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首页> 外文学位 >Ensemble average and ensemble variance behavior of unsteady groundwater flow in unconfined, heterogeneous aquifers: An exact second order model.
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Ensemble average and ensemble variance behavior of unsteady groundwater flow in unconfined, heterogeneous aquifers: An exact second order model.

机译：在无限制，非均质含水层中非稳态地下水流的集合平均和总体方差行为：精确的二阶模型。

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摘要

A new stochastic model for unconfined groundwater flow is proposed. The developed evolution equation for the probabilistic behavior of unconfined groundwater flow results from random variations in hydraulic conductivity. The probabilistic description for the state variable of the nonlinear stochastic unconfined flow process becomes a mixed Lagrangian-Eulerian Fokker-Planck equation (FPE). Furthermore, the FPE is a deterministic, linear partial differential equation (PDE) and has the advantage of providing the probabilistic solution in the form of evolutionary probability density functions.;Subsequently, the Boussinesq equation for one-dimensional unconfined groundwater flow is converted into a nonlinear ordinary differential equation (ODE) and a two-point boundary value problem through the Boltzmann transformation. Similarly, the two-dimensional Boussinesq equation is converted to a nonlinear ODE using the Lie Group theory. Next, these derived ODEs are ensemble averaged with second order cumulant expansion theory and converted into a linear, deterministic partial differential equation (PDE). This new equation is called the FPE, and describes the evolution of the probability density function (PDF) of the hydraulic head. Once a solution of this FPE is obtained, one can then obtain the ensemble average and ensemble variance behavior of the hydraulic head through an expectation operation.;The numerical solutions of the FPE are validated with Monte Carlo simulations under varying stochastic hydraulic conductivity fields. Results from the model application to groundwater flow in heterogeneous unconfined aquifers illustrate that the time-space behavior of the mean and variance of the hydraulic head are in good agreement for both the stochastic model and the Monte Carlo solutions in both one-dimension and two-dimensions. This indicates that the derived FPE, as a stochastic model of the ensemble behavior of unconfined groundwater flow, can provide encouraging results in estimating the time-space behavior of the mean and variance of the hydraulic head in heterogeneous aquifers. Modeling of the hydraulic head variance, as shown here, will provide a measure of confidence around the ensemble mean behavior of the hydraulic head.
机译：提出了一种新的无侧限地下水流随机模型。针对无约束地下水流动的概率行为而开发的演化方程是由水力传导率的随机变化产生的。非线性随机无限制流动过程的状态变量的概率描述变成了混合拉格朗日-欧拉Fokker-Planck方程（FPE）。此外，FPE是确定性的线性偏微分方程（PDE），具有以演化概率密度函数形式提供概率解的优点;随后，将一维无约束地下水流的Boussinesq方程转换为非线性常微分方程（ODE）和通过Boltzmann变换的两点边值问题。类似地，使用李群理论将二维Boussinesq方程转换为非线性ODE。接下来，使用二阶累积量展开理论对这些导出的ODE进行集合平均，并将其转换为线性确定性偏微分方程（PDE）。这个新方程式称为FPE，它描述了液压头的概率密度函数（PDF）的演变。一旦获得了这种FPE的解，就可以通过期望操作获得液压头的整体平均和整体方差行为。；在蒙特卡洛模拟中，在变化的随机水力传导率场下验证了FPE的数值解。该模型应用于非均质非承压含水层中地下水流动的结果表明，在一维模型和二维模型中，随机模型和蒙特卡洛解决方案的水力压头均值和方差的时空行为都非常吻合。尺寸。这表明，导出的FPE作为非约束地下水流的整体行为的随机模型，可以为估算非均质含水层中水头的均值和方差的时空行为提供令人鼓舞的结果。如此处所示，对液压压头变化的建模将提供围绕液压压头总体平均性能的置信度的度量。

著录项

  • 作者

    Cayar, Mesut.;

  • 作者单位

    University of California, Davis.;

  • 授予单位 University of California, Davis.;
  • 学科 Statistics.;Engineering Civil.
  • 学位 Ph.D.
  • 年度 2008
  • 页码 76 p.
  • 总页数 76
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 统计学;建筑科学;
  • 关键词

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