Dissertations / Theses on the topic 'Numerica Modeling'

The main objective of this thesis is to provide a comprehensive numerical tool for the three-dimensional simulation of sedimentary basins. We have used a volume averaging technique to obtain a couple of basin-scale mathematical models. We have used some innovative numerical techniques to deal with such models. A multi-fluid implicit tracking technique is developed and integrated with a Stokes solver that is robust with respect to the variations of the coefficients. The movement of the basin boundaries and the evolution of the faults are treated with an Ale and a Finite Volume scheme respectively. Also some mesh refinement methods are used to guarantee a sufficient accuracy. The numerical experiments show a good qualitative agreement with the measured geometry of the sedimentary layers. (Pubblicata - vedi http://hdl.handle.net/2434/148441)

2013 - 2014
The subject of this thesis is the analysis and development of new numerical methods for Ordinary Di erential Equations (ODEs). This studies are motivated by the fundamental role that ODEs play in applied mathematics and applied sciences in general. In particular, as is well known, ODEs are successfully used to describe phenomena evolving in time, but it is often very di cult or even impossible to nd a solution in closed form, since a general formula for the exact solution has never been found, apart from special cases. The most important cases in the applications are systems of ODEs, whose exact solution is even harder to nd; then the role played by numerical integrators for ODEs is fundamental to many applied scientists. It is probably impossible to count all the scienti c papers that made use of numerical integrators during the last century and this is enough to recognize the importance of them in the progress of modern science. Moreover, in modern research, models keep getting more complicated, in order to catch more and more peculiarities of the physical systems they describe, thus it is crucial to keep improving numerical integrator's e ciency and accuracy. The rst, simpler and most famous numerical integrator was introduced by Euler in 1768 and it is nowadays still used very often in many situations, especially in educational settings because of its immediacy, but also in the practical integration of simple and well-behaved systems of ODEs. Since that time, many mathematicians and applied scientists devoted their time to the research of new and more e cient methods (in terms of accuracy and computational cost). The development of numerical integrators followed both the scienti c interests and the technological progress of the ages during whom they were developed. In XIX century, when most of the calculations were executed by hand or at most with mechanical calculators, Adams and Bashfort introduced the rst linear multistep methods (1855) and the rst Runge- Kutta methods appeared (1895-1905) due to the early works of Carl Runge and Martin Kutta. Both multistep and Runge-Kutta methods generated an incredible amount of research and of great results, providing a great understanding of them and making them very reliable in the numerical integration of a large number of practical problems. It was only with the advent of the rst electronic computers that the computational cost started to be a less crucial problem and the research e orts started to move towards the development of problem-oriented methods. It is probably possible to say that the rst class of problems that needed an ad-hoc numerical treatment was that of sti problems. These problems require highly stable numerical integrators (see Section ??) or, in the worst cases, a reformulation of the problem itself. Crucial contributions to the theory of numerical integrators for ODEs were given in the XX century by J.C. Butcher, who developed a theory of order for Runge-Kutta methods based on rooted trees and introduced the family of General Linear Methods together with K. Burrage, that uni ed all the known families of methods for rst order ODEs under a single formulation. General Linear Methods are multistagemultivalue methods that combine the characteristics of Runge-Kutta and Linear Multistep integrators... [edited by Author]
XIII n.s.

This thesis has been carried out at the Department of Mathematics of the University of Bologna and at the Company HyperLean s.r.l. spin-off of the University Polytechnic of Marche, as part of a collaborative project on "Theoretical and numerical aspects of a hybrid geometric modeling system". The key observation that motivates the interest in this topic is that in different application contexts you have the need to create virtual solid models that integrate real data acquired by 3D scanning, represented by polygonal meshes, with synthetic models, designed by parametric/analytical multi-patches. The research topic covered the study of theoretical and numerical aspects of solid modeling and the development of suitable solutions as part of a "hybrid geometric solid modeling system". In particular, the involvement as regards the professional side of the project covered the development of algorithms for the optimization of the 3D geometry of solid objects and boolean operations between polygonal meshes to improve the LeanCost software (HyperLean's proprietary software). Concerning the academic side, we investigated many aspects of solid modeling, focusing on the B-Rep models and introducing the new paradigm "Extended B-Rep" which is able to integrate "mesh-faces" as part of a B-rep model. To manage the quality of the built model we studied a notion of continuity and join between parametric and discrete representations and we proposed a set of methods that guarantee that the models can be manipulated while maintaining predetermined continuity constraints among the constituent parts. We generalized the most important tools of solid modeling to the Extended B-Reps and proposed solutions to extend the geometric kernels of standard solid modeling systems tobe able to deal with Extended B-rep models. The new geometric solid modeling kernel has been realized in a software supported by the OpenCascade library.

