塔里木盆地绿洲农田土壤水盐运动动力学模式研究

采用了改进型Picard迭代差分法求解土壤水分运动的混合型Richards方程,避免了采用Picard迭代法求解h型Richards方程所出现的质量平衡误差问题.同时,采用迎风二次型插值差分法求解土壤盐分运移的对流扩散方程,避免了采用一般差分格式时所出现的数值弥散问题.最后,将上述动力学模型对塔里木盆地绿洲农田在灌既入渗条件下的土壤水盐运动过程进行了数值模拟,模拟结果与测量值吻合较好.

有植被覆盖条件下土壤水盐运动规律研究

利用改进型Picard迭代差分法求解饱和-非饱和土壤中水分运动的混合型Richards方程，避免了传统利用Picard迭代法求解h型Richards方程所出现的质量平衡误差等问题；利用特征 差分法求解盐分运动的对流扩散方程，也可避免利用一般差分格式时出现数值弥散以及数值波动问题。文中将上述数学模型用于模拟土壤在降雨、蒸发以及有植被覆盖条件下土壤水盐运动规律，对若干导致某些土壤盐碱化的原因也作出定量的解释，并给出土壤盐分的动态发展趋势的中长期预测预报。

饱和-非饱和土中渗流Richards方程有限元算法

发展了一种求解理查森方程的一般有限元算法.该方法采用积分法处理孔隙水压力对时间的导数项,采用集中质量技术处理有限元方程中质量矩阵来保证数值稳定.所采用的质量守恒迭代方法不须改变迭代方式,采用一般的Picard迭代方法.该方法能求解入渗、地下水位瞬变和排水等范围广泛的饱和-非饱和渗流问题.对3个已公开发表具有详细试验数据的算例的模拟表明,该方法对入渗锋、稳定渗流地下水位和非稳定渗流溢出面都模拟很好.Pieard迭代方法效率很高,且无数值振荡发生.

A finite-element algorithm for modeling variably saturated flows

A general numerical algorithm in the context of finite element scheme is developed to solve Richards’ equation, in which a mass-conservative, modified head based scheme (MHB) is proposed to approximate the governing equation, and mass-lumping techniques are used to keep the numerical simulation stable. The MHB scheme is compared with the modified Picard iteration scheme (MPI) in a ponding infiltration example. Although the MHB scheme is a little inferior to the MPI scheme in respect of mass balance, it is superior in convergence character and simplicity. Fully implicit, explicit and geometric average conductivity methods are performed and compared, the first one is superior in simulation accuracy and can use large time-step size, but the others are superior in iteration efficiency. The algorithm works well over a wide variety of problems, such as infiltration fronts, steady-state and transient water tables, and transient seepage faces, as demonstrated by its performance against published experimental data. The algorithm is presented in sufficient detail to facilitate its implementation.