Collaborative Research: A Comparison of Local and Nonlocal Transport Theories

这个项目将评估几个新兴的理论治疗的保守溶质的分散，相对于他们的数据需求和能力，以代表分散。我们将应用经典的本地和非本地的方法，也许是最好的研究和最具代表性的异构网站在北美-在哥伦布，密西西比的MADE网站。 我们将评估传统的对流-弥散方程（ADE），这被认为需要数千万个具有局部速度值的节点，以及几种非局部方法，包括时间-非局部多速率传质（MRMT）和连续时间随机游走（CTRW）方法，和/或空间分数对流-弥散方程（fADE）。 每一个非本地的方法显示出巨大的希望，在减少所需的信息量作出准确的预测，快速和/或不稳定的污染迁移。 然而，给定相同的站点，我们必须问这样的问题：需要多少数据，什么类型的数据，以获得每种方法的给定精度水平？是否有些方法捕获了流程的结果行为，因此具有内在的上级性？是否可以为模型使用和数据收集制定简单的指导方针？ 拟议中的工作将首次系统地评估最近和广泛使用的保守溶质运移理论的准确性和数据需求。 最后的产品将是一个统一的模型，其中包括当前的时间和空间的非局部控制方程的显着特点，并将有关地质复杂性的信息，无论是在当地的速度或在非本地条款的控制方程。 此外，我们将提供一个指南，从局部尺度（及其离散化）到非局部项的信息权衡。 除了广泛研究的MADE站点之外，我们还将对许多类型的合成含水层进行分析。

This project will evaluate several emerging theoretical treatments of the dispersion of a conservative solute, with respect to their data needs and ability to represent dispersion. We will apply classical local, and non-local, methods at perhaps the best-studied and most representative heterogeneous site in North America - the MADE site in Columbus, Mississippi. We will evaluate the traditional advection-dispersion equation (ADE), which is thought to require tens of millions of nodes with local velocity values, and several non-local methods, including the time-non-local multiple-rate mass transfer (MRMT) and continuous time random walk (CTRW) methods, and/or the space-fractional advection-dispersion equation (fADE). Each of the non-local methods show great promise in reducing the amount of information needed to make accurate predictions of anomalously rapid and/or recalcitrant pollution migration. However, given the same site, we must ask the questions: How much data, of what types, are needed to obtain a given level of accuracy for each method? Are some methods capturing the resulting behavior of the process and, thus are inherently superior? Can simple guidelines for model use and data collection be generated? The proposed work would give the first systematic evaluation of the accuracy and data needs of the most recent and widely used theories of conservative solute transport. The final product would be a unifying model that includes the salient features of current time- and space-non-local governing equations, and places information about the geologic complexity in either the local velocities or in non-local terms in the governing equation. Furthermore, we will provide a guide to the tradeoff of information from the local scale (and discretization thereof) to the non-local terms. We will apply the analysis to synthetic aquifers of many types, in addition to the extensively studied MADE site.