Scopo del presente lavoro è proporre un approccio inedito per i modelli di sistemi complessi, sia in caso deterministico che stocastico, con particolare attenzione a metodi numerici, metodologie di controllo e di quantificazione dell’incertezza. Nel Capitolo 1 introduciamo un controllo di tipo Boltzmann per dinamiche di consenso. Tale metodo è basato su equazioni microscopiche a sulla tecnica del model predictive control (MPC) per il controllo instantaneo. Nel Capitolo 2 applichiamo un approccio di tipo MPC nel contesto di reti complesse, dove il controllo agisce sui nodi/agenti influenzando la dinamica dell’intera rete. Osserviamo come l’introduzione di un appropriato termine di selezione, dipendente dal grado di connessione di ogni nodo, riesca a portare l’opinione del sistema di agenti verso il consenso. Il Capitolo 3 riguarda la derivazione di limiti di performace per il controllo MPC nel caso di equazioni di campo medio a orizzonte di controllo variabile. Abbiamo qui dimostrato l’esistenza di tali limiti sulla differenza nel funzionale di costo MPC e di dinamiche con controllo ottimo. Nel Capitolo 4 abbiamo sviluppato schemi numerici per la conservazione delle proprietà strutturali di equazioni di campo medio come: non-negatività, dissipazione dell’entropia e stati di equilibrio. I metodi sono accurati al second’ordine, non richiedono alcuna restrizione di discretizzazione e catturano lo stato stazionario con accuratezza arbitraria. Tali proprietà sono essenziali per una descrizione fisicamente corretta del problema. Abbiamo proposto qui alcune applicazioni a equazioni di tipo Fokker-Planck non-lineari che emergono in modelli di comportamento collettivo tipici delle scienze socio-economiche e della vita. Nel Capitolo 5 gli schemi del capitolo precedente sono applicate a un modello multivariato per dinamiche di opinione su reti complesse, dove le interazioni dipendono dall’opinione stessa e dal numero di connessioni di ogni agente. La generazione di network a partire da un master equation è stata trattata analiticamente dimostrando l’emergenza di distribuzioni stazionarie scale-free o di grafi uniformi. Inoltre, si osserva come la presenza di una porzione di nodi altamente connessi nel grafo forzi la dinamica verso l’opinione di tali agenti. Il Capitolo 6 è dedicato alla costruzione di un modello multivariato per le scienze decisionali. In particolare, introduciamo modelli di tipo cinetico per l’influenza della competenza nell’evoluzione di decisioni in sistemi multi-agente. Il meccanismo di scambio include la tendenza degli agenti a comportarsi come se fossero capaci, o incapaci, al pari del loro partner: fenomeno chiamato equality-bias. Il modello è ispirato da misurazioni empiriche ed è in grado di riprodurre i risultati sperimentali. L’azione di quantità stocastiche sulla dinamica è oggetto del Capitolo 7. Qui consideriamo interazioni soggette a incertezza per il modello di Cucker-Smale utilizzando tecniche di caos polinomiale. Osserviamo come la presenza di code negative nella distribuzione del parametro casuale porti alla divergenza in tempo finito del valore atteso delle velocità del sistema anche in regimi di flocking incondizionato. Un controllo selettivo MPC è poi introdotto per stabilizzare la dinamica e guidare le velocità attese verso una quantità desiderata anche in regimi di divergenza. Il Capitolo 8 è parte di un lavoro in corso di svolgimento. Abbiamo derivato equazioni di tipo campo medio dal modello microscopico di Cucker-Smale con stocasticità. Proponiamo inoltre un nuovo schema numerico che conserva le proprietà strutturali, basato sia su tecniche Monte Carlo che di tipo Galerkin-gPC stocastiche. Test numerici mostrano come tale schema mantenga l’accuratezza spettrale per le quantità statistiche come media e varianza.
The aim of the present manuscript is to investigate a novel perspective in the modeling and control of complex system both in the deterministic and stochastic case, with particular attention to numerical methods, control methodologies and uncertainty quantification. In Chapter 1 we construct a Boltzmann--type control of a consensus dynamics. Based on a microscopic model we design a Boltzmann-type optimal control thanks to the model predictive control (MPC) approach in the case of an instantaneous control. In Chapter 2 we apply the MPC control approach in the context of complex networks where a control acts over a minimum set of nodes/agents influencing the dynamics of the whole network. We observed how the introduction of a suitable selective control depending on the connection degree of each node is capable of driving the overall opinion towards consensus. Chapter 3 regards the derivation of performance bounds for mean--field MPC control with varying horizon. Here we have established a computable and provable bound on the difference in the cost functional for MPC-controlled and optimally controlled dynamics in the case of a large number of agents. In Chapter 4 we developed numerical schemes that conserve structural property of mean--field equations: non--negativity of the solution, entropy dissipation and large time behavior. The methods here developed are second order accurate, they do not require any restriction on the mesh size and are capable to capture the asymptotic steady states with arbitrary accuracy. These properties are essential for a correct description of the underlying physical problem. Applications of the schemes to several nonlinear Fokker-Planck equations describing emerging collective behavior in socio-economic and life sciences are presented. We further applied in Chapter 5 the developed numerical techniques to a multivariate non--local model for opinion dynamics over complex network, where interactions depend on the opinion itself and on the discrete number of connections. It has been proven that for different choices of weights functions the introduced generator of the network may produce stationary scale-free degree distributions as well as uniform random graphs. Further, we observed that the presence of a small portion of highly connected agents may drive the overall dynamics towards their position. In Chapter 6 we further investigate multivariate models with a direct application to decision science. In particular, we introduce and discuss multivariate kinetic models describing the influence of competence in the evolution of decisions in a multiagent system. The exchange mechanism includes the role of the agents’ tendency to behave in the same way as if they were as good, or as bad, as their partner: the so-called equality bias. The presented modeling is inspired by real experiments and reproduces the empirical findings. The role of stochastic quantities in the dynamics is investigated in Chapter 7. Here we analyze the effect of the uncertainty in the interaction parameter in a second-order alignment model of the Cucker-Smale type using a generalized polynomial chaos approach. We observed that the presence of negative tails in the distribution of the random inputs lead to the divergence of the expected velocities of the system of agents, even in the regimes of unconditional flocking. We formalized a selective MPC approach to stabilize the dynamics and to steer the expected velocities toward the desired one, even in the divergence regimes. Chapter 8 is part of an ongoing work. Here we derived mean-field equations from microscopic Cucker-Smale type model dependent on random input in several cases. Further, a novel structure preserving numerical technique based on both Monte Carlo and stochastic Galerkin-gPC methods is addressed. Numerical experiments show that the scheme maintain the spectral accuracy for the statistical quantities of interest, like mean and variance.

