A new stabilised scheme for the Richards’ equation with evapotranspiration

Abstract

A new second-order stabilised numerical method for the Richards' equation with source term is proposed to solve the water infiltration in porous soil. This new method to solve Richard's equation is based on a modification of the head pressure representation with respect to the water content together with the hydraulic conductivity. We show that the modified relations provide stability while preserving the order and accuracy of the numerical solution. Furthermore, a new second-order positivity preserving scheme in time is implemented in substitution of the popular Crank-Nicolson technique. Applications to root suction in critical situations such as water saturation or rarefaction are carried out to highlight the benefits of the method. We also present a strategy to deal with multi-layers problem, by introducing a fixed point strategy to determine the complete solution on the whole domain.