| 非饱和渗流问题的自适应欠松弛变量变换方法 |
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| 引用本文： | 程勇刚,常晓林,李典庆,陈曦.非饱和渗流问题的自适应欠松弛变量变换方法[J].岩土力学,2012,33(9):2857-2862. |
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| 作者姓名： | 程勇刚 常晓林 李典庆 陈曦 |
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| 作者单位： | 1.武汉大学 水资源与水电工程科学国家重点实验室，武汉 430072；2.北京交通大学 土木建筑工程学院，北京 100044 |
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| 基金项目： | 国家自然科学基金项目(No.51028901);高等学校博士学科点专项科研基金资助课题(No.20110141120019);中国博士后科学基金资助项目(No.20110491214) |
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| 摘 要： | 在使用有限元方法求解非饱和土渗流问题时，土-水特征曲线和渗透率函数的强烈非线性经常会造成计算中出现迭代不收敛、计算误差大等问题。基于变量变换的思想，结合时间步长自适应技术提出了一种求解非饱和渗流问题的新方法--欠松弛RFT变换方法（ATUR1）。ATUR1方法通过变量变换，大大降低了Richards方程中未知数在空间和时间上的非线性程度，从而改善这种非线性所带来的计算收敛困难和精度差等问题。欠松弛技术的引入减少了迭代过程中的振荡现象，进一步提高了非线性迭代计算的效率。时间步长自适应技术则有效地控制整个计算过程的误差。数值算例结果说明，ATUR1可以有效地提高计算效率和精度，是一种准确有效的计算方法。
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| 关 键 词： | 非饱和渗流 有限元 变量变换 欠松弛 时间步长自适应 |
| 收稿时间： | 2012-05-10 |
Unsaturated seepage analysis using temporal adaptive transformation method with under-relaxation |
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| CHENG Yong-gang
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CHANG Xiao-lin
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LI Dian-qing
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CHEN Xi.Unsaturated seepage analysis using temporal adaptive transformation method with under-relaxation[J].Rock and Soil Mechanics,2012,33(9):2857-2862. |
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| Authors: | CHENG Yong-gang CHANG Xiao-lin LI Dian-qing CHEN Xi |
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| Institution: | 1. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China; 2. School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China |
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| Abstract: | Finite element method is often used for solving unsaturated soil seepage problem.However,numerical difficulties such as slow convergence rate and inaccurate results are commonly existed in numerical analysis because of the highly nonlinear soil-water characteristic curve and hydraulic conductivity function.Based on a rational function transformation(RFT) method,a new temporal adaptive transformation method with under-relaxation(ATUR1) is proposed to solve the unsaturated soil seepage problem.It is shown that the transformation in ATUR1 can reduce the nonlinearity of solution profiles of the Richards’ equation both spatially and temporally;thus the inefficiencies in the numerical solution process caused by these nonlinearities can be overcome.The under-relaxation technique can further increase the efficiency by curbing the oscillation tendency during iterations;and the temporal errors during the whole simulation can be controlled effectively by the automatic temporal adaptive scheme.Numerical examples show that the proposed ATUR1 method is a robust and efficient numerical method for practical unsaturated soil seepage simulation. |
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| Keywords: | unsaturated seepage finite elements variable transformation under-relaxation temporal adaptive |
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