Symbolic construction of the chemical Jacobian of quasi-steady state (QSS) chemistries for Exascale computing platforms

Hassanaly, Malik; Wimer, Nicholas T.; Felden, Anne; Esclapez, Lucas; Ream, Julia; Henry de Frahan, Marc T.; Rood, Jon; Day, Marc

doi:10.1016/j.combustflame.2024.113740

Title: Symbolic construction of the chemical Jacobian of quasi-steady state (QSS) chemistries for Exascale computing platforms

Journal Article · 20 September 2024 · Combustion and Flame

DOI: https://doi.org/10.1016/j.combustflame.2024.113740 · OSTI ID:2449680

^[1];

^[2];

^[1];

^[3];

^[1];

^[1]

National Renewable Energy Laboratory (NREL), Golden, CO (United States)
Delft Univ. of Technology (Netherlands)
Florida State Univ., Tallahassee, FL (United States)

The Quasi-Steady State Approximation (QSSA) can be an effective tool for reducing the size and stiffness of chemical mechanisms for implementation in computational reacting flow solvers. However, for many applications, the resulting model still requires implicit methods for efficient time integration. Here, in this paper, we outline an approach to formulating the QSSA reduction that is coupled with a strategy to generate C++ source code to evaluate the net species production rates, and the chemical Jacobian. The code-generation component employs a symbolic approach enabling a simple and effective strategy to analytically compute the chemical Jacobian. For computational tractability, the symbolic approach needs to be paired with common subexpression elimination which can negatively affect memory usage. Several solutions are outlined and successfully tested on a 3D multipulse ignition problem, thus allowing portable application across chemical model sizes and GPU capabilities. The implementation of the proposed method is available at https://github.com/AMReX-Combustion/PelePhysics under an open-source license.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: National Renewable Energy Laboratory (NREL), Golden, CO (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF); USDOE Office of Energy Efficiency and Renewable Energy (EERE)

Grant/Contract Number:: AC36-08GO28308; AC05-00OR22725

OSTI ID:: 2449680

Report Number(s):: NREL/JA--2C00-83709; MainId:84482; UUID:7b5e9a12-7cfb-4052-9e12-ab5d91f29138; MainAdminId:73488

Journal Information:: Combustion and Flame, Journal Name: Combustion and Flame Vol. 270; ISSN 0010-2180

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (42)

