TENG Fei, LUO Zhen-dong. A Reduced-Order Extrapolating Simulation Model for Unsaturated Soil Water Flow Problem[J]. Applied Mathematics and Mechanics, 2014, 35(2): 148-161. doi: 10.3879/j.issn.1000-0887.2014.02.004
 Citation: TENG Fei, LUO Zhen-dong. A Reduced-Order Extrapolating Simulation Model for Unsaturated Soil Water Flow Problem[J]. Applied Mathematics and Mechanics, 2014, 35(2): 148-161.

# A Reduced-Order Extrapolating Simulation Model for Unsaturated Soil Water Flow Problem

##### doi: 10.3879/j.issn.1000-0887.2014.02.004
Funds:  The National Natural Science Foundation of China(11271127)
• Rev Recd Date: 2013-12-25
• Publish Date: 2014-02-15
• A reduced-order extrapolating simulation model with sufficiently high accuracy and fews degress of freedom for the two-dimensional unsaturated soil water flow problem was established by means of the Crank-Nicolson finite volume element (CNFVE) method and POD technique. The error estimates of the reduced-order approximate solutions and the algorithm implementation for the reduced-order extrapolating simulation model were provided. Finally, a numerical example was taker to illustrate that the results of numerical computation are consistent with those of theoretical solutions. Moreover, the advantage of the reduced-order extrapolating simulation model lies in its simpler computation and higher accuracy.
•  [1] 雷志栋, 杨诗秀, 谢森传. 土壤水动力学[M]. 北京: 清华大学出版社, 1998. (LEI Zhi-dong, YANG Shi-xiu, XIE Sen-chuan. Soil Water Dynamics [M]. Beijing: Tsinghua University Press, 1988. (in Chinese)) [2] 谢正辉, 曾庆存, 戴永久, 王斌. 有限元集中质量法在非饱和土壤水流中的应用[J]. 气候与环境研究, 1998,3(1): 73-81.(XIE Zheng-hui, ZENG Qing-cun, DAI Yong-jiu, WANG Bin. An application of the mass-lumped finite element method to the unsaturated soil water problem[J]. Studies in Climate and Environment,1998,3(1): 73-81.(in Chinese)) [3] 李焕荣, 罗振东. 二维非饱和土壤水分运动问题的半离散有限体积元模拟[J]. 计算数学, 2011,33(1): 57-68.(LI Huan-rong, LUO Zhen-dong. Semi-discrete finite volume element simulation for two-dimensional unsaturated soil water flow problem[J]. Mathematica Numerica Sinica,2011,33(1): 57-68.(in Chinese)) [4] Li R H, Chen Z Y, Wu W. Generalized Difference Methods for Differential Equations— Numerical Analysis of Finite Volume Methods [M]. New York: Marcel Dekker Inc, 2000. [5] Holmes P, Lumley J L, Berkooz G. Turbulence, Coherent Structures, Dynamical Systems and Symmetry [M]. Cambridge: Cambridge University Press, 1996. [6] Fukunaga K. Introduction to Statistical Recognition [M]. New York: Academic Press, 1990. [7] Jolliffe I T. Principal Component Analysis [M]. 2nd ed. New York, Berlin, Heidelberg: Springer-Verlag, 2002. [8] Selten F M. Baroclinic empirical orthogonal functions as basis functions in an atmospheric model[J]. Journal of the Atmospheric Sciences,1997,54(16): 2099-2114. [9] Sirovich L. Turbulence and the dynamics of coherent structures: Ⅰ-coherent structures; Ⅱ- symmetries and transformations; Ⅲ-dynamics and scaling[J]. Quarterly of Applied Mathematics,1987,45(3): 561-571; 573-590. [10] LUO Zhen-dong, XIE Zheng-hui, SHANG Yue-qiang, CHEN Jing. A reduced finite volume element formulation and numerical simulations based on POD for parabolic equations[J]. Journal of Computational and Applied Mathematics,2011,235(8): 2098-2111. [11] LUO Zhen-dong, LI Hong, ZHOU Yan-jie, HUANG Xiao-ming. A reduced FVE formulation based on POD method and error analysis for two-dimensional viscoelastic problem[J]. Journal of Mathematical Analysis and Applications,2012,385(1): 310-321. [12] LUO Zhen-dong, LI Hong, SUN Ping. A reduced-order Crank-Nicolson finite volume element formulation based on POD method for parabolic equations[J]. Applied Mathematics and Computation,2013,219(11): 5887-5900. [13] 罗振东, 李宏, 陈静. 非饱和土壤水流问题基于POD方法的降阶有限体积元格式及外推算法实现[J]. 中国科学A辑: 数学, 2012,42(12): 1263-1280.(LUO Zhen-dong, LI Hong, CHEN Jing. A reduced-order finite volume element formulation based on POD method and implementation of its extrapolation algorithm for unsaturated soil water flow equation[J]. Sci Sin Math,2012,42(12): 1263-1280.(in Chinese)) [14] Adams R A. Sobolev Spaces [M]. New York: Academic Press, 1975. [15] 罗振东. 混合有限元法基础及其应用[M]. 北京: 科学出版社, 2006.(LUO Zhen-dong. Mixed Finite Element Methods and Applications [M]. Beijing: Science Press, 2006.(in Chinese)) [16] Ciarlet P G. The Finite Element Method for Elliptic Problems [M]. Philadelphia: Society for Industrial and Applied Mathematic, 2002. [17] Rudin W. Functional and Analysis [M]. 2nd ed. New York: McGraw-Hill Companies, Inc, 1973.

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142