Abstract
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.
Highlights
The article is devoted to the numerical modeling of plant root growth
We present a new application of the operator splitting technique combined with discontinuous finite elements
We denote by T + and T − the two mesh elements sharing the edge e so that e = ∂T + ∩ ∂T − where the minus and plus superscripts depend on the direction of the advection vector
Summary
The article is devoted to the numerical modeling of plant root growth. This work has been originally motivated by the need of developing numerical tools for the simulation of plant growth dynamics. In [1] and [2] the authors solved the problem with the finite difference method on Cartesian mesh grids combined with an operator splitting technique. That is why this article focus on the development and implementation of a suitable numerical method for the resolution of the C-Root model on triangular mesh grids, that allow to mesh complex geometries. The idea of the splitting technique is to split the problem into smaller and simpler parts of the problem so that each part can be solved by an efficient and suitable time scheme This methods has been used for a wide range of applications dealing with the advection-reaction-diffusion equation [9]. The paper ends with a conclusion and further improvements
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