Numerical Methods for the Simulation of Flow in Root-Soil Systems

The numerical properties of approximation schemes for a model that simulates water transport in root-soil systems are considered. The model is derived in detail. It is based on a previously proposed model which is reformulated completely in terms of the water potential. The system of equations consists of a parabolic partial differential equation that contains a nonlinear capacity term coupled to two linear ordinary differential equations. A closed form solution is obtained for one of the latter equations. Finite element and finite difference schemes are defined to approximate the solution of the coupled system. Some new techniques which have wide applicability for analyzing the nonlinear capacity term are used, and optimal order error estimates are derived. A postprocessed water mass flux computation is also presented and shown to be superconvergent to the true flux. Computational results which verify the theoretical convergence rates are given.