Table 5 - uploaded by Shaohui Zhang
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Average Relative Errors (%) of Surface Solute Transport by the Full Coupled and Advection Coupled Models
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Full implicit solutions are constructed for all terms of the Saint–Venant equations and advection–dispersion equation. Thereafter, a global coefficient matrix for forming algebraic equations is established to realize the simultaneous solution of both surface water flow and solute transport equations and a full-coupled model between the surface wate...
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... the full-coupled model presents smaller ARE values than the advection coupled model, and the reason is perhaps the splitting errors of bed friction has become important, especially in basin irrigation. The ARE c values for solute transport are calculated and given in Table 5. In general, the full-coupled model can simulate well the solute concentration processes at different observation stations for the three fertigation experiments. ...
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Citations
... Currently, the preferred approach for solving the fully coupled problem is using finite-volume numerical procedures. This approach has been used to model one-dimensional surface flow cases with both borders and furrows (Burguete et al. 2009;Zhang et al. 2016;Brunetti et al. 2018), and two-dimensional border/basin irrigation (Dai et al. 2019). Finite-volume methods were originally developed to model compressible flows, in which shock waves can easily develop, and are therefore inherently better suited for handling discontinuities in the solution and boundary conditions than finite-difference methods. ...
... Abbasi, 2013;Zhang et al., 2016;Naghedifar et al., 2019 ) . Narasimhan, 2005 ) معادله برداری کامل فرم . ...
Development of numerical models for management and assessment of irrigation systems is an important step in the way of establishing farm decision support systems. In this study, a coupled model has been developed for simulation of furrow irrigation using 1D fully hydrodynamic form of Saint-Venant equations and 3D mixed-form of Richards’ equation. The Saint-Venant equations have been discretized by an explicit scheme while the Richards’ equation is solved by an implicit scheme. Furthermore, coordinate transformation technique was employed to handle non-orthogonal grids of 3D Richards’ equation. The model was subsequently validated against experimental and numerical benchmarks and in all cases acceptable accuracy was observed. Root mean squared error and mean absolute error of advance phase were 0.631 s and 2.630 s, respectively. Furthermore, maximum root mean squared error and mean absolute error of pressure head distribution were obtained 0.24 m and 0.45 m, respectively. Finally, the proposed model was employed to simulate furrow irrigation with 5 applications and the results were analyzed. The results showed that the presented model is able to simulate advance phase of furrow irrigation.
... In this century, the zero-inertia and full hydrodynamic forms of the Saint-Venant equations have been frequently used in two-dimensional surface irrigation models (Brufau et al., 2002;Zhang et al., 2016;Dai et al., 2019). Two-dimensional simulation permits to overcome a number of problems that cannot be treated by one-dimensional models, among them, irregular field geometries or the spatial variability of key irrigation variables as leveling and infiltration. ...
... In simulations, the value of the solute dispersivity (D l ) can affect the solute concentration processes. Therefore, the solute concentration processes of FH with different dispersivity values (D l ¼ 0, 0.1, 0.5, and 1 m) were calculated (Zhang et al. 2016). As shown in Fig. 11, four D l values were not sensitive to the concentration ...
... Furthermore, the D l values gradually became sensitive when the observation locations were close to the downstream end. That was probably caused by the rapidness (advection is dominant) of the surface flow, which becomes slow at the downstream domain(Zhang et al. 2016). ...
Numerical models are convenient for the management of basin fertigation. However, the characteristic line approach, commonly applied to solve the advection-dispersion equation, presents disadvantages such as numerical oscillation at the vertical position of the solute concentration wave caused by cubic spline interpolation. To address this problem, a new approach was constructed to solve the advection-dispersion equation. This new approach is a hybrid of the characteristic line and the finite-volume approaches. The zero-inertia equation with a standard diffusion wave type was used to describe the surface water flow, and a new model for basin fertigation was developed. Three basin fertigation experiments were carried out to validate the developed model. The results showed that the simulated solute transport processes did not exhibit any numerical oscillation and overcame the disadvantage of the characteristic line approach in conjunction with the cubic spline interpolation. Overall, the mass conservation ability of the developed solution for the advection-dispersion equation was significantly improved.
One of the important factors in fertilizer application efficiency in surface fertigation is the shape of inflow hydrographs. In this research, a fertigation model is developed to analyse the effect of surge flow on furrow fertigation. Saint‐Venant equations and the advection–dispersion equation were used to estimate water flow and solute transport characteristics, respectively. The field experiments, including different fertigation treatments with surge flow, were conducted to calibrate and evaluate the developed model. Most of the water and nitrate losses occurred through runoff; water losses through runoff ranged from 13.8 to 33.4%, while fertilizer losses varied between 5.1 and 47%. Water and nitrate losses in the second fertigation experiments were higher than those in the first due to the reduction of the surge effect. A comparison between simulated and observed data shows appropriate accuracy of the developed model; the root mean squared error (RMSE) index for nitrate and water runoff losses was 8.4 and 12.1%, respectively. Fertigation during all advance surges was recognized as the desirable option in furrow irrigation with a surge flow. © 2020 John Wiley & Sons, Ltd.
Two-dimensional shallow water and advection-dispersion equations were applied to describe the surface water and solute transport processes in basin fertigation. Then the fully implicit temporal solution was constructed for all terms of the governing equations in triangular spatial grid and an iterative coupled model for basin fertigation was developed. Furthermore, the lower-upper matrix decomposition and symmetric Gauss-Seidel iteration solution methods were applied to construct a noniterative coupled model for basin fertigation. The convergence of the simulated results with decreasing time step was exhibited by the dam-break test. Furthermore, the performance comparison was analyzed on the basis of three basin fertigation experiments. The results show that the noniterative coupled model presents higher efficiency than and accuracy similar to the iterative coupled model. Thus, the noniterative coupled model was proposed for the management and design of basin fertigation. Finally, the noniterative coupled model was applied to obtain the diagram of the relationship between fertilizer application time and uniformity.