In this work we focus on two main topics "Geometric Surface Processing" and "Virtual Modeling". The inspiration and coordination for most of the research work contained in the thesis has been driven by the project New Interactive and Innovative Technologies for CAD (NIIT4CAD), funded by the European Eurostars Programme. NIIT4CAD has the ambitious aim of overcoming the limitations of the traditional approach to surface modeling of current 3D CAD systems by introducing new methodologies and technologies based on subdivision surfaces in a new virtual modeling framework. These innovations will allow designers and engineers to transform quickly and intuitively an idea of shape in a high-quality geometrical model suited for engineering and manufacturing purposes. One of the objective of the thesis is indeed the reconstruction and modeling of surfaces, representing arbitrary topology objects, starting from 3D irregular curve networks acquired through an ad-hoc smart-pen device. The thesis is organized in two main parts: "Geometric Surface Processing" and "Virtual Modeling". During the development of the geometric pipeline in our Virtual Modeling system, we faced many challenges that captured our interest and opened new areas of research and experimentation. In the first part, we present these theories and some applications to Geometric Surface Processing. This allowed us to better formalize and give a broader understanding on some of the techniques used in our latest advancements on virtual modeling and surface reconstruction. The research on both topics led to important results that have been published and presented in articles and conferences of international relevance.
In questa tesi sono trattati due argomenti principali "Geometric Surface Processing" e "Virtual Modeling". L'ispirazione e la coordinazione di gran parte del lavoro di ricerca contenuto nella tesi e' dovuta al progetto New Interactive and Innovative Technologies for CAD (NIIT4CAD), finanziato dall'European Eurostars Programme. NIIT4CAD ha l'ambizioso obiettivo di superare le limitazioni degli approcci tradizionali alla modellazione di superfici dei moderni sistemi di progettazione assistita al calcolatore, introducendo nuove metodologie e tecnologie basate su superfici di suddivisione in un nuovo framework virtuale di modellazione. Tali innovazioni permetteranno progettisti ed ingegneri a trasformare velocemente ed intuitivamente l'idea di una forma in un modello geometrico ad alta qualita' adatto per scopi ingegneristici e di produzione. Uno degli obiettivi della tesi e' proprio la ricostruzione e modellazione di superfici, rappresentanti oggetti a topologia arbitraria, partendo da curve 3D irregolari acquisite tramite un dispositivo smart-pen sviluppato ad-hoc. La tesi e' organizzata in due parti: "Geometric Surface Processing" e "Virtual Modeling". Durante lo sviluppo della pipeline geometrica del nostro sistema di modellazione virtuale, abbiamo affrontato diverse problematiche che hanno attratto il nostro interesse ed aperto nuove aree di ricerca e sperimentazione. Nella prima parte, presentiamo tali teorie ed alcune applicazioni nell'ambito di Geometric Surface Processing. Questo ci permette di formalizzare meglio e dare una visione piu' ampia ad alcune delle tecniche usate nelle ultime versioni del nostro sistema ricostruzione di superfici e modellazione virtuale. Il lavoro di ricerca per entrambi gli argomenti ha portato al raggiungimento di importanti risultati che sono stati pubblicati e presentati in articoli e conferenze di rilevanza internazionale.

The present Thesis reports an articulated research work that covers several aspects connected with the modeling of subsurface hydrology of organic soils in connection to the main hazards induced by land subsidence of peatlands and the conservation and wise use of wetlands in the Venetian area. The dynamics of peatland surface deformation both at long and short time scale is studied and a novel two-step modeling approach is proposed to separate the reversible and irreversible components of the land surface displacement. An empirical relationship is calibrated on the estimated irreversible component of the ground displacements recorded in a 4-year long experimental study in a field site located in the Zennare Basin,Italy. The expected evolution of the Venetian peatland over the present century is then investigated. The study of the hydrology of organic soils is then focused on the hysteretical behavior of the moisture retention curve measured in the peat soils of the Zennare Basin. The results of the application of a modeling approach that couples an hysteresis model with a relationship that links the soil matrix porosity dynamic to water saturation bring out the importance of including the swelling/shrinkage phenomenon in the description and prediction of water flow into organic soils. In the last part of the Thesis the focus is shifted to the hydrological dynamics of salt marshes, delicate intertidal zones characterized by a strong hydrological connection between the atmosphere and the subsurface mainly in terms of air fluxes. A two-phase flow model is developed in order to investigate the effects of air flow in the wetlands dynamics. A pressure-based formulation is chosen to allow for natural treatment of the complex and nonlinear boundary conditions to be imposed at the soil-atmosphere interface to take into account the interplay between evapo-transpiration during emersion periods and tidal fluctuations during soil submersion. The results of the application of the model to some test cases aimed at verifying the effect of the inclusion of the air dynamics in the simulation of the water flow in the vadose zone are presented.
