沟灌地表水流与溶质动力学耦合模拟及验证

沟灌地表水流与溶质动力学耦合模型可为沟灌施肥系统的优化设计与管理提供有力工具,然而已有相关模型无法考虑沟底相对高程随机分布,且存在溶质对流和弥散过程的分裂误差以及由此带来的不稳定性等缺陷。为此,该文采用守恒型全水动力学方程和对流-弥散方程描述沟灌地表水流与溶质运动过程,借助双时间步法和有限体积法,并在地表水位相对高程梯度向量离散式中引入额外项,以精确模拟考虑沟底相对高程随机分布下地表水流推进与消退过程,实现了无条件稳定性下对沟灌地表水流与溶质运动所有物理过程的动力学耦合模拟。借助全程、前半程和后半程施肥时机下9个典型沟灌施肥试验实测数据,验证了模型的模拟效果。结果表明,模型能以优良的拟合度模拟出考虑地表相对高程随机分布下沟灌地表水流推进与消退过程,以及地表溶质浓度演变过程,且水量与溶质量的质量守恒误差小于0.1%,有效克服了已有模型的缺陷,为沟灌施肥系统的优化设计与管理提供了优良的数值分析工具。

Hydrodynamic coupled simulation and validation for surface water flow and solute transport in furrow fertigation

Abstract: Hydrodynamic coupled model of surface water flow and solute transport can provide a powerful tool for design and management of furrow fertigation system. However, the existing models present the shortcomings such as not introducing bed elevation stochastic distribution, splitting solute advection and dispersion processes, as well as the resultant numerical unstable problem. So the exiting models can not be effectively applied to analyze the performance of furrow fertigation system. To solve this problem, the conservative complete hydrodynamic equation and the advection-dispersion equation were applied to describe the surface water flow and solute transport in furrow fertigation, respectively. The finite-volume approach was applied to spatially discretize these governing equations to obtain good mass conservation ability, and then pseudo-time terms were introduced into the governing equations and the fully implicit time scheme was used to reach unconditional stability. After these operations, the conservative complete hydrodynamic and the advection-dispersion equations were turned into a nonlinear algebraic system with diagonal dominance. The Picard iteration approach was introduced to obtain the linearization of this nonlinear algebraic system and all physical processes in furrow fertigation were coupled and simulated in hydrodynamic sense. In the numerical solution development, the water free surface gradient term in conservative complete hydrodynamic equation was added with an extra numerical term. At dry surface domain, this extra numerical term and water free surface gradient term could cancel each other, which represented the real physical process that there were some forces on dry surface domain for water and solute. Consequently, the furrow surface water advance/recession processes under bed elevation stochastic distribution can be accurately simulated. Furrow fertigation experiments were performed to validate the proposed coupled model on October 25, 2015 in Yehe irrigation district, located in Shijiazhuang City, Hebei Province. The experiments were divided into 3 groups i.e. full-time, first-half and second-half time fertilizer applications. Each group contained 3 repetitions and thus there were 9 experimental furrows. Ammonium sulphate was selected as fertilizer. During the experiments, ammonium ion could be fast generated and not be combined with other ions, and thus it was monitored to represent solute. During the experiments, furrow surface water advance/recession processes were observed. Meanwhile, at the distance of 0, 30, 50 and 70 m away from furrow upstream end, 4 observation points were distributed in each furrow to observe the solute concentration change. After experiments, the data including furrow surface water advance/recession processes and solute concentration change at all observation points were applied to validate the proposed coupled model. The validation results showed that the proposed coupled model could well simulate the furrow surface water flow and solute transport, and presented very good mass conservation ability. Specifically, the average relative errors between the observed and simulated data by the proposed coupled model were below 5% and 10% for furrow surface water advance and recession processes, respectively. The average relative errors for solute change were below 8%. By contrast, the average relative errors of advance/recession processes by the existing model were from 15% to 20%. The average relative errors for solute change were more than 10%. Additionally, the mass conservation error for the proposed coupled model was below 0.1% and about 2% for the existing model. Thus, the proposed coupled model overcomes the shortcomings of existing models and provides a useful numerical analysis tool for the management and design of furrow fertigation system.