Operator splitting and discontinuous Galerkin methods for advection-reaction-diffusion problem: application to plant root growth

Peynaud Emilie. 2018. Operator splitting and discontinuous Galerkin methods for advection-reaction-diffusion problem: application to plant root growth. Biomath, 7 (2):1812037, 19 p.

Résumé : The time dependant advection-reaction-diffusion equation is used in the C-Root model to simulate root growth. This equation can also be applied in many others applications in life sciences. In this context the unknown is related to densities and one of the important property of the problem is that the solution is non-negative for positive initial conditions. One of the difficulty at the discrete level is to preserve the positivity of the approximated solution during the simulations. In this work we solved the model using Discontinuous Galerkin elements combined with an operator splitting technique. The DG method is briefly presented then we motivated the use of the operator splitting technique by doing some numerical experiments. Those experiments showed that the same time approximation scheme may not be suitable for all the operators of the model. We validated our implementation of the splitting technique in a simple test case. Then we performed a simulation of a plagiotropic root of Eucalyptus.

Mots-clés Agrovoc : Eucalyptus, racine, croissance, modèle de simulation, mathématique

Mots-clés libres : Time dependent advection-reaction- diffusion, Operator splitting, Discontinuous Galerkin method, Plant root growth simulation

Classification Agris : F62 - Physiologie végétale - Croissance et développement
K10 - Production forestière
U10 - Informatique, mathématiques et statistiques
U30 - Méthodes de recherche

Champ stratégique Cirad : Axe 1 (2014-2018) - Agriculture écologiquement intensive

Auteurs et affiliations

• Peynaud Emilie, CIRAD-BIOS-UMR AMAP (FRA) - auteur correspondant

Source : Cirad-Agritrop (https://agritrop.cirad.fr/587397/)

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