Numerical Modeling of One-Dimensional Flow in Furrow Irrigation by Solving the Full Hydrodynamics Equations using Roe Approach

Flow Simulation and discontinuous shock capturing are important in shallow water equations. Common numerical schemes such as finite difference Preissmann scheme, without performing some modifications, cannot simulate discontinuities. Finite volume methods using Riemann solvers by taking advantage of the characteristics of solving the smooth areas as well, have the ability to simulate discontinuities. In this paper, the second order Roe model of Riemann solver was employed by applying the limiting functions to eliminate the spurious oscillations of the numerical simulation in the surface and subsurface flows (Saint-Venant equations in surface flow and Kostiakov-Lewis in subsurface flow). A Fortran code was developed for Roe-TVD method, the presented model was evaluated using the Preissmann scheme (an implicit finite difference scheme) and two sets of field data (Printz-323 and Walker) based on Root Mean Square Error (RMSE), Standard Error (SE) and Determination Coefficient (R²). It was concluded that Roe model showed better results comparing to the Preissmann scheme in all of the simulations, particularly in outgoing runoff, RMES was improved up to 62%. The applied model was an explicit method and reduced running time and had the ability of application under different field conditions.