Structure-preserving collocation method for parabolic systems Application to a diffusion Process.
Authors
Abstract
In this contribution we present the reduced port Hamiltonian model of a parabolic system obtained by a structure preserving collocation method. It is applied to a nonlinear diffusion process involving two species in gas phase at constant pressure and temperature.
Keywords
port Hamiltonian modeling; model reduction; infinite dimensional systems; transport phenomena
Citation
- Journal: IFAC-PapersOnLine
- Year: 2016
- Volume: 49
- Issue: 24
- Pages: 82–86
- Publisher: Elsevier BV
- DOI: 10.1016/j.ifacol.2016.10.759
- Note: 2th IFAC Workshop on Thermodynamic Foundations for a Mathematical Systems Theory TFMST 2016- Vigo, Spain, 28—30 September 2016
BibTeX
@article{Couenne_2016,
title={{Structure-preserving collocation method for parabolic systems Application to a diffusion Process.}},
volume={49},
ISSN={2405-8963},
DOI={10.1016/j.ifacol.2016.10.759},
number={24},
journal={IFAC-PapersOnLine},
publisher={Elsevier BV},
author={Couenne, F. and Hamroun, B.},
year={2016},
pages={82--86}
}
References
- Baaiu, A., Couenne, F., Lefevre, L., Le Gorrec, Y. & Tayakout, M. Structure-preserving infinite dimensional model reduction: Application to adsorption processes. Journal of Process Control vol. 19 394–404 (2009) – 10.1016/j.jprocont.2008.07.002
- Bossavit, (1998)
- Callen, (1985)
- Courant, T. J. Dirac manifolds. Transactions of the American Mathematical Society vol. 319 631–661 (1990) – 10.1090/s0002-9947-1990-0998124-1
- Dorfman, (1993)
- Duindam, (2009)
- Flanders, (1989)
- Golo, G., Talasila, V., van der Schaft, A. & Maschke, B. Hamiltonian discretization of boundary control systems. Automatica vol. 40 757–771 (2004) – 10.1016/j.automatica.2003.12.017
- Le Gorrec, Y., Zwart, H. & Maschke, B. Dirac structures and Boundary Control Systems associated with Skew-Symmetric Differential Operators. SIAM Journal on Control and Optimization vol. 44 1864–1892 (2005) – 10.1137/040611677
- Krishna, R. & Wesselingh, J. A. The Maxwell-Stefan approach to mass transfer. Chemical Engineering Science vol. 52 861–911 (1997) – 10.1016/s0009-2509(96)00458-7
- Moulla, R., Lefévre, L. & Maschke, B. Pseudo-spectral methods for the spatial symplectic reduction of open systems of conservation laws. Journal of Computational Physics vol. 231 1272–1292 (2012) – 10.1016/j.jcp.2011.10.008
- van der Schaft, A. J. & Maschke, B. M. Hamiltonian formulation of distributed-parameter systems with boundary energy flow. Journal of Geometry and Physics vol. 42 166–194 (2002) – 10.1016/s0393-0440(01)00083-3
- Villadsen, (1978)
- VU, N. M. T., LEFEVRE, L., NOUAILLETAS, R. & BREMOND, S. Geometric discretization for a plasma control model. IFAC Proceedings Volumes vol. 46 755–760 (2013) – 10.3182/20130204-3-fr-2033.00098