La presente Tesi riferisce di un articolato lavoro di ricerca che ha coperto diversi aspetti connessi con la modellazione dei processi idrologici sotterranei nei suoli organici in relazione ai principali rischi indotti dalla subsidenza delle aree torbose e alla conservazione e all’uso consapevole delle aree umide nel comprensorio lagunare veneziano. Sono state analizzate le dinamiche delle deformazioni dei terreni torbosi sia su lunga che su breve scala temporale e si propone un approccio modellistico in due step finalizzato alla separazione dei contributi reversibile e irreversibile della dello spostamento della superficie. Una relazione empirica per la stima degli spostamenti indotti dalla bio-ossidazione della matrice organica è stata quindi calibrata a partire dalla stimata determinata porzione irreversibile degli spostamenti registrati nell’ambito di una campagna sperimentale di 4 anni nel Bacino Zennare, Italia, Si è infine investigato l’evoluzione attesa delle zone torbose nell’area di Venezia nel secolo in corso. Lo studio dell’idrologia dei suoli organici è proseguito con l’analisi del comportamento isteretico della curva di ritenzione capillare misurata nei suoli del Bacino Zennare. I risultati dell’applicazione di un modello che accoppia un modello di isteresi con una relazione empirica che lega la variazione di porosità della matrice solida al grado di saturazione in acqua hanno messo in luce l’importanza delle deformazioni reversibili nella definizione delle curve di risalita capillare nei suoli organici. L’ultima parte è focalizzata sulle dinamiche idrologiche delle zone barenali, delicate aree intertidali caratterizzate da un forte feedback tra l’atmosfera e il sottosuolo, principalmente in termini di flussi d’aria. Si è sviluppato un modello bifase al fine di approfondire gli effetti del flusso d’aria nelle dinamiche sotterranee. È stato adottata una formulazione alle pressioni che consente il trattamento naturale delle complesse condizioni al contorno non lineari sull’interfaccio suolo/atmosfera al fine di includere gli effetti di evapotraspirazione durante i periodi di emersione e le fluttuazioni mareali in quelle di sommersione della superficie barenale. I risultati dell’applicazione del modello ad alcuni casi test finalizzati al verificare l’importanza di considerare il flusso d’aria nella descrizione del flusso idrico nella zona insatura sono infine proposti.

Orientador: Kamal Abdel Radi Ismail
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica
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Resumo: No presente trabalho estuda-se o fenômeno de mudança de fase de um PCM em placas paralelas que compõe um banco de gelo. Parâmetros importantes como o espaçamento entre as placas, a temperatura da placa, a temperatura do fluido de trabalho e a vazão, são considerados numa faixa variável. Desenvolveu-se um modelo numérico para simular o processo de solidificação com o objetivo de determinar a posição da frente de solidificação e a distribuição de temperaturas na fase sólida, além de avaliar a influência dos parâmetros considerados. As equações governantes, considerando transferência de calor unidimensional, foram discretizadas utilizando o método de diferenças finitas e o esquema modificado de espaço de tempo variável (MVTS) para a resolução da malha computacional. Considera-se a temperatura inicial do PCM igual à da solidificação e com propriedades constantes. A modelagem da solidificação foi feita para os casos de temperatura da superfície da placa constante e variável. Para validar o modelo numérico, foi construída uma bancada experimental onde foram feitos diversos testes com os parâmetros mencionados anteriormente. Os resultados numéricos obtidos foram analisados e comparados. Estes mostraram concordância satisfatória com os resultados experimentais para a modelagem realizada com temperatura da placa variável. Os resultados deste trabalho podem ser utilizados para o projeto de armazenadores de calor latente em geometrias planas
Abstract: In the present work, the phase change phenomenon of a PCM in parallel plates that compose an ice bank is studied. Important parameters such as the gap between the plates, the plate temperature, the temperature and flow of the secondary fluid are considered. A numerical model was developed to simulate the solidification process with the aim of determine the position of the solidification front and the temperatures distribution at the solid phase, moreover, to evaluate the influence of the considered parameters. The governing equations, considering one-dimensional heat transfer, had been discretized using the finite differences method and the modified variable time steps scheme (MVTS) to resolve the computational mesh. The PCM was considered initially at solidification temperature and with constant thermal properties. The solidification model was made for the cases of constant plate temperature and variable temperature. To validate the numerical model, an experimental device was constructed where many tests were carried through with the mentioned parameters. The numerical results were analyzed and compared. These ones show satisfactory agreement with the experimental results for the modeling carried through with variable plate temperature. The results of this work can be used for the project of latent heat storage systems with plain geometries
Mestrado
Engenharia Termica e Fluidos
Mestre em Engenharia Mecânica

