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。Picard迭代方法效率很高，且无数值振荡发生。

Finite element algorithm for Richards' equation for saturated unsaturated seepage flow

A general numerical algorithm for finite element scheme is developed to solve the Richards' equation for saturated-unsaturated seepage flow, in which an integral method is proposed to approximate the governing equation, and mass lumping techniques are used to keep the numerical simulation stable. The algorithm works well over a wide variety of problems, as demonstrated by its performance against published experimental data. Solutions obtained are mass conservative within the unsaturated zone,resulting from the form and solution procedure for the governing equation. The algorithm is demonstrated to work well for infiltration fronts, steady-state and transient water tables as well as the transient seepage faces. The convergence efficiency of the Picard iteration is very good and no oscillation occurs. The algorithm is presented in sufficient detail to facilitate its easy implementation, and it is validated by comparison with three published, illustrated sets of experimental data.