Development and analysis of a novel optimization approach for the simulation of the flow in large scale discrete fracture networks with non-conforming finite elements / Sviluppo ed analisi di un nuovo approccio per la simulazione del flusso in network discreti di fratture su larga scala basato su un metodo di ottimizzazione ed elementi finiti su griglie non conformi

The present Thesis reports the description of a new numerical model for the definition of the hydraulic head distribution in Discrete Fracture Networks (DFNs). The solution to the DFN problem is obtained through a PDE constrained minimization approach. The problem on the whole DFN can be split in many small sub-problems on the fractures that can be solved independently from each other, and resorting to the minimization of a cost functional to enforce the compatibility conditions at fracture intersections. In such a way the complexity of the initial problem can be handled more efficiently in parallel computers in an easy and straightforward way, and the meshing process can be performed independently on each fracture and is therefore fast and reliable. Different discretization strategies are investigated to improve the representation of the solution on non-conformng meshes with respect to standard finite elements: the eXtended Finite Elements or th Virtual Finite Elements. Within the proposed approach a mixing of these discretization strategies is possible, improving fexibility in dealing with complex DFN configurations. A large set of numerical results are reported to highlight effectiveness and performances of the method

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

A globally conforming method for solving flow in discrete fracture networks using the Virtual Element Method

A new approach for solving flow in Discrete Fracture Networks (DFN) is developed in this work by means of the Virtual Element Method. Taking advantage of the features of the VEM, we obtain global conformity of all fracture meshes while preserving a fracture-independent meshing process. This new approach is based on a generalization of globally conforming Finite Elements for polygonal meshes that avoids complications arising from the meshing process. The approach is robust enough to treat many DFNs with a large number of fractures with arbitrary positions and orientations, as shown by the simulations. Higher order Virtual Element spaces are also included in the implementation with the corresponding convergence results and accuracy aspects

Efficient combustion parameter prediction and performance optimization for a diesel engine with a low throughput combustion model

In this work, an efficient implementation of a zero-dimensional model is described for the estimation of key engine parameters for combustion control in compression-ignition engines. The direct problems of the estimation of the angle of 50% of fuel mass fraction burnt (MFB50) and of the mean effective pressure (IMEP) are addressed as well as the inverse problems of determining optimal start of injection (SOI) timing for target values of MFB50 and IMEP. The main focus is on the computational cost of the algorithms proposed, designed in order to keep the number of operations as low as possible without compromising the applicability of the methods to different engine configurations and operation points. Execution time of the order of few milliseconds are achieved for parameters prediction and of the order of one tenth of a second for the optimization problems, such that an implementation in engine ECU for model-based control purposes can be envisaged

On simulations of discrete fracture network flows with an optimization-based extended finite element method

Following the approach introduced in [Berrone,Pieraccini,Scialò,2013], we consider the formulation of the problem of fluid flow in a system of fractures as a PDE constrained optimization problem, with discretization performed using suitable extended finite elements; the method allows independent meshes on each fracture, thus completely circumventing meshing problems usually related to the DFN approach. The application of the method to discrete fracture networks of medium complexity is fully analyzed here, accounting for several issues related to viable and reliable implementations of the method in complex problems

Role of mitochondrial reverse electron transport in ROS signaling: Potential roles in health and disease

Reactive Oxygen Species (ROS) can cause oxidative damage and have been proposed to be the main cause of aging and age-related diseases including cancer, diabetes and Parkinson's disease. Accordingly, mitochondria from old individuals have higher levels of ROS. However, ROS also participate in cellular signaling, are instrumental for several physiological processes and boosting ROS levels in model organisms extends lifespan. The current consensus is that low levels of ROS are beneficial, facilitating adaptation to stress via signaling, whereas high levels of ROS are deleterious because they trigger oxidative stress. Based on this model the amount of ROS should determine the physiological effect. However, recent data suggests that the site at which ROS are generated is also instrumental in determining effects on cellular homeostasis. The best example of site-specific ROS signaling is reverse electron transport (RET). RET is produced when electrons from ubiquinol are transferred back to respiratory complex I, reducing NAD+ to NADH. This process generates a significant amount of ROS. RET has been shown to be instrumental for the activation of macrophages in response to bacterial infection, re-organization of the electron transport chain in response to changes in energy supply and adaptation of the carotid body to changes in oxygen levels. In Drosophila melanogaster, stimulating RET extends lifespan. Here, we review what is known about RET, as an example of site-specific ROS signaling, and its implications for the field of redox biology