Understanding the complex feedback mechanisms regulating the land-atmosphere system has become a scientific imperative, as human induced changes may impact the stability of the Biosphere, both locally and globally. The present thesis work aims at improving current understanding and forecasting capabilities of the Soil-Plant-Atmosphere (SPA) continuum. To this purpose a numerical model of soil moisture dynamics is coupled with plant transpiration and photosynthesis. Soil moisture dynamics is modeled by the 3-D Richards equation and plant uptake is described by an Ohm's law type model accounting for water potential gradients and root, xylem and stomatal conductances. The transpiration flux from soil to the atmosphere is driven by the leaf water potential which is controlled by both local soil moisture conditions and atmospheric forcing. The hydraulic model is linked to the atmosphere by the calculation of the stomatal conductance which is optimized for maximum carbon gain considering Fickian mass transfer of CO2 and H2O through stomata and a biochemical model of photosynthesis. The model is used to investigate competition for water among multiple tree rooting systems in a Loblolly pine (Pinus Taeda) plantation and then coupled with a crop growth module to investigate farmland productivity at the field scale. In order to provide a fully-coupled description of the SPA system, the soil-plant model is then coupled with a slab representation of the Atmospheric Boundary Layer (ABL) and used to investigate the role of water table fluctuations and free atmospheric state on convective rainfall initiation. Model results compared well with measurements of soil moisture, sap flow in the plant xylem as well as energy fluxes above the canopy and convective rainfall initiation time. In order to deal with the high degree of uncertainty related to both measurement and model errors the applicability of a data assimilation algorithm has also been explored to incorporate physical measurements into the transient hydrological model. Given the recent development of indirect geophysical surveys to monitor soil-plant interactions in the vadose zone, we tested an innovative iterative particle filter approach for coupled hydro-geophysical inversion of Electrical Resistivity Tomography (ERT) data. Model results demonstrate the ability of the method to improve model prediction and estimate multiple model parameters and this work lays the foundation for application of the methodology to soil-plant-atmosphere modeling.
La comprensione dei molteplici meccanismi che regolano l'interazione tra suolo, vegetazione e atmosfera è oggi divenuta un imperativo nel campo della ricerca scientifica, poichè numerose sono le conseguenze che la presenza antropica puo avere sulla stabilità della Biosfera, a livello sia globale che locale. Questo lavoro di tesi si propone l'obiettivo di sviluppare nuovi strumenti modellistici che consentano una più accurata comprensione e descrizione del sistema suolo-vegetazione-atmosfera. A tal fine, un modello di trapirazione e fotosintesi della vegetazione è stato introdotto in un codice numerico per la descrizione del flusso in mezzi porosi. La dinamica dell'umidita del suolo e descritta dall'equazione tridimensionale di Richards, mentre il trasporto d'acqua attraverso le radici ed all'interno della pianta e definito tramite un modello di resistenze e potenziali idrici basato sulla legge di Ohm. Il flusso traspirativo è regolato dal potenziale fogliare, a sua volta determinato da condizioni locali di umidità del suolo e dalle forzanti atmosferiche. Il modello idraulico di assorbimento radicale è collegato all'atmosfera tramite il calcolo della resistenza stomatica, determinata sulla base di un modello di ottimizzazione dell'apertura degli stomi che massimizza la fotosintesi (descritta per mezzo di un modello biochimico) e minimizza la traspirazione. Tale approccio modellistico è stato impiegato per comprendere i meccanismi di competizione tra diverse piante per l'assorbimento idrico in una piantagione di Pinus Taeda. Il modello è stato inoltre integrato con un modulo di crescita del mais (Zea mays L.) per studiare la produttività agricola alla scala di bacino. Al fine di descrivere in modo completo le interazioni fra vegetazione ed atmosfera, il modello è stato poi accoppiato con la dinamica dello strato limite planetario ed utilizzato per comprendere l'effetto della falda e delle condizioni dell'atmosfera libera sugli eventi di precipitazione dovuti alla formazione di nubi convettive. I risultati modellistici illustrati in questa tesi sono confrontati con osservazioni di contenuto d'acqua nel suolo, misure di flussi xilematici, flussi energetici al di sopra della canopy ed eventi convettivi di precipitazione, dimostrando le ottime capacità predittive del modello sviluppato. Sia le osservazioni che i risultati numerici sono tuttavia caratterizzati da un certo grado di errore. Per ovviare a tale incertezza è stato pertanto studiato un algoritmo di assimilazione dei dati che consente di incorporare le osservazioni fisiche nel modello dinamico idrologico. Dal momento che recenti studi di settore si sono focalizzati sull'utilizzo di metodi geofisici indiretti per la caratterizzazione dei processi di interazione fra suolo e vegetazione, in questo lavoro di tesi è stato sviluppato un metodo particle filter iterativo per l'inversione idro-geofisica accoppiata di dati di tomografia elettrica. I risultati presentati in questa tesi dimostrano l'abilità del metodo proposto di migliorare le previsioni e stimare i parametri del modello e pongono le basi per un nuovo approccio alla simulazione numerica del sistema suolo-vegetazione-atmosfera.

