权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Filtered density function uncertainty assessments for reactivetransport in groundwater

地下水反应输运的过滤密度函数不确定性评估

基本信息

批准号：
221406899
负责人：
Professorin Dr. Sabine Attinger
金额：
--
依托单位：
Lehrstuhl für Angewandte Mathematik I
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2012
资助国家：
德国
起止时间：
2011-12-31 至 2017-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/221406899?language=en
关键词：
Filtered density function uncertainty assessments

项目摘要

Modelling the fate of contaminants in groundwater requires solutions for reactant species concentrations, representative at some spatial scales, as well as assessments of uncertainty induced by sub-scale aquifer's heterogeneity. Under stochastic parameterizations of hydraulic conductivity, one arrives at systems of stochastic partial differential equations and the complete solution is given byprobability density functions of species concentrations. When instead of stochastic averaging one performs a spatial filtering of system's heterogeneity, one defines the filtered density function(FDF), which plays the same role as a probability density in uncertainty assessments. In this way, the spatial scale of the prediction is explicitly defined and the cumbersome Monte Carlo reference solutions are replaced by less expensive direct numerical simulations consisting of solving reactive transport problems on finer grids. Although a long standing approach in turbulence, the FDF method has not yet been applied to groundwater. In developing a FDF method for reactive transport in groundwater we schedule two main tasks. The first one consists of modelling sub-grid processes. Here, the challenge is the interdependence between up-scaling flow and transport and modeling sub-grid mixing. The second task is to develop accurate and computationally efficient solvers for the FDF problem. This involves solutions to filtered equations for flow and to FDF evolution equations. The latter will be solved with a global random walk method which supersedes the limitations of currently used particles methods and, therefore, could also improve the efficiency of FDF simulations in turbulence. A guiding line in designing the FDF method will be its applicability to Bayesian inference for monitored contaminated sites.

模拟地下水中污染物的命运需要在某些空间尺度上具有代表性的反应物质浓度的解决方案，以及对亚尺度含水层异质性引起的不确定性的评估。在水力传导性的随机参数化下，得到了随机偏微分方程系统，并用物种浓度的概率密度函数给出了系统的完全解。当人们对系统的异质性进行空间滤波而不是随机平均时，人们定义了过滤密度函数（FDF），它在不确定性评估中起着与概率密度相同的作用。通过这种方式，预测的空间尺度被明确定义，繁琐的蒙特卡罗参考解被更便宜的直接数值模拟所取代，直接数值模拟包括在更细的网格上解决反应输运问题。虽然FDF方法是一种长期存在的湍流方法，但尚未应用于地下水。在开发地下水反应输运的FDF方法时，我们安排了两个主要任务。第一种方法是对子网格过程进行建模。在这里，挑战在于上尺度流动和输运之间的相互依赖以及模拟子网格混合。第二个任务是为FDF问题开发精确且计算效率高的求解器。这涉及到流动的过滤方程和FDF演化方程的解。后者将用全局随机游走方法解决，该方法取代了目前使用的粒子方法的局限性，因此也可以提高湍流中FDF模拟的效率。设计FDF方法的指导方针是它对监测污染场地的贝叶斯推断的适用性。