潜水摄动有限元的随机数值模拟

陈家军; 李森; 孟占利; 杨周喜

潜水摄动有限元的随机数值模拟

1.
环境模拟与污染控制国家重点联合实验室, 北京师范大学环境学院, 北京 100875
2.
陕西省咸阳市勘察测绘院, 陕西咸阳 712000

基金项目:

教育部重点基金项目 104012

国家自然科学基金资助项目 40772148

详细信息

作者简介:
陈家军(1962-), 男, 博士, 教授, 研究方向为环境模拟与污染治理.E-mail: jeffchen@bnu.edu.cn

中图分类号: P641
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- 被引次数: 0
出版历程
- 收稿日期: 2007-03-28
- 刊出日期: 2008-03-25

Stochastic Numerical Modeling of Groundwater in a Phreatic Aquifer with Perturbation Finite Element Method

1.
State Key Joint Laboratory of Environment Simulation and Pollution Control, School of Environment, Beijing Normal University, Beijing 100875, China
2.
Xianyang In stitute of Prospecting and Mapping, Xianyang 712000, China

摘要

摘要: 潜水水流的动态随机模拟是一个复杂而难解决的问题.通过建立二维潜水非稳定流模拟的摄动随机有限元模型, 把控制方程的主要参数渗透系数和给水度随机变量、及源汇项和边界条件看作随机变量.在充分考虑4种随机因素的条件下, 推导出求解潜水二维非稳定流均值和方差的9个方程; 重点介绍了不同方程数值离散的特殊处理方法.通过设定理想例子对模拟结果进行了分析, 表明随机变量中边界条件值方差、渗透系数方差变化对水头方差变化的影响很小, 给水度方差的变化对水头方差的变化影响很大.本模型考虑因素全面, 对一般的潜水非稳定流随机模拟都可应用.本研究给出了边界、渗透系数、给水度的随机因素对潜水动态模拟的影响, 丰富和补充了地下水运动的随机理论.
- 潜水 /
- 摄动有限元 /
- 随机模拟 /
- 非稳定流
Abstract: Dynamically stochastic simulation of flow in a phreatic aquifer is a complicated and challenging issue. A perturbation finite element model for transient two-dimensional flow in a phreatic aquifer is developed and presented in this paper. In the model, stochastic variables include hydraulic conductivity and specific yield in governing equation, as well as source/sink and boundary conditions, 9 equations are derived in order to solve expectation and variance of two-dimensional unsteady flow and specific numeric treatment is adopted for different equation discreteness. In the end, simulated results are analyzed by a hypothetical example, and it shows that the influence of variation of boundary condition variance and hydraulic conductivity variance is little and that of variation of specific yield variance is significant. This model can be applied to general stochastic simulation of unsteady flow in a phreatic aquifer due to the fact that it takes into account all relevant factors. The study presents the influence on dynamic simulation of flow in phreatic water by stochastic variables of boundary condition, hydraulic conductivity and specific yield and it offers an alternative theory of stochastic simulation of ground water flow.
- flow in a phreatic aquifer /
- perturbation finite element /
- stochastic simulation /
- unsteady flow.

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图 1 计算区节点和单元划分

Fig. 1. Node and element division of calculation region

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图 2 同模拟时间下均值数值解与解析解对比

Fig. 2. Comparison of numerical and analytic solutions for simulated mean value

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图 3 随机变量方差变化时同一水平线上水头方差变化

Fig. 3. Variance variations of water head in level line to variance variation of stochastic variables

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表 1 随机参数最初设定值

Table 1. Initial value of stochastic parameters

表 2 位时均值数值解与解析解对比

Table 2. comparison of numerical and analytical solutions of mean value of groundwater level

表 3 透系数方差变化

Table 3. Variance variation of permeability coefficient

表 4 随机变量方差变化时水头方差的变化

Table 4. Variance variations of water head tO variance variation of stochastic variables

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