In the first part of this work we want to propose a model able to reproduce correctly the dynamics of a crowd in bounded domains (for example rooms and corridors) and in presence of obstacles, and also to discuss the emergence of some behaviors induced by panic. Starting from the analysis of a microscopic description for a small crowd one can deduce some mesoscopic and macroscopic models when the number of agents increases and the crowd is more comparable to gases and fluids. In the second part we want to propose some multi-temperature models for gas mixtures by means of standard tools of kinetic theory. Some descriptions are proposed also in presence of chemical reactions and of an internal structure for molecules to take non-translational degrees of freedom into account. The resulting models are tested on the classical problem of the steady shock wave and the occurence of smooth solutions and sub-shocks is discussed for varying parameters.

The overall aim of the work described in this thesis is to bring a number of contributions to hydrology and hydrological modeling in the framework of a specific physically-based numerical model for integrated surface subsurface and flow-transport processes, the CATchment-HYdrology Flow-Transport (CATHY_FT) model. These contributions revolve around three main themes: the enhancement of the numerical performance of hydrological models for flow and transport phenomena, the improvement of our current understanding of complex boundary conditions in order to reduce the errors associated with their modeling, and the testing and benchmarking of distributed physically-based models for groundwater flow and transport processes. The work to achieve the general objective is elaborated into four stages. First, the Larson-Niklasson post-processing algorithm is implemented in CATHY_FT to reconstruct mass-conservative velocities from a linear, or P1, Galerkin solution of Richards' equation. This is done to improve the accuracy and mass balance properties of the companion advective transport model (finite volume-based), which rely on accurate velocity fields as input. Through a comparison between the results from the reconstructed velocities and the P1 Galerkin velocities, it is shown that a locally mass-conservative velocity field is necessary to obtain accurate transport results. Second, a detailed and novel analysis of the behavior of seepage face boundaries is performed with the flow model of CATHY_FT. The numerical simulations examine the model's performance under complex conditions such as heterogeneity and coupled surface/subsurface flow. It is shown that the overall numerical solution can be greatly affected by the way seepage face boundaries are handled in hydrological models and that careful considerations are required when using simple approximations, in the presence of heterogeneous slopes, and for seepage faces forming on a portion of the land surface. Third, CATHY_FT is implemented and run at the Landscape Evolution Observatory of the Biosphere 2 facility, Arizona. A detailed modeling analysis is performed of the experimental data collected during an isotope tracer experiment and from an intensively-measured hillslope, including quantity and quality of groundwater discharge and point-scale flow and transport data. This flow and tracer data is used to incrementally explore complex phenomena and associated hypotheses (e.g., heterogeneity, fractionation, and dispersion), progressing from flow to transport and from integrated to point-scale response analysis. This incremental approach highlights the challenges in testing and validating the new generation of integrated hydrological models when considering many types and levels of observation data. Finally, a concluding analysis is performed that relates to all three themes of the thesis, describing some of the features of the CATHY_FT model, discussing key issues associated to its further development, and testing its physical and numerical behavior for both real and synthetic scenarios. This final stage of the thesis addresses the myriad challenges faced in accurately and efficiently resolving the difficult behavior of the advection-dispersion equation for subsurface solute transport, in properly handling the complex boundary conditions for solute interactions across the land surface, and generally in capturing process interactions and feedbacks between flow and transport phenomena in surface and subsurface environments.
Lo scopo di questa tesi e' fornire dei contributi all'idrologia e alla modellazione idrologica nell'ambito di un modello numerico specifico, il modello CATchment HYdrology Flow-Transport (CATHY_FT), utilizzato per simulare processi integrati di superficie e sotterranei e di flusso e trasporto. Questi contributi riguardano tre temi principali: il miglioramento del comportamento numerico di modelli idrologici che simulano fenomeni di flusso e trasporto, l'approfondimento di condizioni al contorno complesse con l'obbiettivo di ridurre gli errori relativi alla loro modellazione e il test e l'analisi comparativa di modelli a base fisica utilizzati per simulare processi di flusso e trasporto sotterranei. Il lavoro per raggiungere l'obbiettivo generale viene diviso in quattro step. Nel primo step l'algoritmo di Larson-Niklasson e' implementato in CATHY_FT per ricostruire velocita' conservatrici della massa a partire da una soluzione lineare (o P1) di Galerkin dell'equazione di Richards, in modo da permettere al modello di trasporto avvettivo (basato sui volumi finiti) di conservare la massa, cosa che dipende strettamente dall'accuratezza del campo di velocita' che questo utilizza. Confrontando i risultati ottenuti con le velocita' derivanti dalla soluzione P1 di Galerkin e quelle ricostruite, viene mostrato che un campo di velocita' localmente conservativo e' necessario per ottenere risultati accurati con il trasporto. Nella seconda fase viene effettuata un'analisi dettagliata del comportamento delle condizioni ai limiti nella zona del fronte di infiltrazione con il modello di flusso di CATHY_FT. Le simulazioni numeriche esaminano il comportamento del modello in condizioni complesse come quelle di eterogeneita' e di flusso di superficie e sotterraneo accoppiato. Viene dimostrato che la soluzione numerica puo' essere fortemente influenzata dal modo in cui la zona di infiltrazione viene trattata nei modelli idrologici e che considerazioni accurate sono sempre necessarie quando si usano approssimazioni, in presenza di versanti eterogenei e per le zone di infiltrazione che si formano nella superficie terrestre. Come terzo step, CATHY_FT viene testato al Landscape Evolution Observatory del Biosphere 2 in Arizona. Viene eseguita un'analisi dettagliata di dati sperimentati raccolti durante un esperimento di tracciante isotopico e da un versante artificiale intensivamente controllato. Le informazioni comprendono la qualita' e la quantita' della portata sotterranea e dati puntuali di flusso e trasporto. Questi dati di flusso e tracciante sono utilizati per esplorare fenomeni complessi e le ipotesi associate (e.g., eterogeneita', frazionamento e dispersione), procedendo dalla risposta di flusso a quella di trasporto e dalla risposta integrata a quella puntuale. Questo approccio incrementale evidenzia le sfide legate alla validazione della nuova generazione di modelli idrologici integrati quando si guarda a diversi tipi e livelli di dati osservati. Infine, viene eseguita un'analisi conclusiva che si lega a tutti e tre i temi della tesi, descrivendo alcune caratteristiche del modello CATHY_FT, discutendo problemi chiave legati al suo sviluppo futuro e testando il suo compertamento fisico e numerico sia per scenari sintetici che reali. Questo step finale della tesi affronta la miriade di sfide legate alla risoluzione accurata ed efficace del comportamento difficile dell'equazione di avezione-dispersione per processi di trasporto di soluto sotterraneo, alla risoluzione appropriata delle condizioni ai limiti complesse per rappresentare le interazioni di soluto attraverso la superficie terrestre e, in generale, alla rappresentazione delle interazioni tra i fenomeni di flusso e trasporto nell'ambiente superficiale e sotterraneo.

