Filtered density function uncertainty assessments for reactivetransport in groundwater

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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.