splitting schemes

Journal Article · Wed Jul 08 00:00:00 EDT 2020 · Combustion and Flame

DOI:https://doi.org/10.1016/j.combustflame.2020.06.033· OSTI ID:1647151

Lapointe, Simon ^[1]; Mondal, Sudeepta ^[1]; Whitesides, Russell A. ^[1]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Most computational fluid dynamics simulations of practical combustion applications employ operator-splitting schemes, where chemistry and transport are separated and integrated with distinct numerical methods. The changes in composition due to chemistry are evaluated by solving ordinary differential equations (ODE) in each cell of the computational domain, which typically dominates the computational cost when detailed chemistry is considered. In this work, a data-driven approach for the selection of chemistry ODE solvers in operator-splitting schemes is presented. Neural networks are used to predict the ODE solvers CPU times and errors for a given thermochemical state. This allows the selection of an optimal ODE solver on a cell-by-cell, timestep-by-timestep basis. The models are trained using a wide set of thermochemical states generated through partially-stirred reactors and flames simulations. The methodology is validated by quantifying the prediction errors, the classification accuracy, and the computational speedup. The model predicts the optimal ODE solver for 70 to 95% of the validation cases and decreases the computional cost by a factor of 3 or more. The generalizability of the methodology to different chemical mechanisms and different fuels is assessed and it is shown that the model’s performance is only slightly degraded and its applicability is significantly enhanced if the inputs to the neural networks are restricted to a small set of thermochemical state variables present in most chemical mechanisms. In conclusion, the models are used in an homogeneous reactor case and a multi-dimensional CFD simulation of a diesel spray at high pressure where a speedup of more than 3 is achieved.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE; USDOE National Nuclear Security Administration (NNSA); USDOE Office of Energy Efficiency and Renewable Energy (EERE), Transportation Office. Vehicle Technologies Office

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1647151

Alternate ID(s):: OSTI ID: 1809111

Report Number(s):: LLNL-JRNL--802163; 1005565

Journal Information:: Combustion and Flame, Journal Name: Combustion and Flame Journal Issue: na Vol. 220; ISSN 0010-2180

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (41)

