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Research Article

Using computational singular perturbation as a diagnostic tool in ODE and DAE systems: a case study in heterogeneous catalysis

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Pages 201-227 | Received 06 Aug 2021, Accepted 26 Oct 2021, Published online: 22 Nov 2021

References

  • S. Lam, Singular perturbation for stiff equations using numerical methods, in Recent Advances in the Aerospace Sciences, C. Casci, ed., Plenum Press, New York, 1985, pp. 3.
  • S. Lam and D. Goussis, Understanding complex chemical kinetics with computational singular perturbation, Proc. Comb. Inst. 22 (1988), pp. 931–941.
  • S. Lam and D. Goussis, Computational singular perturbation; theory and applications, Report 1986-MAE, Princeton Univ., 1991.
  • S. Lam and D. Goussis, The analytic foundation of CSP, Report 1800-MAE, Princeton Univ., 1991.
  • S. Lam, Using CSP to understand complex chemical kinetics, Combust. Sci. Technol. 89 (1993), pp. 375–404.
  • S. Lam and D. Goussis, The CSP method for simplifying kinetics, Int. J. Chem. Kinet. 26 (1994), pp. 461–486.
  • M. Valorani, D. Goussis, and H. Najm, Using CSP to analyze computed reactive flows, 8th SIAM Int. Conf. On Numerical Combustion, March, Amelia Island, FL, 2000.
  • A. Zagaris, H. Kaper, and T. Kaper, Analysis of the CSP reduction method for chemical kinetics, SIAM Conference on Applications of Dynamical Systems, May 27-31, 2003 at Snowbird, Utah, 2003.
  • J. Lee, H. Najm, S. Lefantzi, J. Ray, M. Frenklach, M. Valorani, and D. Goussis, A CSP and tabulation based adaptive chemistry model, Combust. Theor. Model. 11 (2007), pp. 73–102.
  • J. Prager, H. Najm, M. Valorani, and D. Goussis, Skeletal mechanism generation with CSP and validation for premixed n-Heptane flames, Proc. Comb. Inst. 32 (2009), pp. 509–517.
  • M. Valorani, D. Goussis, and H. Najm, Using CSP to analyze computed reacting flows, Eighth International Conference on Numerical Combustion, SIAM, 2000.
  • M. Valorani, F. Creta, F. Donato, H. Najm, and D. Goussis, Skeletal mechanism generation and analysis for n-heptane with CSP, Proc. Comb. Inst. 31 (2007), pp. 483–490.
  • M. Valorani, F. Creta, F. Donato, H. Najm, and D. Goussis, Skeletal mechanism generation and analysis for n-heptane with CSP, 31st Symposium on Combustion, August, Heidelberg, Germany. 2006.
  • M. Valorani, F. Creta, F. Donato, H. Najm, and D. Goussis, A CSP-based skeletal mechanism generation procedure: Auto-ignition and premixed laminar flames in n-heptane/air mixtures, ECCOMAS CFD 2006, September, Delft, Holland. 2006.
  • M. Valorani, F. Creta, D. Goussis, J. Lee, and H. Najm, An Automatic Procedure for the Simplification of Chemical Kinetics Mechanisms based on CSP, in Computational Fluid and Solid Mechanics 2005, Bathe K.J., eds., Elsevier Science, Amsterdam, Netherlands, 2005. pp. 900–904.
  • M. Valorani, F. Creta, D. Goussis, J. Lee, and H. Najm, Chemical kinetics simplification via CSP, Combust. Flame. 146 (2006), pp. 29–51.
  • M. Valorani, D. Goussis, and H. Najm, Enhanced CSP diagnostic tools to analyze reacting flows, Ninth Int. Conf. on Numerical Combustion, April, Sorrento, Italy, 2002.
  • M. Valorani, H. Najm, and D. Goussis, CSP analysis of a transient flame-vortex interaction: Time scales and manifolds, Combust. Flame. 134 (2003), pp. 35–53.
  • H.N. Najm, M. Valorani, D.A. Goussis, and J. Prager, Analysis of methane-air edge flame structure, Combust. Theor. Model. 14 (2010), pp. 257–294.
  • R. Malpica Galassi, M. Valorani, H.N. Najm, C. Safta, M. Khalil, and P.P. Ciottoli, Chemical model reduction under uncertainty, Combust. Flame. 179 (2017), pp. 242–252.
  • V. Fratalocchi and J.B.W. Kok, The computational singular perturbation/perfectly stirred reactor approach in reduced chemistry of premixed ethanol combustion, Combust. Sci. Technol. 189 (2017), pp. 1659–1680.
