| 二维非饱和土壤水流方程基于POD方法的有限元格式 |
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| 引用本文： | 狄振华,罗振东,谢正辉,王爱文.二维非饱和土壤水流方程基于POD方法的有限元格式[J].北京交通大学学报(自然科学版),2011,35(3). |
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| 作者姓名： | 狄振华 罗振东 谢正辉 王爱文 |
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| 作者单位： | 北京交通大学理学院,北京100044;中国科学院大气物理研究所,北京100029;北京交通大学理学院,北京,100044;中国科学院大气物理研究所,北京,100029;北京信息科技大学理学院,北京,100192 |
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| 基金项目： | 国家自然科学基金资助项目(10871022,11061009,40821092); 国家“863计划”项目资助(2010CB428403,2009CB421407,2010CB951001) |
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| 摘 要： | 将特征正交分解(Proper Orthogonal Decomposition,POD)应用于二维非饱和土壤水流方程通常的有限元格式,将其简化为一个计算量少但具有足够高精度的POD有限元格式,并给出POD有限元解的误差估计.数值例子表明:POD有限元解能有效地表达土壤水流的运动特征,保证了POD有限元解和通常有限元解误差足够小,而且POD有限元格式有较少的自由度,比通常的有限元格式大大节省了计算量和内存容量,从而验证POD方法的有效性.
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| 关 键 词： | 特征正交分解 有限元格式 误差分析 二维非饱和土壤水流方程 |
A reduced finite element scheme based on POD two-dimensional unsaturated soil water flow equation |
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| DI Zhenhua,LUO Zhendong,XIE Zhenghui,WANG Aiwen.A reduced finite element scheme based on POD two-dimensional unsaturated soil water flow equation[J].JOURNAL OF BEIJING JIAOTONG UNIVERSITY,2011,35(3). |
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| Authors: | DI Zhenhua LUO Zhendong XIE Zhenghui WANG Aiwen |
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| Institution: | DI Zhenhua1,2,LUO Zhendong1,XIE Zhenghui2,WANG Aiwen3(1.School of Science,Beijing Jiaotong University,Beijing 100044,China,2.Institute of Atmospheric Physics,Chinese Academy of Sciences,Beijing 100029,3.School of Science,Beijing Information Science and Technology University,Beijing 100192,China) |
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| Abstract: | Proper orthogonal decomposition(POD) is applied into the finite element scheme(FES) for the two-dimensional unsaturated soil water flow equation,and a new lower dimensional and high accurate FES for the equation is established.The error estimates among the true solution,the usual FES solution,and the reduced FES solution based on POD basis are proved.At last,it is shown by a numerical example that the POD solution can express soil water flow availably,computation load is greatly saved by using reduced FES a... |
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| Keywords: | proper orthogonal decomposition(POD) finite element scheme error analysis the two-dimensional unsaturated soil flow equation |
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