Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-05T05:27:13.380Z Has data issue: false hasContentIssue false

Transport Equation Reduction for a Mathematical Model in PlantGrowth

Published online by Cambridge University Press:  01 March 2011

S. Boujena*
Affiliation:
Department of Mathematics and computing, Hassan II University, Sciences Faculty, POB 5366 Maarif, Casablanca, Morocco
A. Chiboub
Affiliation:
Department of Mathematics and computing, Hassan II University, Sciences Faculty, POB 5366 Maarif, Casablanca, Morocco
J. Pousin
Affiliation:
Université de Lyon, INSA de Lyon, ICJ UMR CNRS 5028, 69100 Villeurbanne cedex France
*
Corresponding author. E-mail: [email protected]
Get access

Abstract

In this article a variational reduction method, how to handle the case of heterogenousdomains for the Transport equation, is presented. This method allows to get rid of therestrictions on the size of time steps due to the thin parts of the domain. In the thinpart of the domain, only a differential problem, with respect to the space variable, is tobe approximated numerically. Numerical results are presented with a simple example. Thevariational reduction method can be extended to thin domains multi-branching in 3dimensions, which is a work in progress.

Type
Research Article
Copyright
© EDP Sciences, 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Références

O. Besson, J. Pousin. Solution for Linear Conservation Laws with velocity in L . Archive for Rational Mechanics and Analysis, 2007.
S. Boujena , A. Chiboub, J. Pousin. Variational reduction for the transport equation in a multiple branching plant growth model. Congrès International JANO 9 , 9emes journée d’Analyse Numérique et d’Optimisation. Mohammedia, Maroc, 2008.
Boujena, S., Chiboub, A., Pousin, J.. Variational reduction for the transport equation in a multiple branching plant growth model. Mathematical Modelling of Natural Phenomena, 5 (Supplement 2010), No. 7, 1115. CrossRef
N. Bessonov, V. Volpert. Dynamic models of plant growth, Mathematics and mathematical modeling. Publibook, Paris, 2007.
M. Crouzeix, L. Mignot. Analyse numérique des équations différentielles. Masson, Paris, 1996.
F. Fontvieille, Décomposition asymptôtique et éléments finis. Thèse de doctorat, université Claude Bernard- Lyon I, 2004.
Fontvieille, F., Panasenko, G., Pousin, J.. FEM implementation for the asymptotic partial decomposition. Applicable Analysis, 86 (2007), No. 5 , 519536. CrossRefGoogle Scholar
G.P. Panasenko. Multi-scale Modelling for structures and composites. Springer Verlag, 2005.
Panasenko, G.P.. Method of asymptotic partial decomposition of domain. Math. Models and Methods in Appl. Sci., 1 (1998), No. 8, 139156. CrossRefGoogle Scholar
M. Picq, J. Pousin. Variational reduction for the transport equation and plants growth. In Proccedings of the Conference Modelling of the Heterogeneous Materials with Applications in Constructions and Biological Engineering. Czech Technical University Prague, 2007.