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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2019, Vol. 36 ›› Issue (4): 389-405.doi: 10.3969/j.issn.1005-3085.2019.04.003

• • 上一篇    下一篇

土壤溶质迁移方程的迎风稳定有限点法

秦新强,  苏李君,  王  兴,  李永真,  王岳玲   

  1. 西安理工大学应用数学系，西安  710048
  • 收稿日期:2017-02-17 接受日期:2019-04-10 出版日期:2019-08-15 发布日期:2019-10-15
  • 基金资助:
    国家自然科学基金(51409212)；陕西省自然科学基金(2017JQ1011; 2018JQ5094).

Wind Stability Finite Point Method for Soil Solute Transport Equations

QIN Xin-qiang,  SU Li-jun,  WANG Xing,  LI Yong-zhen,  WANG Yue-ling   

  1. Department of Applied Mathematics, Xi'an University of Technology, Xi'an 710048
  • Received:2017-02-17 Accepted:2019-04-10 Online:2019-08-15 Published:2019-10-15
  • Supported by:
    The National Natural Science Foundation of China (51409212); the Natural Science Foundation of Shaanxi Province (2017JQ1011; 2018JQ5094).

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摘要： 针对土壤溶质迁移方程具有对流项的特性，构造了迎风稳定有限点方法．该方法采用自适应迎风格式使其支持域偏向于迎风侧，以获取到上游信息，在对流占优的情况下，避免数值震荡现象．通过对一维和二维土壤溶质迁移方程的数值计算，详细分析了在不同布点、不同时间步长、不同影响因子的作用下，新算法数值解的收敛性、收敛阶与稳定性．数值结果表明本文方法在边界及梯度变化大的区域内，可以有效地提高计算精度，达到消除数值震荡的目的．

关键词: 有限点法, 移动最小二乘, 迎风格式, 土壤溶质迁移方程

Abstract: A finite point method for windward stability of soil solute transport equation is proposed. This method adopts an adaptive windward format to make its support field lean to the windward side, so it can obtain upstream information and avoid numerical oscillation when convection is dominant. The convergence, the order of convergence and the stability of the numerical solution of the new algorithm are analyzed in detail under the action of different distribution points, different time steps and different influence factors through the numerical calculation of the one-dimensional and two-dimensional soil solute transport equation. Numerical results show that the proposed method can effectively improve the computational accuracy and eliminate the numerical oscillation in the boundary region and gradient variations large region.

Key words: finite point method, moving least squares, the wind format, soil solute transport equations

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