Modelling and Numerical Analysis of Flow under Furrow Irrigation

In order to simulate shallow flowson the soil surface and penetration into the depth, the Saint-Venant equations were developed. Due to the lack of analytical solutionfor solving these types of equations, researchers generally suggest numerical methods as a solution.In the present study, from the hydraulic models of surface irrigation, the full hydrodynamic model due to its accurate simulation of the flow, and from the numerical methods, two numerical models, includingthe characteristic line method (HD-CH) and the explicit diffusiveLAXmethod (HD-LAX), were used to discretize the governing equations of surface irrigation. Afterwards, a computer program was developed using MATLAB programming language.In order to evaluate the numerical methods, four furrow data series were used, which were measured through testing in the farm. In addition, under the same conditions, the proposed method was compared with the hydrodynamic model of SIRMOD and SRFR softwares and was consequently validated. The perceived results revealedthat both numerical models simulate various flow processes under furrow conditionsatan acceptable accuracy.However, the results of the evaluation indicators demonstrated that the HD-LAX model, due to the solution method of the second degree of accuracy, withthe average coefficient of determination, error statistics, and model efficiency of (0.834, 1.36, 0.91) and (0.815, 1.43, 0.88), respectively forthe forward and backward stages, and with the relative errors of 7.44 % and 19.8 %, has a higher accuracy than the HD-CH model,in estimating the volume of water infiltration and runoff, and it also needsless computational time for simulating different furrow flow processes.The results of calculations, through comparing the proposed HD-LAX method with the HD-SIRMOD and HD-SRFR methods, showed thatin the forward stage, the proposed method and the HD-SIRMOD model do not have any significant difference,while the HD-SRFR model, at the confidence level of 1%,has some differences with the observed values.