This research focuses on small scale laboratory tools to characterize the rheological behavior of the matrix (maximum diameter of sediment analyzed equal to 19 mm) of real debris flows affecting Eastern Italian Alps. The main aim is to define novel, easily reproducible and low-cost procedures that make available to a wider audience, in particular to the end users of numerical models, this kind of information. The research seeks therefore to delineate a connection between the laboratory data and the numerical models because, as mentioned by Calligaris and Zini (2012), the current main objective of debris-flow modeling is to clearly describe the input variables in order to better understand the formation of debris flow fans and to predict, mitigate or control the hazard posed by these phenomena to communities situated into the mountain areas. This research takes into account monophasic numerical models because of their widespread and proven efficiency (Rickenmann et al., 2006; Bisantino et al., 2009; Calligaris and Zini, 2012). Summarizing, the detailed aims of this research are: - Debris-flow behavior investigation through small scale laboratory tools and original and easily reproducible procedures; - Identify methodologies for applying the laboratory data to the numerical modeling and to calibrate the rheological parameters; - Verify the methodologies identified through a performance analysis of numerical simulations of real and well documented debris flows. Initially, the objectives have been pursued through a literature review focused, in particular, on the methodologies for analyzing debris-flow behaviors. In the following laboratory investigation, the results of two different tools are displayed: the vane spindle rheometer Brookfield DVIII Ultra and the tilting plane rheometer of the Institute for Hydrological and Geological Protection of the Italian Research Council (CNR IRPI) (D’Agostino and Cesca, 2009-a; D’Agostino et al., 2010). Moreover, a standard and easily repeatable procedure, based on the two-dimensional simplification suggested by Hungr (1995), is proposed to estimate the mean basal shear stress, which develops during the runout phase. Interesting considerations about flow regime and depositional features have been achieved thanks to the velocity recorded in the tilting plane laboratory test. Considering the definition of procedures to calibrate the rheological parameters, two approaches have been proposed. The first is based on the tilting plane rheometer results while the second uses the relation between magnitude and debris-flow mobility (Rickenmann, 1999; Lorente et al., 2003) and a specifically-shaped index. In the last part of the research work, a performance analysis about two monophasic numerical models is presented. The compared models are FLO-2D (O’Brien et al., 1993) and RAMMS (Rapid Mass MovementS, Christen et al. 2010). The models have been tested in the simulation of some debris flows with heterogeneous characteristics: different rheological behavior, magnitude and topographic situation. The efficiency of the laboratory tests in the calibration of the rheological parameters of the model has been also investigated through this performance analysis. The output of the model has been assessed through two indexes: the first analyzes the positive accuracy (Scheidl e Rickenmann, 2010), whereas the second expresses the model efficiency quantifying the excess deposit simulation.
