We develop and test a modeling approach to quantify turbulence-driven solute transport and mixing in porous media. Our approach addresses two key elements: (a) the spatial variability of the effective diffusion coefficient which is typically documented in the presence of a sediment–fluid interface and (b) the need to provide a model that can yield the complete distribution of the concentration probability density function, not being limited only to the mean concentration value and thus fully addressing solute mixing. Our work is motivated by the importance of solute transport processes in the hyporheic zone, which can have strong implications in natural attenuation of pollutants. Our approach combines Lagrangian schemes to address transport and mixing in the presence of spatial variability of effective diffusion. An exemplary scenario we consider targets a setup constituted by a homogeneous (fully saturated) porous medium underlying a clear water column where turbulent flow is generated. Solute concentration histories obtained through a model based solely on diffusive transport are benchmarked against an analytical solution. These are then compared against the results obtained by modeling the combined effects of diffusion and mixing. A rigorous sensitivity analysis is performed to evaluate the influence of model parameters on solute concentrations and mixing, the latter being quantified in terms of the scalar dissipation rate.

Our work is focused on the analysis of solute mixing under the influence of turbulent flow propagating in a porous system across the interface with a free fluid. Such a scenario is representative of solute transport and chemical mixing in the hyporheic zone. The study is motivated by recent experimental results (Chandler et al. Water Res Res 52(5):3493–3509, 2016) which suggested that the effective diffusion parameter is characterized by an exponentially decreasing trend with depth below the sediment-water interface. This result has been recently employed to model numerically downstream solute transport and mixing in streams. Our study provides a quantification of the uncertainty associated with the interpretation of the available experimental data. Our probabilistic analysis relies on a Bayesian inverse modeling approach implemented through an acceptance/rejection algorithm. The stochastic inversion workflow yields depth-resolved posterior (i.e., conditional on solute breakthrough data) probability distributions of the effective diffusion coefficient and enables one to assess the impact on these of (a) the characteristic grain size of the solid matrix associated with the porous medium and (b) the turbulence level at the water-sediment interface. Our results provide quantitative estimates of the uncertainty associated with spatially variable diffusion coefficients. Finally, we discuss possible limitations about the generality of the conclusions one can draw from the considered dataset.

This study investigates the surface processes taking place in an ungauged catchment in the Foro region in Eritrea (East Africa). We focus on estimating river discharge, sediment transport, and surface runoff to characterize hydrological fluxes in the area and provide a preliminary quantification of sediment transport and erosion. In this context, an overarching objective of the research is the study of the catchment associated with the Foro Dam. The latter comprises a silted reservoir formerly employed for agricultural water supply. The main traits associated with the system behavior across the watershed are assessed for a variety of combinations of the parameters governing the hydrological model selected. A detailed sensitivity analysis is performed to quantify the effects of the hydrological parameters on the estimated results. Numerical analyses are then performed to obtain an appraisal of expected water and sediment fluxes. Outputs of interest are largely dominated by the curve number parameter.

Diffusive transport in media with discontinuous properties is a challenging problem that arises in many applications. This paper focuses on one dimensional discontinuous media with generalized permeable boundary conditions at the discontinuity interface. It presents novel analytical expressions from the method of images to simulate diffusive processes, such as mass or thermal transport. The analytical expressions are used to formulate a generalization of the existing Skew Brownian Motion, HYMLA, and Uffink’s method, here named as GSBM, GHYMLA, and GUM, respectively, to handle generic interface conditions. The algorithms rely upon the random walk method and are tested by simulating transport in a bimaterial and in a multilayered medium with piecewise constant properties. The results indicate that the GUM algorithm provides the best performance in terms of accuracy and computational cost. The methods proposed can be applied for simulation of a wide range of differential problems.

We consider heat transport within a discontinuous domain by relying on the modeling approach proposed by Baioni et al. Such approach has been specifically designed to address diffusive processes in media with discontinuous physical properties and generalized boundary conditions at the discontinuities. Three algorithms are here applied to estimate the conductive heat transport in a bimaterial medium. The algorithms undergo testing using two test cases that share the same computational domain but differ in terms of their initial conditions. According to the numerical results all the algorithms ensure the conservation of thermal energy and preserve thermal equilibrium under steady state conditions. The Generalized Uffink Method (GUM) and Generalized HYMLA demonstrate sensitivity to the choice of the time step, whereas the Generalized Skew Brownian Motion appears to be unaffected by the value of $$\Delta t$$Δ t . The GUM algorithm presents an optimal trade-off between accuracy and computational time.