Mechanism reduction for the oscillatory oxidation of hydrogen: Sensitivity and quasi-steady-state analyses Tomlin, Alison S.; Pilling, Michael J.; Turányi, Tamás Combustion and Flame, Vol. 91, Issue 2 https://doi.org/10.1016/0010-2180(92)90094-6	journal	November 1992
A strong-connectivity algorithm and its applications in data flow analysis Sharir, M. Computers & Mathematics with Applications, Vol. 7, Issue 1 https://doi.org/10.1016/0898-1221(81)90008-0	journal	January 1981
Including analytically reduced chemistry (ARC) in CFD applications Felden, Anne; Pepiot, Perrine; Esclapez, Lucas Acta Astronautica, Vol. 158 https://doi.org/10.1016/j.actaastro.2019.03.035	journal	May 2019
Linear time reduction of large kinetic mechanisms with directed relation graph: n-Heptane and iso-octane Lu, Tianfeng; Law, Chung K. Combustion and Flame, Vol. 144, Issue 1-2 https://doi.org/10.1016/j.combustflame.2005.02.015	journal	January 2006
Strategies for mechanism reduction for large hydrocarbons: n-heptane Lu, T.; Law, C. Combustion and Flame, Vol. 154, Issue 1-2 https://doi.org/10.1016/j.combustflame.2007.11.013	journal	July 2008
Direct numerical simulations of ignition of a lean n-heptane/air mixture with temperature inhomogeneities at constant volume: Parametric study Yoo, Chun Sang; Lu, Tianfeng; Chen, Jacqueline H. Combustion and Flame, Vol. 158, Issue 9 https://doi.org/10.1016/j.combustflame.2011.01.025	journal	September 2011
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
Formation, growth, and transport of soot in a three-dimensional turbulent non-premixed jet flame Attili, Antonio; Bisetti, Fabrizio; Mueller, Michael E. Combustion and Flame, Vol. 161, Issue 7 https://doi.org/10.1016/j.combustflame.2014.01.008	journal	July 2014
Experimental and modeling study on the high-temperature oxidation of Ammonia and related NOx chemistry Mathieu, Olivier; Petersen, Eric L. Combustion and Flame, Vol. 162, Issue 3 https://doi.org/10.1016/j.combustflame.2014.08.022	journal	March 2015
Direct numerical simulation of a temporally evolving air/n-dodecane jet at low-temperature diesel-relevant conditions Borghesi, Giulio; Krisman, Alexander; Lu, Tianfeng Combustion and Flame, Vol. 195 https://doi.org/10.1016/j.combustflame.2018.02.020	journal	September 2018
Influence of operating conditions on flow field dynamics and soot formation in an aero-engine model combustor Grader, Martin; Gerlinger, Peter Combustion and Flame, Vol. 258 https://doi.org/10.1016/j.combustflame.2023.112712	journal	December 2023
GPU based simulation of reactive mixtures with detailed chemistry in combination with tabulation and an analytical Jacobian Dijkmans, Thomas; Schietekat, Carl M.; Van Geem, Kevin M. Computers & Chemical Engineering, Vol. 71 https://doi.org/10.1016/j.compchemeng.2014.09.016	journal	December 2014
A minimally-dissipative low-Mach number solver for complex reacting flows in OpenFOAM Hassanaly, Malik; Koo, Heeseok; Lietz, Christopher F. Computers & Fluids, Vol. 162 https://doi.org/10.1016/j.compfluid.2017.11.020	journal	January 2018
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
DeepFlame: A deep learning empowered open-source platform for reacting flow simulations Mao, Runze; Lin, Minqi; Zhang, Yan Computer Physics Communications, Vol. 291 https://doi.org/10.1016/j.cpc.2023.108842	journal	October 2023
A compact skeletal mechanism for n-dodecane with optimized semi-global low-temperature chemistry for diesel engine simulations Yao, Tong; Pei, Yuanjiang; Zhong, Bei-Jing Fuel, Vol. 191 https://doi.org/10.1016/j.fuel.2016.11.083	journal	March 2017
Jacobian-free Newton–Krylov methods: a survey of approaches and applications Knoll, D. A.; Keyes, D. E. Journal of Computational Physics, Vol. 193, Issue 2 https://doi.org/10.1016/j.jcp.2003.08.010	journal	January 2004
High order conservative finite difference scheme for variable density low Mach number turbulent flows Desjardins, Olivier; Blanquart, Guillaume; Balarac, Guillaume Journal of Computational Physics, Vol. 227, Issue 15 https://doi.org/10.1016/j.jcp.2008.03.027	journal	July 2008
Towards dense linear algebra for hybrid GPU accelerated manycore systems Tomov, Stanimire; Dongarra, Jack; Baboulin, Marc Parallel Computing, Vol. 36, Issue 5-6 https://doi.org/10.1016/j.parco.2009.12.005	journal	June 2010
Toward accommodating realistic fuel chemistry in large-scale computations Lu, Tianfeng; Law, Chung K. Progress in Energy and Combustion Science, Vol. 35, Issue 2 https://doi.org/10.1016/j.pecs.2008.10.002	journal	April 2009
A directed relation graph method for mechanism reduction Lu, Tianfeng; Law, Chung K. Proceedings of the Combustion Institute, Vol. 30, Issue 1 https://doi.org/10.1016/j.proci.2004.08.145	journal	January 2005