A Semi-implicit Numerical Scheme for Reacting Flow Knio, Omar M.; Najm, Habib N.; Wyckoff, Peter S. Journal of Computational Physics, Vol. 154, Issue 2 https://doi.org/10.1006/jcph.1999.6322	journal	September 1999
On upgrading the numerics in combustion chemistry codes Schwer, Douglas A.; Tolsma, John E.; Green, William H. Combustion and Flame, Vol. 128, Issue 3 https://doi.org/10.1016/S0010-2180(01)00352-2	journal	February 2002
A comprehensive modeling study of iso-octane oxidation Curran, H. Combustion and Flame, Vol. 129, Issue 3 https://doi.org/10.1016/S0010-2180(01)00373-X	journal	May 2002
A Comprehensive Modeling Study of n-Heptane Oxidation Curran, H. J.; Gaffuri, P.; Pitz, W. J. Combustion and Flame, Vol. 114, Issue 1-2 https://doi.org/10.1016/S0010-2180(97)00282-4	journal	July 1998
Understanding complex chemical kinetics with computational singular perturbation Lam, S. H.; Goussis, D. A. Symposium (International) on Combustion, Vol. 22, Issue 1 https://doi.org/10.1016/S0082-0784(89)80102-X	journal	January 1989
Chemical mechanism for high temperature combustion of engine relevant fuels with emphasis on soot precursors Blanquart, G.; Pepiot-Desjardins, P.; Pitsch, H. Combustion and Flame, Vol. 156, Issue 3 https://doi.org/10.1016/j.combustflame.2008.12.007	journal	March 2009
Accelerating multi-dimensional combustion simulations using GPU and hybrid explicit/implicit ODE integration Shi, Yu; Green, William H.; Wong, Hsi-Wu Combustion and Flame, Vol. 159, Issue 7 https://doi.org/10.1016/j.combustflame.2012.02.016	journal	July 2012
Directions in internal combustion engine research Reitz, Rolf D. Combustion and Flame, Vol. 160, Issue 1 https://doi.org/10.1016/j.combustflame.2012.11.002	journal	January 2013
Simulations of transient n-heptane and n-dodecane spray flames under engine-relevant conditions using a transported PDF method Bhattacharjee, Subhasish; Haworth, Daniel C. Combustion and Flame, Vol. 160, Issue 10 https://doi.org/10.1016/j.combustflame.2013.05.003	journal	October 2013
A study of direct and Krylov iterative sparse solver techniques to approach linear scaling of the integration of chemical kinetics with detailed combustion mechanisms Perini, Federico; Galligani, Emanuele; Reitz, Rolf D. Combustion and Flame, Vol. 161, Issue 5 https://doi.org/10.1016/j.combustflame.2013.11.017	journal	May 2014
A dynamic adaptive method for hybrid integration of stiff chemistry Gao, Yang; Liu, Yufeng; Ren, Zhuyin Combustion and Flame, Vol. 162, Issue 2 https://doi.org/10.1016/j.combustflame.2014.07.023	journal	February 2015
Optimized chemical mechanism for combustion of gasoline surrogate fuels Cai, Liming; Pitsch, Heinz Combustion and Flame, Vol. 162, Issue 5 https://doi.org/10.1016/j.combustflame.2014.11.018	journal	May 2015
Modelling n-dodecane spray and combustion with the transported probability density function method Pei, Yuanjiang; Hawkes, Evatt R.; Kook, Sanghoon Combustion and Flame, Vol. 162, Issue 5 https://doi.org/10.1016/j.combustflame.2014.12.019	journal	May 2015
Large eddy simulation of a reacting spray flame with multiple realizations under compression ignition engine conditions Pei, Yuanjiang; Som, Sibendu; Pomraning, Eric Combustion and Flame, Vol. 162, Issue 12 https://doi.org/10.1016/j.combustflame.2015.08.010	journal	December 2015
On the merits of extrapolation-based stiff ODE solvers for combustion CFD Imren, A.; Haworth, D. C. Combustion and Flame, Vol. 174 https://doi.org/10.1016/j.combustflame.2016.09.018	journal	December 2016
An investigation of GPU-based stiff chemical kinetics integration methods Curtis, Nicholas J.; Niemeyer, Kyle E.; Sung, Chih-Jen Combustion and Flame, Vol. 179 https://doi.org/10.1016/j.combustflame.2017.02.005	journal	May 2017
Sparse, iterative simulation methods for one-dimensional laminar flames Lapointe, Simon; Whitesides, Russell A.; McNenly, Matthew J. Combustion and Flame, Vol. 204 https://doi.org/10.1016/j.combustflame.2019.02.030	journal	June 2019
pyJac: Analytical Jacobian generator for chemical kinetics Niemeyer, Kyle E.; Curtis, Nicholas J.; Sung, Chih-Jen Computer Physics Communications, Vol. 215 https://doi.org/10.1016/j.cpc.2017.02.004	journal	June 2017
Second-order splitting schemes for a class of reactive systems Ren, Zhuyin; Pope, Stephen B. Journal of Computational Physics, Vol. 227, Issue 17 https://doi.org/10.1016/j.jcp.2008.05.019	journal	September 2008
Semi-implicit iterative methods for low Mach number turbulent reacting flows: Operator splitting versus approximate factorization MacArt, Jonathan F.; Mueller, Michael E. Journal of Computational Physics, Vol. 326 https://doi.org/10.1016/j.jcp.2016.09.016	journal	December 2016
Analysis of operator splitting errors for near-limit flame simulations Lu, Zhen; Zhou, Hua; Li, Shan Journal of Computational Physics, Vol. 335 https://doi.org/10.1016/j.jcp.2017.01.044	journal	April 2017
Kinetic modeling of gasoline surrogate components and mixtures under engine conditions Mehl, Marco; Pitz, William J.; Westbrook, Charles K. Proceedings of the Combustion Institute, Vol. 33, Issue 1 https://doi.org/10.1016/j.proci.2010.05.027	journal	January 2011
