土壤水流中溶质输运的CN有限元解系数向量的降维方法

侯晓丽; 罗振东; 符辉

doi:10.21656/1000-0887.450226

土壤水流中溶质输运的CN有限元解系数向量的降维方法

doi: 10.21656/1000-0887.450226

侯晓丽^{1, 2,},
罗振东^1, ,,
符辉²

1.
湖南三一工学院院士专家工作站, 长沙 410128
2.
湖南农业大学环境与生态学院, 长沙 410128

基金项目:

国家自然科学基金 11671106

详细信息

作者简介:
侯晓丽(1990—), 女, 讲师, 博士生(E-mail: 50901655@ncepu.edu.cn)

通讯作者:
罗振东(1958—), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: zhdluo@ncepu.edu.cn)

中图分类号: O242.21
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- 文章访问数: 77
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- PDF下载量: 11
- 被引次数: 0
出版历程
- 收稿日期: 2024-08-06
- 刊出日期: 2025-11-01

A Reduced-Dimension Method of CN Finite Element Solution Coefficient Vectors for Solute Transport in Soil Flow

HOU Xiaoli^{1, 2
,},
LUO Zhendong^{1
, ,},
FU Hui²

1.
Academician Expert Workstation, Hunan Sany Polytechnic College, Changsha 410128, P. R. China
2.
College of Environment and Ecology, Hunan Agricultural University, Changsha 410128, P. R. China

摘要

摘要: 利用特征投影分解(proper orthogonal decomposition, POD)方法建立土壤水流中溶质输运的一种很少未知量和精度足够高的Crank-Nicolson(CN)有限元解系数向量的降维外推仿真模型, 并分析这种降维外推仿真模型解的存在性和稳定性及误差. 用数值实验检验该模型的有效性和理论结果的正确性.
- 特征投影分解 /
- 土壤水流中溶质输运 /
- 降维外推仿真模型 /
- 存在性、稳定性和误差估计
Abstract: The proper orthogonal decomposition (POD) method was used to establish a dimensionally reduced extrapolation simulation model of the Crank-Nicolson (CN) finite element solution coefficient vectors with few degrees of freedom and sufficiently high accuracy for solute transport in soil flow. The existence, stability, and errors of the solutions to the reduced-dimension extrapolation simulation model were analyzed. Some numerical tests were used to verify the validity of the reduced-dimension extrapolation model and the correctness of the theoretical results.

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图 1 t=4时，CN有限元降维解的后视图(左图)和经典CN有限元解的后视图(右图)

Figure 1. The rear view of the CN finite element reduced-dimension solution at t=4 (left) and the rear view of the classical CN finite element solution at t=4 (right)

下载: 全尺寸图片幻灯片

图 2 t=8时，CN有限元降维解的后视图(左图)和经典CN有限元解的后视图(右图)

Figure 2. The rear view of the CN finite element reduced-dimension solution at t=8 (left) and the rear view of the classical CN finite element solution at t=8 (right)

下载: 全尺寸图片幻灯片

图 3 t=4时，CN有限元降维解的前视图(左图)和经典CN有限元解的前视图(右图)

Figure 3. The front view of the CN finite element reduced-dimension solution at t=4 (left) and the front view of the classical CN finite element solution at t=4 (right)

下载: 全尺寸图片幻灯片

图 4 t=8时，CN有限元降维解的前视图(左图)和经典CN有限元解的前视图(右图)

Figure 4. The front view of the CN finite element reduced-dimension solution at t=8 (left) and the front view of the classical CN finite element solution at t=8 (right)

下载: 全尺寸图片幻灯片

图 5 当t=8 s时, 具有不同POD数目的CN有限元降维解的误差

Figure 5. For t=8 s, the errors of CN finite element reduced-dimension solutions with different POD numbers

下载: 全尺寸图片幻灯片

参考文献(15)

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