Section: New Results

New results related to FreeFem++

In [6] , we consider a model of soil water and nutrient transport with plant root uptake. The geometry of the plant root system is explicitly taken into account in the soil model. We first describe our modeling approach. Then, we introduce an adaptive mesh refinement procedure enabling us to accurately capture the geometry of the root system and small-scale phenomena in the rhizosphere. Finally, we present a domain decomposition technique for solving the problems arising from the soil model as well as some numerical results.

In [15] , we study an interface transport scheme of a two-phase flow of an incompressible viscous immiscible fluid. The problem is discretized by the characteristics method in time and finite elements in space. The interface is captured by the Level-Set function. Appropriate boundary conditions for the problem of mould filling are investigated, a new natural boundary condition under pressure effect for the transport equation is proposed and an algorithm for computing the solution is presented. Finally, numerical experiments show and validate the effectiveness of the proposed scheme.