NDLI: A perturbation stochastic finite-element method for groundwater flow models based on an undetermined-coefficients approach

Content Provider	Springer Nature Link
Author	Yao, Leihua He, Pengpeng Song, Shikun
Copyright Year	2010
Abstract	A new perturbation technique and finite-element method, which incorporates an undetermined-coefficients approach, is proposed to conduct stochastic simulation for problems of groundwater flow. Formulas of the mean value and variance of groundwater head are derived to exclude the process of computing the first and second-order derivatives of groundwater head with respect to stochastic variables (coefficient of transmissibility, storage coefficient, etc.) in the calculation process of common finite element methods. For ordinary stochastic groundwater problems, the statistical properties of groundwater head can be easily obtained by using the proposed method, which is especially efficient for the stochastic problems that have fewer input stochastic variables. A stochastic numerical simulation of a two-dimensional confined-groundwater flow problem has been conducted to validate effectiveness and determine the limitations of the proposed method. The results illustrate that the accuracy and efficiency of the method proposed are satisfactory, and that the computing time is shorter when there is a small number of input stochastic variables.Une nouvelle technique faisant appel à la théorie des perturbations à éléments finis incorporant une base paramétrique aléatoire est proposée pour résoudre des problèmes de flux souterrain par simulation stochastique. Les formules de la moyenne et de la variance de la charge hydraulique sont dérivées pour éviter le calcul des dérivées première et seconde de la charge par rapport aux variables stochastiques (coefficient de transmissivité, coefficient d’emmagasinement, etc.) des méthodes habituelles de calcul par éléments finis. Pour la résolution stochastique des problèmes courants d’écoulement souterrain, les caractéristiques statistiques de la charge peuvent être facilement obtenues par la méthode proposée, particulièrement efficace dans le cas des problèmes comportant un petit nombre de variables stochastiques. La simulation stochastique d’un problème d’écoulement souterrain captif bidimentionnel a été effectuée pour valider le bien fondé de la méthode proposée et en établir les limites. Les résultats montrent que précision et bien fondé de la méthode proposée sont satisfaisants et que le temps de calcul est plus court quand le nombre de variables stochastiques est plus petit.Se propone una nueva técnica de perturbación y método de elementos finitos, que incorpora un enfoque de coeficientes no determinados, para llevar a cabo simulaciones estocásticas para problemas de flujo de agua subterránea. Se deducen fórmulas del valor medio y de la varianza de la carga hidráulica del agua subterránea para excluir los procesos de computar las derivadas de primer y segundo orden de la carga hidráulica de agua subterránea con respecto a variables estocásticas (coeficiente de transmisividad, coeficiente de almacenamiento, etc) en el proceso de cálculo de métodos comunes de elementos finitos. Para los problemas estocásticos comunes de aguas subterráneas, las propiedades estadísticas de la carga hidráulica de agua subterránea pueden ser fácilmente obtenidas usando el método propuesto, el cual es especialmente eficiente para problemas estocásticos que tienen menos variables estocásticas de entrada. Se desarrolla una simulación numérica estocástica de un problema de flujo bidimensional de aguas subterráneas confinadas para validar la efectividad y determinar las limitaciones del método propuesto. Los resultados muestran que la exactitud y eficiencia del método propuesto son satisfactorios, y que el tiempo de cómputo es más corto donde hay un número menor de variables estocásticas de entrada.引入待定系数法, 提出了求解地下水水流随机模拟问题的摄动随机有限元法。推导出了地下水水头均值和方差的表达式, 使得传统有限元法求解过程中避免了计算地下水水头对随机变量的一阶导数和二阶导数。对于一般的随机地下水问题, 地下水水头的统计特征可以很容易应用所提出的方法求得; 尤其当解决随机变量个数较少的随机问题时, 效率更高。以二维承压地下水水流问题的随机数值模拟为例, 验证所提出的方法的有效性, 并探讨其局限性。模拟结果表明, 该法的精度和效率令人满意; 当随机变量的个数较少时, 计算耗时更短。Propõe-se uma nova técnica de perturbação para o método de elementos finitos que incorpora uma abordagem por coeficientes indeterminados para a simulação estocástica de problemas de escoamento de água subterrânea. São derivadas fórmulas para o valor da média e da variância da carga hidráulica destinadas a excluir o processo de cálculo das derivadas de primeira e segunda ordem da carga hidráulica em ordem a variáveis estocásticas (coeficiente de transmissividade, coeficiente de armazenamento, etc.) no processo de cálculo dos métodos de elementos finitos comuns. Para problemas estocásticos vulgares de água subterrânea, as propriedades estatísticas da carga hidráulica podem ser facilmente obtidas usando o método proposto, que é especialmente eficiente para os problemas estocásticos que têm menos variáveis estocásticas de entrada. Foi conduzida uma simulação numérica estocástica de um problema de escoamento bidimensional de água subterrânea confinada para validar a efectividade e determinar as limitações do método proposto. Os resultados mostram que a precisão e a eficiência do método proposto são satisfatórias e que o tempo de cálculo é menor quando há um pequeno número de variáveis de entrada estocásticas.
Starting Page	1603
Ending Page	1609
Page Count	7
File Format	PDF
ISSN	14312174
Journal	Hydrogeology Journal
Volume Number	18
Issue Number	7
e-ISSN	14350157
Language	Portuguese
Publisher	Springer-Verlag
Publisher Date	2010-09-07
Publisher Institution	International Association of Hydrogeologists
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Groundwater flow Perturbation Undetermined-coefficients approach Stochastic finite-element method Numerical modeling Stochastic variable Waste Water Technology Water Pollution Control Water Management Aquatic Pollution Geology Hydrogeology
Content Type	Text
Resource Type	Article
Subject	Earth and Planetary Sciences Water Science and Technology

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