Operator splitting for solving C-Root, a minimalist and continuous model of root system growth

Root systems are complex structures and it is still a great challenge to model them. There are different types of plant growth models. At one extreme, architecturals models, and at another extreme, density based models. Modeling root system growth with continuous equations is attractive for at least two reasons. First, since the development of roots is defined independently of the number of roots, such models can be used to work at field scale. Secondly, continuous models are formulated with partial differential equations (PDE) and thus are good candidates for coupling with other models like nutrient models or soil models which are of the same nature. Considering this type of applications, it obviously implies that coefficients of the PDE equations are functions of space and time. Thus appropriate numerical schemes should be used to solve and calibrate the models. These schemes has to be stable, accurate and efficient. Bonneu et al ([4]) introduces a continuous and minimalist model, named C-Root, for modeling the root system growth. In this paper, we focus on this model to study different operator splitting approaches for solving it. Some numerical results obtained, for a one-dimensional case, with data about eucalyptus roots are given.