  • D.G. Patsatzis, E.A. Tingas, D.A. Goussis, and S.M. Sarathy, Computational singular perturbation analysis of brain lactate metabolism, PLoS. ONE. 14 (2019), pp. 1–37.
  • D.A. Goussis and H.N. Najm, Model reduction and physical understanding of slowly oscillating processes: The Circadian cycle, Multiscale. Model. Simul. 5 (2006), pp. 1297–1332.
  • T.J. Snowden, P.H. van der Graaf, and M.J. Tindall, Methods of model reduction for large-scale biological systems: A survey of current methods and trends, Bull. Math. Biol. 79 (2017), pp. 1449–1486.
  • M. Valorani and D. Goussis, Explicit time-scale splitting algorithm for stiff problems: auto-ignition of gaseous-mixtures behind a steady shock, J. Comput. Phys. 169 (2001), pp. 44–79.
  • X. Han, M. Valorani, and H.N. Najm, Explicit time integration of the stiff chemical langevin equations using computational singular perturbation, J. Chem. Phys. 150 (2019), pp. 194101.
  • J. Prager, H. Najm, M. Valorani, and D. Goussis, Structure of n-heptane/air triple flames in partially-premixed mixing layers, Combust. Flame. 158 (2011), pp. 2128–2144.
  • S. Gupta, H.G. Im, and M. Valorani, Analysis of n-heptane auto-ignition characteristics using computational singular perturbation, Proc. Combust. Inst. 34 (2013), pp. 1125–1133.
  • D. Goussis, Quasi steady state and partial equilibrium approximations: Their relation and their validity, Combust. Theor. Model. 16 (2012), pp. 869–926.
  • A.H. Motagamwala and J.A. Dumesic, Microkinetic modeling: A tool for rational catalyst design, Chem. Rev. 121 (2021), pp. 1049–1076. pMID: 33205961.
  • L.C. Grabow and M. Mavrikakis, Mechanism of methanol synthesis on cu through Co2 and co hydrogenation, ACS. Catal. 1 (2011), pp. 365–384.
  • R. Cortright and J. Dumesic, Kinetics of heterogeneous catalytic reactions: Analysis of reaction schemes, Advances in Catalysis, Vol. 46, Academic Press, 2001, pp. 161–264.
  • O. Deutschmann, Modeling of the interactions between catalytic surfaces and gas-phase, Catal. Lett.145 (2015), pp. 272–289.
  • R. Quiceno, J. Pérez-Ramírez, J. Warnatz, and O. Deutschmann, Modeling the high-temperature catalytic partial oxidation of methane over platinum gauze: Detailed gas-phase and surface chemistries coupled with 3d flow field simulations, Appl. Catal. A: General 303 (2006), pp. 166–176.
  • R.J. Kee, H.Z.M.E. Coltrin, and P. Glarborg, Chemically Reacting Flow: Theory, Modeling, and Simulation, 2nd ed., Wiley, Hoboken, New Jersey, 2017.
  • M.E. Coltrin, R.J. Kee, and F.M. Rupley, Surface chemkin: A general formalism and software for analyzing heterogeneous chemical kinetics at a gas-surface interface, Int. J. Chem. Kinet. 23 (1991), pp. 1111–1128.
  • K. Blondal, J. Jelic, E. Mazeau, F. Studt, R.H. West, and C.F. Goldsmith, Computer-generated kinetics for coupled heterogeneous/homogeneous systems: A case study in catalytic combustion of methane on platinum, Ind. Eng. Chem. Res. 58 (2019), pp. 17682–17691.
  • M. Salciccioli, Y. Chen, and D.G. Vlachos, Microkinetic modeling and reduced rate expressions of ethylene hydrogenation and ethane hydrogenolysis on platinum, Ind. Eng. Chem. Res. 50 (2011), pp. 28–40.
  • D. Goodwin, R.L. Speth, H.K. Moffat, and B.W. Weber. 2021. Cantera: An Object-oriented Software Toolkit for Chemical Kinetics, Thermodynamics, and Transport Processes. https://www.cantera.org.https://doi.org/10.5281/zenodo.4527812
  • R.J. Kee, F.M. Rupley, E. Meeks, and J.A. Miller, CHEMKIN-III: A FORTRAN chemical kinetics package for the analysis of gas-phase chemical and plasma kinetics. Tech. Rep. SAND-96-8216 1996. doi:https://doi.org/10.2172/481621.
  • TChem, preprint (2020). Available at https://github.com/sandialabs/TChem (accessed 1 December 2020).
  • K. Kim, O. Diaz-Ibarra, C. Safta, and H.N. Najm, TChem v2.0 – a software toolkit for the analysis of complex kinetic models, Tech. Rep. SAND2020-10762, Sandia National Laboratories, Livermore, CA, 2020.
