A PDE-constrained optimization formulation for discrete fracture network flows

We investigate a new numerical approach for the computation of the 3D flow in a discrete fracture network that does not require a conforming discretization of partial differential equations on complex 3D systems of planar fractures. The discretization within each fracture is performed independently of the discretization of the other fractures and of their intersections. Independent meshing process within each fracture is a very important issue for practical large scale simulations making easier mesh generation. Some numerical simulations are given to show the viability of the method. The resulting approach can be naturally parallelized for dealing with systems with a huge number of fractures

Flow simulations in porous media with immersed intersecting fractures

A novel approach for fully 3D flow simulations in porous media with immersed networks of fractures is presented. The method is based on the discrete fracture and matrix model, in which fractures are represented as two-dimensional objects in a three-dimensional porous matrix. The problem, written in primal formulation on both the fractures and the porous matrix, is solved resorting to the constrained minimization of a properly designed cost functional that expresses the matching conditions at fracture-fracture and fracture-matrix interfaces. The method, originally conceived for intricate fracture networks in impervious rock matrices, is here extended to fractures in a porous permeable rock matrix. The purpose of the optimization approach is to allow for an easy meshing process, independent of the geometrical complexity of the domain, and for a robust and efficient resolution tool, relying on a strong parallelism. The present work is devoted to the presentation of the new method and of its applicability to flow simulations in poro-fractured domains

Uncertainty quantification in Discrete Fracture Network models: stochastic fracture transmissivity

We consider flows in fractured media, described by Discrete Fracture Network (DFN) models. We perform an Uncertainty Quantification analysis, assuming the fractures' transmissivity coefficients to be random variables. Two probability distributions (log-uniform and log-normal) are used within different laws that express the coefficients in terms of a family of independent stochastic variables; truncated Karhunen-Loève expansions provide instances of such laws. The approximate computation of quantities of interest, such as mean value and variance for outgoing fluxes, is based on a stochastic collocation approach that uses suitable sparse grids in the range of the stochastic variables (whose number defines the stochastic dimension of the problem). This produces a non-intrusive computational method, in which the DFN flow solver is applied as a black-box. A very fast error decay, related to the analytical dependence of the observed quantities upon the stochastic variables, is obtained in the low dimensional cases using isotropic sparse grids; comparisons with Monte Carlo results show a clear gain in efficiency for the proposed method. For increasing dimensions attained via successive truncations of Karhunen-Loève expansions, results are still good although the rates of convergence are progressively reduced. Resorting to suitably tuned anisotropic grids is an effective way to contrast such curse of dimensionality: in the explored range of dimensions, the resulting convergence histories are nearly independent of the dimension

Numerical investigation on a block preconditioning strategy to improve the computational efficiency of DFN models

[EN] The simulation of underground flow across intricate fracture networks can be addressed by means of discrete fracture network models. The combination of such models with an optimization formulation allows for the use of nonconforming and independent meshes for each fracture. The arising algebraic problem produces a symmetric saddle-point matrix with a rank-deficient leading block. In our work, we investigate the properties of the system to design a block preconditioning strategy to accelerate the iterative solution of the linearized algebraic problem. The matrix is first permuted and then projected in the symmetric positive-definite Schur-complement space. The proposed strategy is tested in applications of increasing size, in order to investigate its capabilities.Gazzola, L.; Ferronato, M.; Berrone, S.; Pieraccini, S.; Scialò, S. (2022). Numerical investigation on a block preconditioning strategy to improve the computational efficiency of DFN models. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. 346-354. https://doi.org/10.4995/YIC2021.2021.12234OCS34635

On the Fundamental Periods of Vibration of Flat-Bottom Ground-Supported Circular Silos containing Gran-like Material

Despite the significant amount of research effort devoted to understanding the structural behavior of grain-silos, each year a large number of silos still fails due to bad design, poor construction, with a frequency much larger than other civil structures. In particular, silos frequently fails during large earthquakes, as occurred during the 1999 Chi-Chi, Taiwan earthquake when almost all the silos located in Taichung Port, 70 km far from the epicenter, collapsed. The EQE report stated that "the seismic design of practice that is used for the design and construction of such facilities clearly requires a major revision". The fact indicates that actual design procedures have limits and therefore significant advancements in the knowledge of the structural behavior of silo structures are still necessary. The present work presents an analytical formulation for the assessment of the natural periods of grain silos. The predictions of the novel formulation are compared with experimental findings and numerical simulations

Coupling traffic models on networks and urban dispersion models for simulating sustainable mobility strategies

AbstractThe aim of the present paper is to investigate the viability of macroscopic traffic models for modeling and testing different traffic scenarios, in order to define the impact on air quality of different strategies for the reduction of traffic emissions. To this aim, we complement a well assessed traffic model on networks (Garavello and Piccoli (2006) [1]) with a strategy for estimating data needed from the model and we couple it with the urban dispersion model Sirane (Soulhac (2000) [2])

Onboard Data Reduction for Multispectral and Hyperspectral Images via Cloud Screening

In this paper we propose a lossless and lossy onboard compression algorithm for multispectral and hyperspectral images, based on the recent CCSDS-123.0-B-2 standard, which takes advantage of cloud screening in order to perform data volume reduction, by avoiding to transmit pixels that are covered by clouds. In particular, we develop methods addressing two problems: i) how to signal the cloud mask in the compressed file, and ii) how to handle cloudy pixels in order to maximize the amount of compression. Experimental results on a set of LANDSAT 8 ETM+ and AVIRIS images show a significant data volume reduction with respect to the plain use of the CCSDS-123.0-B-2 standard

Machine learning for flux regression in discrete fracture networks

AbstractIn several applications concerning underground flow simulations in fractured media, the fractured rock matrix is modeled by means of the Discrete Fracture Network (DFN) model. The fractures are typically described through stochastic parameters sampled from known distributions. In this framework, it is worth considering the application of suitable complexity reduction techniques, also in view of possible uncertainty quantification analyses or other applications requiring a fast approximation of the flow through the network. Herein, we propose the application of Neural Networks to flux regression problems in a DFN characterized by stochastic trasmissivities as an approach to predict fluxes

Predicting flux in Discrete Fracture Networks via Graph Informed Neural Networks

Discrete Fracture Network (DFN) flow simulations are commonly used to determine the outflow in fractured media for critical applications. Here, we extend the formulation of spatial graph neural networks with a new architecture, called Graph-Informed Neural Network (GINN), to speed up the Uncertainty Quantification analyses for DFNs. We show that the GINN model allows better Monte Carlo estimates of the mean and standard deviation of the outflow of a test case DFN