Faster solvers for large kinetic mechanisms using adaptive preconditioners McNenly, Matthew J.; Whitesides, Russell A.; Flowers, Daniel L. Proceedings of the Combustion Institute, Vol. 35, Issue 1 https://doi.org/10.1016/j.proci.2014.05.113	journal	January 2015
Simultaneous formaldehyde PLIF and high-speed schlieren imaging for ignition visualization in high-pressure spray flames Skeen, Scott A.; Manin, Julien; Pickett, Lyle M. Proceedings of the Combustion Institute, Vol. 35, Issue 3 https://doi.org/10.1016/j.proci.2014.06.040	journal	January 2015
Reduced chemical model for low and high-temperature oxidation of fuel blends relevant to internal combustion engines Lapointe, S.; Zhang, K.; McNenly, M. J. Proceedings of the Combustion Institute, Vol. 37, Issue 1 https://doi.org/10.1016/j.proci.2018.06.139	journal	January 2019
Three-dimensional direct numerical simulation of a turbulent lifted hydrogen jet flame in heated coflow: a chemical explosive mode analysis Lu, T. F.; Yoo, C. S.; Chen, J. H. Journal of Fluid Mechanics, Vol. 652 https://doi.org/10.1017/S002211201000039X	journal	May 2010
An Analytical Jacobian Approach to Sparse Reaction Kinetics for Computationally Efficient Combustion Modeling with Large Reaction Mechanisms Perini, Federico; Galligani, Emanuele; Reitz, Rolf D. Energy & Fuels, Vol. 26, Issue 8 https://doi.org/10.1021/ef300747n	journal	July 2012
CVODE, A Stiff/Nonstiff ODE Solver in C Cohen, Scott D.; Hindmarsh, Alan C.; Dubois, Paul F. Computers in Physics, Vol. 10, Issue 2 https://doi.org/10.1063/1.4822377	journal	January 1996
Turbulence Modeling of Internal Combustion Engines Using RNG κ-ε Models Han, Z.; Reitz, R. D. Combustion Science and Technology, Vol. 106, Issue 4-6 https://doi.org/10.1080/00102209508907782	journal	January 1995
Stochastic Modeling of Partially Stirred Reactors Chen, J. -Y. Combustion Science and Technology, Vol. 122, Issue 1-6 https://doi.org/10.1080/00102209708935605	journal	January 1997
Variational Inference: A Review for Statisticians Blei, David M.; Kucukelbir, Alp; McAuliffe, Jon D. Journal of the American Statistical Association, Vol. 112, Issue 518 https://doi.org/10.1080/01621459.2017.1285773	journal	July 2016
Integration of large chemical kinetic mechanisms via exponential methods with Krylov approximations to Jacobian matrix functions Bisetti, Fabrizio Combustion Theory and Modelling, Vol. 16, Issue 3 https://doi.org/10.1080/13647830.2011.631032	journal	June 2012
Development of a Stiffness-Based Chemistry Load Balancing Scheme, and Optimization of Input/Output and Communication, to Enable Massively Parallel High-Fidelity Internal Combustion Engine Simulations Kodavasal, Janardhan; Harms, Kevin; Srivastava, Priyesh Journal of Energy Resources Technology, Vol. 138, Issue 5 https://doi.org/10.1115/1.4032623	journal	February 2016
On the Construction and Comparison of Difference Schemes Strang, Gilbert SIAM Journal on Numerical Analysis, Vol. 5, Issue 3 https://doi.org/10.1137/0705041	journal	September 1968
Recent Progress in Extrapolation Methods for Ordinary Differential Equations Deuflhard, P. SIAM Review, Vol. 27, Issue 4 https://doi.org/10.1137/1027140	journal	December 1985
A Supernodal Approach to Sparse Partial Pivoting Demmel, James W.; Eisenstat, Stanley C.; Gilbert, John R. SIAM Journal on Matrix Analysis and Applications, Vol. 20, Issue 3 https://doi.org/10.1137/S0895479895291765	journal	January 1999
On Information and Sufficiency Kullback, S.; Leibler, R. A. The Annals of Mathematical Statistics, Vol. 22, Issue 1 https://doi.org/10.1214/aoms/1177729694	journal	March 1951
A fully coupled computational fluid dynamics and multi-zone model with detailed chemical kinetics for the simulation of premixed charge compression ignition engines Babajimopoulos, A.; Assanis, D. N.; Flowers, D. L. International Journal of Engine Research, Vol. 6, Issue 5 https://doi.org/10.1243/146808705X30503	journal	October 2005
Some application of splitting-up methods to the solution of mathematical physics problems [Some application of splitting-up methods to the solution of mathematical physics problems] Marchuk, Gurij Ivanovich Applications of Mathematics, Vol. 13, Issue 2 https://doi.org/10.21136/AM.1968.103142	journal	January 1968
Comparison of Diesel Spray Combustion in Different High-Temperature, High-Pressure Facilities Pickett, Lyle M.; Genzale, Caroline L.; Bruneaux, Gilles SAE International Journal of Engines, Vol. 3, Issue 2 https://doi.org/10.4271/2010-01-2106	journal	August 2010
Relationship Between Diesel Fuel Spray Vapor Penetration/Dispersion and Local Fuel Mixture Fraction Pickett, Lyle M.; Manin, Julien; Genzale, Caroline L. SAE International Journal of Engines, Vol. 4, Issue 1 https://doi.org/10.4271/2011-01-0686	journal	April 2011

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Data-driven selection of stiff chemistry ODE solver in operator-splitting schemes

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