Global random walk stochastic simulations for the assessment of the contamination risk in groundwater systems

地下水系统污染的可预测性将通过使用全球随机游动方法(GRW)的随机模拟来研究。为此，将使用在高性能并行计算机上通过GRW模拟计算的传输实现的统计系综来估计遍历范围。后者被定义为实际可观测值与随机模型提供的预测值的均方根偏差，在很大程度上量化了遍历性。这些研究将集中在预渐近区域和由输运对初始溶质羽流形状和尺寸的非线性依赖所引起的记忆效应。将发展基于福克-普朗克方程和伊索方程的随机分析，并用于解释随机模拟结果。为了提高计算效率，算法GRW还将被用作遍历模拟过程的一部分。这种方法利用了地下水速度场地质统计模型的遍历性，通过对单一速度实现的模拟，从空间平均推断运移统计数据，从而具有有限的相关范围。

The predictability of contamination in groundwater systems will be investigated via stochastic simulations using the Global Random Walk method (GRW). To this aim, statistical ensembles of transport realizations, computed by GRW simulations on high performance parallel computers, will be used to estimate ergodicity ranges. The latter are defined by the root mean square deviation of actual observables from predictions provided by stochastic models and quantify the ergodicity in a large sense. The investigations will focus on pre-asymptotic regime and on memory effects induced by the nonlinear dependence of transport on the shape and dimensions of the initial solute plumes. Stochastic analyses based on Fokker-Plank and Itô equations will be developed and used for the interpretation of the stochastic simulations results. To increase the computational efficiency, the algorithm GRW also will be used as part of an ergodic simulations procedure. This approach exploits the ergodicity of the geo-statistical model of the groundwater velocity field with finite correlation range by inferring transport statistics from space averages over simulations done for a single velocity realization.