A multiscale flux basis for mortar mixed discretizations of reduced Darcy-Forchheimer fracture models

In this paper, a multiscale flux basis algorithm is developed to efficiently solve a flow problem in fractured porous media. Here, we take into account a mixed-dimensional setting of the discrete fracture matrix model, where the fracture network is represented as lower-dimensional object. We assume the linear Darcy model in the rock matrix and the non-linear Forchheimer model in the fractures. In our formulation, we are able to reformulate the matrix-fracture problem to only the fracture network problem and, therefore, significantly reduce the computational cost. The resulting problem is then a non-linear interface problem that can be solved using a fixed-point or Newton-Krylov methods, which in each iteration require several solves of Robin problems in the surrounding rock matrices. To achieve this, the flux exchange (a linear Robin-to-Neumann co-dimensional mapping) between the porous medium and the fracture network is done offline by pre-computing a multiscale flux basis that consists of the flux response from each degree of freedom on the fracture network. This delivers a conserve for the basis that handles the solutions in the rock matrices for each degree of freedom in the fractures pressure space. Then, any Robin sub-domain problems are replaced by linear combinations of the multiscale flux basis during the interface iteration. The proposed approach is, thus, agnostic to the physical model in the fracture network. Numerical experiments demonstrate the computational gains of pre-computing the flux exchange between the porous medium and the fracture network against standard non-linear domain decomposition approaches

GPR Method for the Detection and Characterization of Fractures and Karst Features: Polarimetry, Attribute Extraction, Inverse Modeling and Data Mining Techniques

The presence of fractures, joints and karst features within rock strongly influence the hydraulic and mechanical behavior of a rock mass, and there is a strong desire to characterize these features in a noninvasive manner, such as by using ground penetrating radar (GPR). These features can alter the incident waveform and polarization of the GPR signal depending on the aperture, fill and orientation of the features. The GPR methods developed here focus on changes in waveform, polarization or texture that can improve the detection and discrimination of these features within rock bodies. These new methods are utilized to better understand the interaction of an invasive shrub, Juniperus ashei, with subsurface flow conduits at an ecohydrologic experimentation plot situated on the limestone of the Edwards Aquifer, central Texas. First, a coherency algorithm is developed for polarimetric GPR that uses the largest eigenvalue of a scattering matrix in the calculation of coherence. This coherency is sensitive to waveshape and unbiased by the polarization of the GPR antennas, and it shows improvement over scalar coherency in detection of possible conduits in the plot data. Second, a method is described for full-waveform inversion of transmission data to quantitatively determine fracture aperture and electromagnetic properties of the fill, based on a thin-layer model. This inversion method is validated on synthetic data, and the results from field data at the experimentation plot show consistency with the reflection data. Finally, growing hierarchical self-organizing maps (GHSOM) are applied to the GPR data to discover new patterns indicative of subsurface features, without representative examples. The GHSOMs are able to distinguish patterns indicating soil filled cavities within the limestone. Using these methods, locations of soil filled cavities and the dominant flow conduits were indentified. This information helps to reconcile previous hydrologic experiments conducted at the site. Additionally, the GPR and hydrologic experiments suggests that Juniperus ashei significantly impacts infiltration by redirecting flow towards its roots occupying conduits and soil bodies within the rock. This research demonstrates that GPR provides a noninvasive tool that can improve future subsurface experimentation

Gis and mathematical groundwater simulation as tools for hydrogeological conceptual modeling and vulnerability assessment of Porto Torres industrial zone aquifer (nw Sardinia)

The object of this study has been to develop an integrated technique of GIS and groundwater modeling program to improve hydrogeological setting understanding of Porto Torres industrial zone and to perform intrinsic vulnerability evaluation of the aquifer to contamination. To reach this purpose, GIS interfaced to the hydrogeological software GMS has been used to efficiently manage a wide range of geographical information and data. Hydrogeological understanding has been facilitated by a tree-dimensional schematization of aquifer domain and by numerical modeling, that has been finalized to provide proof to support or dismiss assumptions made on conceptual model implementation. Finally, based on GIS elaborations and groundwater simulation, SINTACS method has been applied to evaluate vulnerability degree of the Mesozoic aquifer