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Recent advances in satellite technologies, statistical and mathematical models, and computational resources have paved the way for operational use of satellite data in monitoring and forecasting natural hazards. We present a review of the use of satellite data for Earth observation in the context of geohazards preventive monitoring and disaster evaluation and assessment. We describe the techniques exploited to extract ground displacement information from satellite radar sensor images and the applicability of such data to the study of natural hazards such as landslides, earthquakes, volcanic activity, and ground subsidence. In this context, statistical techniques, ranging from time series analysis to spatial statistics, as well as continuum or discrete physics-based models, adopting deterministic or stochastic approaches, are irreplaceable tools for modeling and simulating natural hazards scenarios from a mathematical perspective. In addition to this, the huge amount of data collected nowadays and the complexity of the models and methods needed for an effective analysis set new computational challenges. The synergy among statistical methods, mathematical models, and optimized software, enriched with the assimilation of satellite data, is essential for building predictive and timely monitoring models for risk analysis.

Although the indications contained in the European New Green Deal aim to inhibit the opening of new waste disposal sites through a circular economy of waste materials, the management of an extremely large number of municipal solid waste landfills (MSWLF) at different stages of their life cycle is a highly topical issue. Recent national regulations in Italy require the operators to monitor subsoil conditions for 30 years, but do not define clear and unambiguous guidelines.According to analyses carried out at various landfill sites in northern Italy, monitoring activities were often found to be set up with wells equipped with piezometers. This approach is not optimal because when any contaminants are intercepted by the wells, the conditions of the subsoil may already be compromised. Therefore, the goal of our work is to develop methodologies to test and define an effective monitoring protocol that allows to mitigate the environmental and ecological risks associated with the subsurface propagation of pollutants at MSWLF sites.The analysis of the subsoil conditions involves the design of monitoring methodologies and the interpretation of the obtained results, exploiting geological, hydrogeological and geophysical knowledge and skills. Accordingly, we rely on a research methodology based on the mutual and continuous exchange between the involved disciplines, starting from the initial geological assumptions that will be used to define a physical model of the subsurface. We mainly resort to indirect non-invasive techniques, in particular to the direct current (DC) electrical resistivity tomography (ERT) that on the one hand is indicated for identifying conductive anomalies associated with the propagation of pollutants, but on the other hand constitutes a complex ill-posed numerical problem. The major issues are related to the spatial resolution and the penetration depth of the technique that in turn control the capability to detect presence and the conditions of the extremely thin high-density polyethylene (HDPE) membrane used to isolate the landfill waste from the surroundings.To tackle the abovementioned issues, we decided to perform properly downscaled laboratory experiments in order to test the effectiveness of DC methodology in controlled and well-known settings. Processing and interpretation of the collected geoelectrical data are supported by a new modelling code in Python programming language that is being developed.We deem that the integration of lab and modelling tests is necessary to propose a sound standard approach to address complex and multidisciplinary problems related to landfill risk management.

The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults, while the latter are connected to the properties of the rock matrix which might vary abruptly in space. The development of approximation schemes has recently focused on the overcoming of such difficulties with the objective of obtaining numerical schemes with good approximation properties. In this work we carry out a numerical study on the performance of the Mixed Virtual Element Method (MVEM) for the solution of a single-phase flow model in fractured porous media. This method is able to handle grid cells of polytopal type and treat hybrid dimensional problems. It has been proven to be robust with respect to the variation of the permeability field and of the shape of the elements. Our numerical experiments focus on two test cases that cover several of the aforementioned critical aspects.

This work deals with the efficient iterative solution of the system of equations stemming from mimetic finite difference discretization of a hybrid-dimensional mixed Darcy problem modeling flow in fractured porous media. We investigate the spectral properties of a mixed discrete formulation based on mimetic finite differences for flow in the bulk matrix and finite volumes for the fractures, and present an approximation of the factors in a set of approximate block factorization preconditioners that accelerates convergence of iterative solvers applied to the resulting discrete system. Numerical tests on significant three-dimensional cases have assessed the properties of the proposed preconditioners.

We present ADM-LTS, an adaptive multilevel space-time-stepping scheme for transport in heterogeneous porous media. At each time step, firstly, the flow (pressure) solution is obtained. Then, the transport equation is solved using the ADM-LTS method, which consists of two stages. In the first stage, an initial solution is obtained by imposing the coarsest space-time grid. This initial solution is then improved, in the second stage, by imposing a space-time adaptive grid on the cells where the solution does not satisfy the desired quality. The quality control is based on error estimators with user-defined threshold values. The time-integration procedure, in which the coarsest-scale solution provides local flux boundary conditions for sub-domains with local time refinement, is strictly mass conservative. In addition, the method employs space-time fine grid cells only at the moving saturation fronts. In order to ensure local mass conservation at all levels, finite-volume restriction operators and unity prolongation operators are developed. Several numerical experiments have been performed to analyze the efficiency and accuracy of the proposed ADM-LTS method for both homogeneous and heterogeneous permeability fields on two and three dimensional domains. The results show that the method provides accurate solutions, at the same time it maintains the computational efficiency. The ADM-LTS implementation is publicly available at https://gitlab.com/darsim2simulator.

In this work we present the mathematical models for single-phase flow in fractured porous media. An overview of the most common approaches is considered, which includes continuous fracture models and discrete fracture models. For the latter, we discuss strategies that are developed in literature for its numerical solution mainly related to the geometrical relation between the fractures and porous media grids.