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非饱和渗流模拟中非均匀空间网格的改进方法

朱帅润 何博 吴礼舟 李绍红 卿毅伟

朱帅润,何博,吴礼舟,等. 非饱和渗流模拟中非均匀空间网格的改进方法[J]. 水文地质工程地质,2023,50(1): 32-40 doi:  10.16030/j.cnki.issn.1000-3665.202110013
引用本文: 朱帅润,何博,吴礼舟,等. 非饱和渗流模拟中非均匀空间网格的改进方法[J]. 水文地质工程地质,2023,50(1): 32-40 doi:  10.16030/j.cnki.issn.1000-3665.202110013
ZHU Shuairun, HE Bo, WU Lizhou, et al. An improved method for inhomogeneous space grid in the simulation of unsaturated flow[J]. Hydrogeology & Engineering Geology, 2023, 50(1): 32-40 doi:  10.16030/j.cnki.issn.1000-3665.202110013
Citation: ZHU Shuairun, HE Bo, WU Lizhou, et al. An improved method for inhomogeneous space grid in the simulation of unsaturated flow[J]. Hydrogeology & Engineering Geology, 2023, 50(1): 32-40 doi:  10.16030/j.cnki.issn.1000-3665.202110013

非饱和渗流模拟中非均匀空间网格的改进方法

doi: 10.16030/j.cnki.issn.1000-3665.202110013
基金项目: 国家自然科学基金项目(41790432;42277183);国家重点研发计划项目(2018YFC1504702)
详细信息
    作者简介:

    朱帅润(1992-),男,博士研究生,主要从事岩土工程数值计算方法等方面的研究工作。E-mail:zhushuairun@sjtu.edu.cn

  • 中图分类号: TV139.1

An improved method for inhomogeneous space grid in the simulation of unsaturated flow

  • 摘要: Richards方程在非饱和渗流模拟及其他相关领域应用广泛。在数值求解过程中,可以采用有限差分方法进行数值离散并迭代求解,为了获得较可靠的数值解,常规的均匀网格空间步长往往是较小的。在一些不利数值条件下,如入渗于干燥土壤,迭代计算费时甚至精度也不能得到很好改善。因此,文章提出Chebyshev空间网格改进方法,结合有限差分方法对Richards方程进行数值离散以获得线性方程组,并通过经典的Picard迭代方法进行迭代求解线性方程组以得到Richards方程的数值解。通过均质土和分层土2个不利情况下的非饱和渗流算例,又结合模型解析解和软件Hydrus-1D,对比研究了改进网格方法与均匀网格方法获得数值解的精度。结果表明,提出的Chebyshev网格方法相较于传统的均匀网格,可以在较少的节点数下获得较高的数值精度,又具有较小的计算开销,有较好的应用前景。
  • 图  1  均匀网格和Chebyshev网格的示意图

    Figure  1.  Schematic diagram of uniform grid and Chebyshev grid.

    图  2  不同数值条件下不同网格方法的最大相对误差的比较

    Figure  2.  Comparison of the maximum relative error of different grid methods under different numerical conditions

    图  3  不同网格方法下获得的数值解和精确解的比较

    Figure  3.  Comparison of the numerical solutions obtained by different grid methods and exact solutions

    图  4  两层非饱和土的Chebyshev网格

    Figure  4.  Chebyshev grid of two-layer unsaturated soil

    图  5  不同工况下的数值解比较

    Figure  5.  Comparison of numerical solutions for different cases.

    图  6  Van Genuchten 模型拟合得到的SWCC

    Figure  6.  SWCC fitted by Van Genuchten model.

    图  7  不同方法下获得的数值解的比较

    Figure  7.  Comparison of the numerical solutions obtained by different methods

    表  1  t=5 h时的数值精度

    Table  1.   Numerical accuracy at t=5 h

    条件RSERE/%
    N均匀网格法Chebyshev网格法均匀网格法Chebyshev网格法
    1000.114.7×10−35.010.0502
    1500.102.6×10−34.530.1217
    2000.092.1×10−34.050.1476
    下载: 导出CSV

    表  2  饱和土壤的水力传导系数

    Table  2.   Hydraulic conductivity values for saturated soils

    土壤类型饱和水力传导系数/(m·s−1
    无杂质的砂石10−2~1
    粗砂10−4~10−2
    细砂10−5~10−4
    粉土10−7~10−5
    黏土<10−8
    下载: 导出CSV

    表  3  工况1至8的水力传导系数

    Table  3.   Hydraulic conductivity for cases 1 to 8

    工况数12345678
    Ks1/
    (m·s−1
    10−110−110−110−110−110−110−110−1
    Ks2/
    (m·s−1
    10−210−310−410−510−610−710−810−9
    下载: 导出CSV

    表  4  数值精度比较

    Table  4.   Comparison of the numerical accuracy

    方法RSERE/%MRE/%
    均匀网格$6.70\times10^{-2} $2.8145.1
    Chebyshev网格$5.58\times10^{-2} $2.2034.2
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-10-11
  • 录用日期:  2022-02-21
  • 修回日期:  2022-02-08
  • 网络出版日期:  2022-12-02
  • 刊出日期:  2023-01-13

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