J. Burguete

Conservative numerical simulation of multi-component transport in two-dimensional unsteady shallow water flow

An explicit finite volume model to simulate two-dimensional shallow water flow with multi-component transport is presented. The governing system of coupled conservation laws demands numerical techniques to avoid unrealistic values of the transported scalars that cannot be avoided by decreasing the size of the time step. The presence of non conservative products such as bed slope and friction terms, and other source terms like diffusion and reaction, can make necessary the reduction of the time step given by the Courant number. A suitable flux difference redistribution that prevents instability and ensures conservation at all times is used to deal with the non-conservative terms and becomes necessary in cases of transient boundaries over dry bed. The resulting method belongs to the category of well-balanced Roe schemes and is able to handle steady cases with flow in motion. Test cases with exact solution, including transient boundaries, bed slope, friction, and reaction terms are used to validate the numerical scheme. Laboratory experiments are used to validate the techniques when dealing with complex systems as the @k-@e model. The results of the proposed numerical schemes are compared with the ones obtained when using uncoupled formulations.

Fertigation in Furrows and Level Furrow Systems. I: Model Description and Numerical Tests

The simulation of fertigation in furrows and level furrow systems faces a number of problems resulting in relevant restrictions to its widespread application. In this paper, a simulation model is proposed that addresses some of these problems by: (1) implementing an infiltration model that adjusts to the variations in wetted perimeter; (2) using a friction model that adjusts to different flows and which uses an absolute roughness parameter; (3) adopting an equation for the estimation of the longitudinal diffusion coefficient; and (4) implementing a second-order TVD numerical scheme and specific treatments for the boundary conditions and the junctions. The properties of the proposed model were demonstrated using three numerical tests focusing on the numerical scheme and the treatments. The application of the model to the simulation of furrows and furrow systems is presented in a companion paper, in which the usefulness of the innovative aspects of the proposed model is demonstrated.

Fertigation in Furrows and Level Furrow Systems. II: Field Experiments, Model Calibration, and Practical Applications

Furrow fertigation can be an interesting practice when compared to traditional overland fertilizer application. In the first paper of this series, a model for furrow fertigation was presented. The simulation model combined overland water flow (Saint-Venant equations), solute transport (advection-dispersion), and infiltration. Particular attention was paid to the treatment of junctions present in level furrow systems. In this paper, the proposed model is validated using five furrow fertigation evaluations differing in irrigation discharge, fertilizer application timing, and furrow geometry. Model parameters for infiltration and roughness were estimated using error minimization techniques. The error norm was based on observed and simulated values of advance time, flow depth, and fertilizer concentration. Model parameters could be adequately predicted from just one discharge experiment, although the use of more experiments resulted in decreased error. The validated model was applied to the simulation of a level furrow system from the literature. The model adequately reproduced irrigation advance and flow depth. Fertigation events differing in application timing were simulated to identify conditions leading to adequate fertilizer uniformity.

2D modelling of erosion/deposition processes with suspended load using

This work describes a finite volume model applied to solve the coupled shallow water/load transport equations, where low concentrations of sediment load are assumed so that the concentration of the solid fraction is assumed not to influence the equations governing the dynamics. The unsteady simulation of erodible bed requires special attention in the discretization of the bed and friction source terms as important instabilities can arise in some situations. The upwind discretization of the time variable bed slope source terms is presented to provide an exact balance of the numerical fluxes and to guarantee steady-state solutions contrary to the pointwise formulation that leads to instabilities destroying the computation. Robust numerical schemes are presented for both moving and fixed boundaries. In the last case a numerical technique is provided to keep the concentration load bounded for values of CFL (Courant–Friedrichs–Lewy) greater than one and therefore decreasing the necessary computational cost.

Solid-set sprinklers irrigation of field boundaries: experiments and modeling

Numerous studies have analyzed the solid-set sprinkler irrigation system performance. However, the effect of field-boundaries irrigation has not been considered in the whole-field performance. The objectives of this study were (1) to characterize two different solutions to irrigate field boundaries (full-circle sprinkler equipped with a deflecting plate, DP, and partial-circle sprinklers, PC); (2) to calibrate and validate a ballistic model to adequately simulate these solutions; and (3) to analyze the two different designs (DP or PC) from a whole-field perspective. Two types of experiments were designed. The first was carried out with an isolated sprinkler under no windy conditions to estimate drop size distribution parameters. The second was performed in a solid-set sprinkler layout under windy conditions to calibrate and validate the ballistic model. The experimental design allows the comparison of both solutions under equal technical and meteorological conditions. Comparisons between designs (DP or PC) were established for a whole-field area in terms of irrigation performance and crop yield. From a technical point of view, PC sprinklers perform better than DP sprinklers. From an economical point of view, the shape and orientation of the plot and the legal requirements of the irrigation system design (minimum distance of the sprinkler line to the border) have an important effect on the optimal solution to irrigate field boundaries.

Diffusive-Wave Based Hydrologic-Hydraulic Model with Sediment Transport. II: Validation and Practical Application

AbstractThe development of a distributed two-dimensional (2D) hydrologic-hydraulic simulation model was presented in Paper I. The simulation model combined overland flow (kinematic/diffusive wave models), hillslope sediment transport, and groundwater flow apart from the water exchange mechanisms between zones. Particular attention was paid to the upwind discretization of the surface flow equations. In this paper, the proposed model is validated by using four test cases with exact solutions, one academic test case, and two laboratory test cases. The model adequately reproduced front advance over dry beds of any slope and water table evolution in simple cases. As practical application of the model, the simulation of real events in two experimental basins is also presented. The work is focused on the influence of the choice of the empirical parameters on the model results concerning solid and liquid discharges. Also, because of the lack of information referring the boundary and initial conditions of the grou...