NUMERICAL-METHODS FOR THE SIMULATION OF FLOW IN ROOT-SOIL SYSTEMS

The numerical properties of approximation schemes for a model that sim ulates 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 syste m of equations consists of a parabolic partial differential equation t hat 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 t echniques which have wide applicability for analyzing the nonlinear ca pacity 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 v erify the theoretical convergence rates are given.