The Saint-Venant and Richards equation system in surface irrigation: numerical coupling for the advance phase in border irrigation

A numerical scheme for the coupled system of Saint-Venant and Richards equations in border irrigation advance phase is presented. The solution of Saint-Venant equations is approximated by a finite-difference Lagrangian scheme; for the Richards equation finite elements for the space discretization and implicit finite-differences for the time discretization are used. It is shown that a discretization of the momentum equation based on: i) the space derivates and the friction slope in a cell are approximated forward in time, ii) the time derivates are approximated by a ponderated form in time and space, and iii) the coefficients are computed in the previous time, has a basic advantage in the monotone numerical solution it produces versus a discretization based on the use of values of all corners of the calculus cell.