| Abstract | Modeling the water uptake by plant roots is a key issue in studying soil processes, which are governed by water dynamics: a comprehensive understanding and forecast of such dynamics is a relevant issue in managing water resources. Typically, movement of water in soils and uptake by roots are described by the Richards' equation with a sink term, and numerical treatment of this problem is still a challenge, together with its practical implementations in user-friendly softwares. In order to tackle this problem, in the present paper we propose a simple and computationally fast algorithm developed as a Python code, implementing a numerical approach based on the shooting method, a classical tool for handling boundary value problems (BVPs) arising here from a discretization recently introduced for Richards' equation: such a method is applied to the linearized Richards' equation with Gardner's hydraulic functions. This method is implemented also in MATLAB, in order to accomplish comparisons with built-in MATLAB solver for parabolic partial differential equations. The Python code is made available to readers, and is intended to be an easy tool for handling this problem in the framework of Gardner's constitutive relations, filling the gap of other commercial codes, which do not provide choice of Gardner functions. Many numerical simulations are performed: the results are promising, since the proposed method behaves efficiently and in some cases it is able to converge even when the MATLAB solver fails; mass balance properties and order of accuracy issues are also investigated. |
| Text | 455684 2021 10.1007/s11269 021 02850 2 Scopus 2 s2.0 85107396544 Richards equation Root water uptake models Shooting method MATLAB software Python Shooting the Numerical Solution of Moisture Flow Equation with Root Water Uptake Models A Python Tool Difonzo F.V.; Masciopinto C.; Vurro M.; Berardi M. Department of Computer Science, Faculty of Electrical Engineering, Czech Technical University in Prague, Karlovo nam. 13, 120 00 Nove M sto, Prague, Department of Computer Science, Faculty of Electrical Engineering, Czech Technical University in Prague, Karlovo nam. 13, 120 00 Nove M sto, Prague, Czech Republic, , Czech Republic; Code Architects Automation, Via Campania 3, Santeramo in Colle, 70029, Code Architects Automation, Via Campania 3, 70029, Santeramo in Colle, Italy, , Italy; Dipartimento di Matematica, Universita degli Studi di Bari Aldo Moro, Via E. Orabona 4, Bari, 70125, Dipartimento di Matematica, Universita degli Studi di Bari Aldo Moro, Via E. Orabona 4, 70125, Bari, Italy, , Italy; Istituto di Ricerca sulle Acque, Consiglio Nazionale delle Ricerche, via F. De Blasio 5, Bari, 70132, Istituto di Ricerca sulle Acque, Consiglio Nazionale delle Ricerche, via F. De Blasio 5, 70132, Bari, Italy, , , Italy; Istituto di Ricerca sulle Acque, Consiglio Nazionale delle Ricerche, via F. De Blasio 5, Bari, 70132, Istituto di Ricerca sulle Acque, Consiglio Nazionale delle Ricerche, via F. De Blasio 5, 70132, Bari, Italy, , , Italy Modeling the water uptake by plant roots is a key issue in studying soil processes, which are governed by water dynamics a comprehensive understanding and forecast of such dynamics is a relevant issue in managing water resources. Typically, movement of water in soils and uptake by roots are described by the Richards equation with a sink term, and numerical treatment of this problem is still a challenge, together with its practical implementations in user friendly softwares. In order to tackle this problem, in the present paper we propose a simple and computationally fast algorithm developed as a Python code, implementing a numerical approach based on the shooting method, a classical tool for handling boundary value problems BVPs arising here from a discretization recently introduced for Richards equation such a method is applied to the linearized Richards equation with Gardner s hydraulic functions. This method is implemented also in MATLAB, in order to accomplish comparisons with built in MATLAB solver for parabolic partial differential equations. The Python code is made available to readers, and is intended to be an easy tool for handling this problem in the framework of Gardner s constitutive relations, filling the gap of other commercial codes, which do not provide choice of Gardner functions. Many numerical simulations are performed the results are promising, since the proposed method behaves efficiently and in some cases it is able to converge even when the MATLAB solver fails; mass balance properties and order of accuracy issues are also investigated. 35 Published version http //www.scopus.com/record/display.url eid=2 s2.0 85107396544 origin=inward Shooting the Numerical Solution of Moisture Flow Equation with Root Water Uptake Models A Python Tool Published version of the paper Difonzo2021_Article_ShootingTheNumericalSolutionOf.pdf Articolo in rivista Reidel 0920 4741 Water resources management Water resources management Water resour. manag. michele.vurro VURRO MICHELE marco.berardi BERARDI MARCO costantino.masciopinto MASCIOPINTO COSTANTINO |
