×

zbMATH — the first resource for mathematics

Forward, tangent linear, and adjoint Runge-Kutta methods for stiff chemical kinetic simulations. (English) Zbl 1202.65090
Summary: We investigate numerical methods for direct decoupled sensitivity and discrete adjoint sensitivity analysis of stiff systems based on implicit Runge-Kutta schemes. Efficient implementations of tangent linear and adjoint schemes are discussed for two families of methods: fully implicit three-stage Runge-Kutta and singly diagonally-implicit Runge-Kutta. High computational efficiency is attained by exploiting the sparsity patterns of the Jacobian and Hessian. Numerical experiments with a large chemical system used in atmospheric chemistry illustrate the power of the stiff Runge-Kutta integrators and their tangent linear and discrete adjoint models. Through the integration with the Kinetic PreProcessor KPP-2.2 these numerical techniques become readily available to a wide community interested in the simulation of chemical kinetic systems.

MSC:
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L04 Numerical methods for stiff equations
34A34 Nonlinear ordinary differential equations and systems
80A30 Chemical kinetics in thermodynamics and heat transfer
80M25 Other numerical methods (thermodynamics) (MSC2010)
Software:
ODESSA; VODE; LSODE; RODAS
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Baguer M. L., Approximation and Optimization in the Carribbean II pp 14– (1995)
[2] DOI: 10.1137/0910062 · Zbl 0677.65075
[3] DOI: 10.1137/0916069 · Zbl 0836.65080
[4] Carter, W. P.L. 2000.Documentation of the SAPRC-99 chemical mechanism for VOC reactivity assessment: final report to California air resources board, 95–308. California Air Resources Board Contract, 92–329. California Air Resources Board
[5] CHEMKIN reactor models home page. Available at:http://www.reactiondesign.com/products/open/chemkin.html
[6] Curtis A. R., Tech. Rep. Computer Science and Systems Division (1987)
[7] DOI: 10.1016/j.atmosenv.2003.08.020
[8] DOI: 10.1016/S0098-1354(02)00128-X
[9] DOI: 10.1023/A:1026067610565
[10] DOI: 10.1063/1.447938
[11] Giles M. B., Tech. Rep. NA00/10 (2000)
[12] DOI: 10.1145/198429.198437 · Zbl 0888.65096
[13] DOI: 10.1007/s002110000178 · Zbl 0991.49020
[14] Hairer E., Stiff and Differential-Algebraic Problems (1996) · Zbl 0859.65067
[15] Hairer E., Solving Ordinary Differential Equations I. Nonstiff Problems (1993) · Zbl 0789.65048
[16] DOI: 10.1093/imanum/11.4.457 · Zbl 0738.65073
[17] DOI: 10.1145/42288.214371 · Zbl 0639.65043
[18] Miehe, P. and Sandu, A. 2006.Forward, Tangent Linear, and Adjoint Runge Kutta Methods in KPP–2.2, 120–127. Berlin Heidelberg: Springer-Verlag. ICCS 2006, III, LNCS 3993 · Zbl 1157.80405
[19] DOI: 10.2172/15013302
[20] DOI: 10.5194/acp-5-445-2005
[21] Sandu, A. 2006.On the Properties of Runge Kutta Discrete Adjoints, Edited by: Alexandrov, V. N. 550–557. Berlin Heidelberg: Springer-Verlag. ICCS 2006, Part IV, LNCS 3994 · Zbl 1157.65421
[22] Sandu A., Tech. Rep. Computer Science Department at Virginia Tech (2006)
[23] Sandu A., KPP – user’s manual
[24] DOI: 10.5194/acp-6-187-2006
[25] DOI: 10.1016/j.atmosenv.2003.08.019
[26] DOI: 10.1016/S1352-2310(97)83212-8
[27] Tang Y., J. Geophys. Res. 108 (2003)
[28] Trentmann J., J. Geophys. Res. 108 (2003)
[29] von Glasow R., J. Geophys. Res. 107 (2002)
[30] von Kuhlmann R., J. Geophys. Res. 108 (2003)
[31] Walther A., Technical University Dresden technical report WR-06-2004
[32] DOI: 10.1002/qj.49712757616
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.