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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。
It is significant to effectively simulate the unsaturated seepage process in many aspects such as stability analysis of soil slope, seepage of earth-rock dam and pollutant migration. The Richards equation describing unsaturated seepage is a strongly nonlinear partial differential equation that usually needs to be solved by numerical methods such as finite element method combined with effective iterative methods. Picard iterative method is a practical non-linear calculation method, which is widely used in the field of unsaturated seepage. However, the problem of convergent oscillation, slow speed and precision reduction often occur. In order to improve the computational performance, an efficient self-adaptive relaxation Picard method is proposed based on the finite element method. By simulating one-dimensional and two-dimensional seepage cases, the accuracy and efficiency of the algorithm and the procedure are verified by comparison with the results of traditional methods. The test results show that this method can effectively reduce the numerical oscillation and improve the convergence rate while ensuring the accuracy of calculation. The research results have certain reference value for the development and application of unsaturated seepage finite element program.