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Application of the polynomial chaos expansion to the simulation of chemical reactors with uncertainties. (English) Zbl 1242.65015
Summary: We consider the simulation of probabilistic chemical reactions in isothermal and adiabatic conditions. Models for reactions under isothermal conditions result in advection equations, adiabatic conditions yield the reactive Euler equations. In order to treat with scattering data, the equations are projected onto the polynomial chaos space. Scattering data can largely affect the estimation of quantities in the system, including variable optimization. This is demonstrated on a selective non-catalytic reduction of nitric oxide.
65C30Stochastic differential and integral equations
60H15Stochastic partial differential equations
35R60PDEs with randomness, stochastic PDE
60H35Computational methods for stochastic equations
80A32Chemically reacting flows (thermodynamic aspects)
65P20Numerical chaos
[1]D., Anderson J.: Hypersonic and high temperature gas dynamics, (2006)
[2]K., Annamalai; K., Puri I.: Combustion science and engineering, (2007)
[3]F. Augustin Zur Numerik des Polynomiellen Chaos bei Differentialgleichungen, Master thesis, Techn. Universität München (Fachbereich Mathematik, Prof. Rentrop), April 2007.
[4]F., Augustin; A., Gilg; M., Paffrath; P., Rentrop; U., Wever: Polynomial chaos for the approximation of uncertainties: chances and limits, European journal of applied mathematics 19, 149-190 (2008) · Zbl 1148.65004 · doi:10.1017/S0956792508007328
[5]H., Cameron R.; T., Martin W.: The orthogonal development of nonlinear functionals in series of Fourier – Hermite functionals, Ann. math. Bd. 48, No. April (2), 385-392 (1947) · Zbl 0029.14302 · doi:10.2307/1969178
[6]J., Chorin A.; E., Marsden J.: A mathematical introduction to fluid mechanics, (2000)
[7]F., Drbal L.; G., Boston P.; L., Westra K.: Power plant engineering, (1995)
[8]W. Duo, Kinetic studies of the reactions involved in the selective non-catalytic reduction of nitric oxide, Phd thesis, Technical University of Denmark, 1990.
[9]F., Froment G.; B., Bischoff K.: Chemical reactor analysis and design, (1990)
[10]G., Ghanem R.: Ingredients for a general purpose stochastic finite elements implementation, Comput. methods appl. Eng. 168, 19-34 (1999) · Zbl 0943.65008 · doi:10.1016/S0045-7825(98)00106-6
[11]G., Ghanem R.; D., Spanos P.: Stochastic finite elements: A spectral approach, (1991) · Zbl 0722.73080
[12]M. Herzog, Zur Numerik von stochastischen Störungen in der Finiten Elemente Methode, Diplomarbeit, Techn. Universität München (Fachbereich Mathematik, Prof. Rentrop), Dezember 2005.
[13]C., Hirsch: Numerical computation of internal and external flows, vol. 1, (1988)
[14]C., Hirsch: Numerical computation of internal and external flows, vol. 2, (1995)
[15]A. Hmaidi, Modeling and numerical simulations of reactive 1-D, Euler gas equations, Bachelor’s thesis, Techn. Universität München (Fachbereich Mathematik, Prof. Rentrop), September 2005.
[16]W., Hundsdorfer; G., Verwer J.: Numerical solution of time-dependent advection-diffusion-reaction equations, (2003)
[17]J., Ingham: Chemical engineering dynamics, (2007)
[18]S., Janson: Gaussian Hilbert spaces, (1997)
[19]G.E. Karniadakis, C.-H. Su, D. Xiu, D. Lucor, C. Schwab, R.A. Todor, Generalized polynomial chaos solution for differential equations with random inputs, Report Nr. 2005-01, ETH Zürich, Seminar für Angewandte Mathematik, January 2005.
[20]J., Leveque R.: Finite volume methods for hyperbolic problems, (2002)
[21]J., Liu: Monte Carlo strategies in scientific computing, (2001)
[22]L., Luyben W.: Chemical reactor design and control, (2007)
[23]P., Le Maître O.; M., Knio O.: Spectral methods for uncertainty quantification with applications to computational fluid dynamics, (2010)
[24]J., Morokoff W.; E., Caflisch Russel: Quasi-Monte Carlo integration, J. comput. Phys. 122, 218-230 (1995) · Zbl 0863.65005 · doi:10.1006/jcph.1995.1209
[25]Nist Scientific Databases NIST Chemistry WebBook, available at http://webbook.nist.gov/chemistry/.
[26]M., østberg; K., Dam-Johansen: Empirical modeling of the selective non-catalytic reduction of NO: comparison with large-scale experiments and detailed kinetic modeling, Chem. eng. Sci. 49, No. 12, 1897-1904 (1994)
[27]M., Paffrath; U., Wever: Adapted polynomial chaos expansion for failure detection, J. comput. Phys., 263-281 (2007) · Zbl 1124.65011 · doi:10.1016/j.jcp.2007.04.011
[28]T., Reagan M.; N., Najm H.; P., Pébay P.; M., Knio O.; G., Ghanem R.: Quantifying uncertainty in chemical systems modeling, Int. J. Chem. kinet. 37, No. 6, 368-382 (2005)
[29]M. Teigeler, Nicht-katalytische Reduzierung der Stickoxidemission am NFZ-Dieselmotor, Phd thesis, Universität Kaiserslautern (Fachbereich Maschinenbau und Verfahrenstechnik), 1998.
[30]M. Villegas, Numerical simulation of reactive flows via polynomial chaos, Master thesis, Techn. Universität München (Fachbereich Mathematik, Prof. Rentrop), August 2008.
[31]J., Warnatz; U., Maas; W., Dibble R.: Verbrennung, (2001)
[32]N., Wiener: The homogeneous chaos, Am. J. Math. 60, 897-936 (1938) · Zbl 0019.35406 · doi:10.2307/2371268
[33]D., Xiu; E., Karniadakis G.: The Wiener – Askey polynomial chaos for stochastic differential equations, SIAM J. Sci. comput. 24, No. 2, 619-644 (2002) · Zbl 1014.65004 · doi:10.1137/S1064827501387826
[34]D., Xiu; E., Karniadakis G.: Modeling uncertainty in flow simulations via generalized polynomial chaos, J. comput. Phys. 187, 137-167 (2003) · Zbl 1047.76111 · doi:10.1016/S0021-9991(03)00092-5
[35]B., Zeldovich Y.: The oxidation of nitrogen in combustion and explosions, Acta physicochim. U.R.S.S. 21, No. 4, 577-628 (1946)