基于自适应松弛Picard法的高效非饱和渗流有限元分析

An efficient finite element procedure for unsaturated flow based on adaptive relaxed Picard method

有效地模拟非饱和渗流过程对土质边坡稳定性分析、土石坝渗流、污染物迁移等众多领域有着重要的意义。描述非饱和渗流的Richards方程是具有强烈非线性的偏微分方程,通常需要采用有限元等数值方法并结合有效的迭代方法进行求解。Picard迭代法是实用的非线性计算方法,在非饱和渗流领域应用广泛,但经常会出现收敛震荡、速度缓慢和精度降低的问题。为提高计算性能,结合有限元法提出了一种高效的自适应松弛Picard法。通过模拟一维和二维渗流算例,并与传统方法的结果进行对比,对算法和程序的准确性、高效性和鲁棒性进行了验证。测试结果表明,该方法可以在保证计算精度的同时有效地减少数值震荡,提高收敛速度。研究成果对非饱和渗流有限元程序的开发和应用有一定的参考价值。

Effectively simulating unsaturated flow is of great significance in many areas such as the soil slope stability analysis, seepage of earth-rockfill dam, contaminant transport. Due to the strongly nonlinear characteristics of Richards equation for the unsaturated flow, numerical solution schemes such as the finite element method with an efficient iterative algorithm usually have to be employed. Picard method as a practical nonlinear iterative method is widely applied to the unsaturated flow field; but usually suffers from convergence oscillation, slow convergence rate and inaccurate solution. In order to improve the computing performance, an efficient finite element procedure based on the adaptive relaxed Picard method is developed. Through the simulations of 1D and 2D unsaturated seepage problems, accuracy, efficiency and robustness of the proposed procedure are validated by comparing with the traditional methods. It is shown that the adaptive relaxed Picard method can effectively reduce the convergence oscillation and significantly improve the convergence rate with the accuracy guaranteed. The proposed procedure provides a helpful reference for the program development and application to unsaturated flow.