| 非饱和渗流Richards方程数值求解的欠松弛方法 |
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| 引用本文： | 陈曦,于玉贞,程勇刚.非饱和渗流Richards方程数值求解的欠松弛方法[J].岩土力学,2012,33(Z1):237-243. |
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| 作者姓名： | 陈曦 于玉贞 程勇刚 |
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| 作者单位： | 1. 北京交通大学 土木建筑工程学院，北京 100044；2. 清华大学 水沙科学与水利水电工程国家重点实验室，北京 100084; 3. 武汉大学 水资源与水电工程科学国家重点实验室，武汉 430072 |
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| 基金项目： | 国家自然科学基金资助项目(No.50879039);973计划课题资助(No.2010CB732103);中央高校基本科研业务费专项资金资助(No.2011JBM070) |
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| 摘 要： | 非饱和土渗流理论是岩土工程问题的基础理论，在土石坝渗流、污染物传输、冻土渗流相变和边坡稳定分析等领域有着广泛的应用。非饱和土渗流Richards方程的数值求解过程中，某些参数如水力传导系数计算不当可能引起非线性方法，如Picard方法或Newton方法的迭代收敛震荡，从而导致非线性迭代方法收敛缓慢和精度降低。为了消除或降低迭代收敛震荡对求解精度和计算性能的影响，目前主要采用欠松弛方法。通过一维入渗算例和二维非均质土坝渗流算例演示已有欠松弛方法的局限性，进而提出新的短项混合欠松弛法，并对其实用性和可靠性进行验证。
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| 关 键 词： | 非饱和渗流 Richards方程 有限元 迭代收敛震荡 欠松弛法 |
| 收稿时间： | 2002-05-28 |
Under-relaxation methods for numerical solution of Richards equation of variably saturated flow |
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| CHEN Xi,YU Yu-zhen,CHENG Yong-gang.Under-relaxation methods for numerical solution of Richards equation of variably saturated flow[J].Rock and Soil Mechanics,2012,33(Z1):237-243. |
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| Authors: | CHEN Xi YU Yu-zhen CHENG Yong-gang |
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| Institution: | 1. School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China; 2. State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China; 3. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China |
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| Abstract: | Variably saturated flow theory is the fundamental theory of geotechnical engineering;and it has wide applications to seepage of earth rockfill dam,contaminant transport,seepage and phase transformation of frozen soil,and slope stability analysis.In numerical solution of Richards equation for variably saturated flow,inappropriate computation of some parameters,particularly for the hydraulic conductivity,may lead to convergence oscillation of nonlinear iterative methods such as Picard method or Newton method,and consequently result in slow convergence and inaccurate solution.To eliminate or reduce the influence of iterative convergence oscillation,the under-relaxation method is often employed.By using 1D problem and 2D heterogeneous earth dam,the limitations of available under-relaxation methods are demonstrated.Furthermore,a novel short-term mixed under-relaxation method is proposed with verified practicability and reliability. |
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| Keywords: | variably saturated flow Richards equation finite elements iterative convergence oscillation under-relaxation |
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