Structure of a spatially developing turbulent lean methane–air Bunsen flame Sankaran, Ramanan; Hawkes, Evatt R.; Chen, Jacqueline H. Proceedings of the Combustion Institute, Vol. 31, Issue 1 https://doi.org/10.1016/j.proci.2006.08.025	journal	January 2007
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
Large Eddy Simulation of an industrial gas turbine combustor using reduced chemistry with accurate pollutant prediction Jaravel, T.; Riber, E.; Cuenot, B. Proceedings of the Combustion Institute, Vol. 36, Issue 3 https://doi.org/10.1016/j.proci.2016.07.027	journal	January 2017
Ensemble-LES analysis of perturbation response of turbulent partially-premixed flames Hassanaly, Malik; Raman, Venkat Proceedings of the Combustion Institute, Vol. 37, Issue 2 https://doi.org/10.1016/j.proci.2018.06.209	journal	January 2019
Pareto-efficient combustion modeling for improved CO-emission prediction in LES of a piloted turbulent dimethyl ether jet flame Wu, Hao; Ma, Peter C.; Jaravel, Thomas Proceedings of the Combustion Institute, Vol. 37, Issue 2 https://doi.org/10.1016/j.proci.2018.08.010	journal	January 2019
Probabilistic modeling of forced ignition of alternative jet fuels Tang, Yihao; Hassanaly, Malik; Raman, Venkat Proceedings of the Combustion Institute https://doi.org/10.1016/j.proci.2020.06.309	journal	September 2020
HPC-enabling technologies for high-fidelity combustion simulations Mira, Daniel; Pérez-Sánchez, Eduardo J.; Borrell, Ricard Proceedings of the Combustion Institute, Vol. 39, Issue 4 https://doi.org/10.1016/j.proci.2022.07.222	journal	January 2023
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
On the error of the quasi-steady-state approximation Turanyi, T.; Tomlin, A. S.; Pilling, M. J. The Journal of Physical Chemistry, Vol. 97, Issue 1 https://doi.org/10.1021/j100103a028	journal	January 1993
Systematic Approach To Obtain Analytic Solutions of Quasi Steady State Species in Reduced Mechanisms The Journal of Physical Chemistry A, Vol. 110, Issue 49 https://doi.org/10.1021/jp064482y	journal	December 2006
The steady state and equilibrium approximations: A geometrical picture Fraser, Simon J. The Journal of Chemical Physics, Vol. 88, Issue 8 https://doi.org/10.1063/1.454686	journal	April 1988
The partial‐equilibrium approximation in reacting flows Rein, Martin Physics of Fluids A: Fluid Dynamics, Vol. 4, Issue 5 https://doi.org/10.1063/1.858267	journal	May 1992
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
Depth-First Search and Linear Graph Algorithms Tarjan, Robert SIAM Journal on Computing, Vol. 1, Issue 2 https://doi.org/10.1137/0201010	journal	June 1972
The Pele Simulation Suite for Reacting Flows at Exascale de Frahan, Marc T. Henry; Esclapez, Lucas; Rood, Jon Proceedings of the 2024 SIAM Conference on Parallel Processing for Scientific Computing (PP), p. 13-25 https://doi.org/10.1137/1.9781611977967.2	book	January 2024
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers Hindmarsh, Alan C.; Brown, Peter N.; Grant, Keith E. ACM Transactions on Mathematical Software, Vol. 31, Issue 3 https://doi.org/10.1145/1089014.1089020	journal	September 2005
Eine Theorie der photochemischen Reaktionsgeschwindigkeiten Bodenstein, Max Zeitschrift für Physikalische Chemie, Vol. 85U, Issue 1 https://doi.org/10.1515/zpch-1913-8512	journal	October 1913
PeleLMeX: an AMR Low Mach Number Reactive Flow Simulation Code without level sub-cycling Esclapez, Lucas; Day, Marc; Bell, John Journal of Open Source Software, Vol. 8, Issue 90 https://doi.org/10.21105/joss.05450	journal	October 2023
Growth of Rounding Errors and Repetitivity of Large Eddy Simulations Senoner, Jean-Mathieu; García, Marta; Mendez, Simon AIAA Journal, Vol. 46, Issue 7 https://doi.org/10.2514/1.34862	journal	July 2008
Development of Comprehensive Detailed and Reduced Reaction Mechanisms for Combustion Modeling Law, C. K.; Sung, C. J.; Wang, H. AIAA Journal, Vol. 41, Issue 9 https://doi.org/10.2514/2.7289	journal	September 2003
SymPy: symbolic computing in Python Meurer, Aaron; Smith, Christopher P.; Paprocki, Mateusz PeerJ Computer Science, Vol. 3 https://doi.org/10.7717/peerj-cs.103	journal	January 2017

Similar Records

The ALPAL Matrix Editor for symbolic Jacobians

Conference · 1990 · OSTI ID:6991543

Painter, J F

PeleLMeX: an AMR Low Mach Number Reactive Flow Simulation Code without level sub-cycling

Journal Article · 2023 · Journal of Open Source Software · OSTI ID:2228465

Esclapez, Lucas; Day, Marc; Bell, John; +11 more

The Matrix Editor for symbolic Jacobians in ALPAL

Conference · 1991 · OSTI ID:5503219

Painter, J F

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
97 MATHEMATICS AND COMPUTING
analytic Jacobian
high-performance computing
quasi-steady state chemistry

Title: Symbolic construction of the chemical Jacobian of quasi-steady state (QSS) chemistries for Exascale computing platforms

Citation Formats

References (42)

Similar Records

Related Subjects