A 3D-1D virtual element method for modeling root water uptake

ter uptake during the growth of a root system. By rigorously reducing the coupled Richards-Stokes problem to a well-posed 3D-1D formulation, we solve it in a PDE-constrained optimization framework, enabling a direct quantification of root water uptake. To address the non-linearity of the 3D Richards equation and the coupling with the 1D variables, we propose a tailored solving strategy that ensures an accurate and efficient approximation of the solutions. For the first time, the Virtual Element Method is employed to discretize the three-dimensional soil sample, significantly enhancing the method’s capacity to handle complex geometries. Indeed, this enables efficient meshing of domains containing stones and other impervious obstacles of arbitrary shapes. Several numerical examples are provided, showcasing the accuracy of the method and demonstrating its applicability both on static and dynamic root systems.