  • K. Kim, C. Safta, and O.H. Diaz-Ibarra, Tchem 2.0 [Computer Software] preprint (2020). Available at https://doi.org/https://doi.org/10.11578/dc.20210930.4.
  • G.P. Smith, D.M. Golden, M. Frenklach, N.W. Moriarty, B. Eiteneer, M. Goldenberg, C.T. Bowman, R.K. Hanson, S. Song, W.C. Gardiner, Jr., V. Vitali, V.V. Lissianski, and Z. Qin, GRI-Mech v3.0, preprint (2011). Available at http://www.me.berkeley.edu/gri_mech (accessed: 26 August 2020).
  • CSPlib, preprint (2021). Available at https://github.com/sandialabs/CSPlib (accessed 11 May 2021).
  • O. Diaz-Ibarra, K. Kim, C. Safta, and H.N. Najm, CSPlib – a software toolkit for the analysis of dynamical systems and chemical kinetic models, Tech. Rep. SAND2021-1212, Sandia National Laboratories, Livermore, CA, 2021.
  • D. Goussis, M. Valorani, F. Creta, and H. Najm, Inertial manifolds with CSP, in Computational Fluid and Solid Mechanics 2003, K. Bathe, ed., Vol. 2, Elsevier Science, Cambridge, MA, 2003, pp. 1951–1954.
  • M. Valorani, D. Goussis, F. Creta, and H. Najm, Higher order corrections in the approximation of low dimensional manifolds and the construction of simplified problems with the CSP method, J. Comput. Phys. 209 (2005), pp. 754–786.
  • A. Zagaris, H. Kaper, and T. Kaper, Analysis of the CSP reduction method for chemical kinetics, Nonlinear Sci. 14 (2004), pp. 59–91.
  • M. Hadjinicolaou and D. Goussis, Asymptotic solution of stiff PDEs with the CSP method – the reaction diffusion equation, SIAM J. Sci. Comput. 20 (1999), pp. 781–810.
  • M. Salloum, A. Alexanderian, O. Le Maître, H. Najm, and O. Knio, Simplified CSP analysis of a stiff stochastic ODE system, Comput. Methods Appl. Mech. Eng. 217–220 (2012), pp. 121–138.
  • M. Valorani, P. Ciottoli, R. Malpica Galassi, S. Paolucci, T. Grenga, and E. Martelli, Enhancements of the G-scheme framework, Flow Turbul. Combust. 101 (2018), pp. 1023–1033.
  • M. Valorani, F. Creta, P. Ciottoli, R.M. Galassi, D. Goussis, H. Najm, S. Paolucci, H.G. Im, E.A. Tingas, D. Manias, A. Parente, and T. Grenga, Computational singular perturbation method and tangential stretching rate analysis of large scale simulations of reactive flows: Feature tracking, time scale characterization, and cause/effect identification. Part 1, basic concepts, in Data Analysis for Direct Numerical Simulations of Turbulent Combustion, H. Pitsch and A. Attili, eds., 1st ed., Vol. 1, chap. 3, Springer International Publishing, Springer Nature Switzerland AG, 2020, pp. 43–64.
  • M. Valorani, F. Creta, D.A. Goussis, J.C. Lee, and H.N. Najm, An automatic procedure for the simplification of chemical kinetic mechanisms based on csp, Combust. Flame. 146 (2006), pp. 29–51.
  • H.N. Najm, O.H. Diaz-Ibarra, K. Kim, and F. Rob, Csplib, [Computer Software], preprint (2021). Available at https://doi.org/https://doi.org/10.11578/dc.20210930.3 .
  • Tines, preprint (2021). Available at: https://github.com/sandialabs/tines (accessed 11 May 2021).
  • K. Kim and O. Diaz-Ibarra, Tines – time integration, Newton and Eigen solver v. 1.0 [Computer Software], preprint (2021). Available at https://www.osti.gov/doecode/biblio/50966 .
  • SACADO, preprint (2021). Available at https://docs.trilinos.org/dev/packages/sacado/doc/html/index.html (accessed 2 April 2021).
  • E.T. Phipps, R.A. Bartlett, D.M. Gay, and R.J. Hoekstra, Large-scale transient sensitivity analysis of a radiation-damaged bipolar junction transistor via automatic differentiation, in Advances in Automatic Differentiation, C.H. Bischof, H.M. Bücker, P. Hovland, U. Naumann, and J. Utke, eds., Springer, Berlin, Heidelberg, 2008, pp. 351–362.
  • M. Valorani and S. Paolucci, The G-scheme: A framework for multi-scale adaptive model reduction, J. Comput. Phys. 228 (2009), pp. 4665–4701.
  • S.G. Krantz and H.R. Parks, The Implicit Function Theorem, History, Theory, and Applications, Birkhauser, 2003.
  • M. Valorani, (2021). Private communication.

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