Il lavoro di ricerca, presentato in questo elaborato di tesi, riguarda lo studio della reologia delle colate detritiche attraverso indagini di laboratorio a piccola scala che permettono la caratterizzazione di miscele di acqua e sedimento che riproducono la fase matriciale e una parte della frazione solida (massimi diametri utilizzati in laboratorio pari a 19 mm) di colate detritiche verificatesi nelle Alpi e Prealpi orientali italiane. L’obiettivo è individuare procedure innovative, facilmente riproducibili e a basso costo per la definizione delle caratteristiche reologiche e fisiche che descrivono la dinamica delle colate detritiche, in modo da rendere disponibile questa tipologia di indagine a un pubblico più vasto e in particolar modo agli utenti dei modelli numerici monofasici. Per quanto riguarda i modelli analizzati nello studio, la scelta è ricaduta nei monofasici poiché sono la tipologia di modelli che, ad ora, è maggiormente diffusa e la cui efficacia è stata comprovata in diversi studi scientifici (Rickenmann et al., 2006; Bisantino et al., 2009; Calligaris e Zini, 2012). Il lavoro di ricerca, oltre al mero studio delle caratteristiche reologiche, vuole dare quindi un contributo alla definizione di procedure per la calibrazione dei parametri di input dei modelli numerici in quanto, come descritto anche da Calligaris e Zini (2012), attualmente l’obiettivo fondamentale nel campo dello studio delle colate detritiche è definire chiaramente le variabili di input dei modelli numerici per meglio comprendere la formazione dei conoidi da colata detritica e per predire, mitigare e controllare il pericolo che questi fenomeni hanno nei confronti delle comunità che vivono in questi territori. Riepilogando, gli obiettivi di questo studio sono: - studiare il comportamento delle colate detritiche a piccola scala con l’utilizzo di diversi strumenti, cercando di identificare nuove procedure per la definizione delle caratteristiche reologiche utili anche a fini modellistici; - determinare l’applicabilità dei risultati ottenuti a piccola scala alla scala reale e in particolare nella modellazione numerica delle colate detritiche, e identificare metodologie per la calibrazione dei parametri di input della modellazione numerica; - valutare i risultati ottenuti attraverso la loro applicazione alla modellazione di eventi reali di colata detritica, anche attraverso l’utilizzo di diversi modelli numerici sui quali poter effettuare un confronto ed un’analisi di performance. Gli obiettivi prefissati sono stati raggiunti inizialmente attraverso un’analisi bibliografica dello stato dell’arte concernente la fisica delle colate detritiche e in particolar modo ai metodi utilizzati per la misura delle grandezze fisiche che ne descrivono il comportamento. Le conoscenze acquisite sono state quindi messe a frutto attraverso un’indagine di laboratorio che ha visto l’utilizzo di due diverse strumentazioni per lo studio delle caratteristiche reologiche della frazione più fina che compone colate detritiche reali verificatesi in territorio alpino. Gli strumenti utilizzati sono un reometro con giranti a vano Brookfield DVIII Ultra e il reometro a piano inclinato presente nei laboratori del C.N.R. di Padova (D’Agostino e Cesca, 2009-a; D’Agostino et al., 2010). Oltre all’applicazione di procedure già riportate in letteratura, nell’ambito delle misure con reometro a piano inclinato è stato messo a punto, partendo dalle considerazioni di Hungr (1995), un metodo innovativo per la definizione degli sforzi tangenziali medi agenti al fondo nella fase di arresto di una colata detritica. Successivi test realizzati su piano inclinato, avvalendosi dell’uso di fotocellule per la misura della velocità del fronte del flusso di detriti all’interno di una canaletta, hanno permesso di effettuare interessanti considerazioni sui regimi di flusso che governano la fase di arresto e deposizione delle colate detritiche. Il secondo obiettivo, relativo alla definizione di metodologie per la calibrazione dei parametri di input della modellazione numerica, è stato perseguito attraverso due approcci diversi che prevedono l’utilizzo o meno dei risultati di laboratorio. La prima procedura proposta si basa su prove reologiche su piano inclinato mentre la seconda utilizza la relazione tra magnitudo dell’evento e mobilità già descritta in letteratura (Rickenmann, 1999; Lorente et al., 2003) e un indice reologico realizzato ad hoc. Nell’ultima fase del lavoro di ricerca si è realizzato un confronto e un’analisi di performance su due modelli bidimensionali monofasici, ampiamente utilizzati nel campo della modellazione delle colate detritiche, FLO-2D (O’Brien et al., 1993) e RAMMS (Rapid Mass MovementS, Christen et al. 2010). In questa fase di lavoro è stata valutata l’attendibilità dei due modelli nella modellazione di colate detritiche dalle caratteristiche diverse per comportamento reologico e volumetria in gioco, e nella modellazione di situazioni topografiche diverse (libertà di divagazione del flusso o presenza di opere di trattenuta importanti). In questa fase è stata inoltre valutata l’applicabilità dei test dinamici su reometro a piano inclinato per la calibrazione dei parametri utilizzati in FLO-2D. La bontà dei risultati delle modellazioni è stata misurata sulla base di un confronto tra l’area del deposito reale e quella simulata dal modello attraverso l’applicazione di due indici. Il primo misura l’accuratezza positiva della simulazione (indice utilizzato da Scheidl e Rickenmann, 2010) mentre il secondo, realizzato ad hoc, misura l’efficienza del modello valutando quanto il flusso modellato vada a coprire aree che nella realtà non sono state interessate dalla colata.

Shallow water models of geophysical flows must be adapted to geometric characteristics in the presence of a general bottom topography with non-negligible slopes and curvatures, such as a mountain landscape. In this thesis we derive an intrinsic shallow water model starting from the Navier-Stokes equations defined on a local reference frame anchored on the bottom surface. The resulting equations are characterized by non-autonomous flux functions and source terms embodying only geometric information. We show that the proposed model is rotational invariant, admits a conserved energy, is well-balanced, and it is formally a second order approximation of the Navier-Stokes equations with respect to a geometry-based order parameter. We then derive numerical discretization schemes compatibles with the intrinsic setting of the formulation, starting from studying a first order upwind Godunov Finite Volume scheme intrinsically defined on the bottom surface. We analyze convergence properties of the resulting scheme both theoretically and numerically. Simulations on several synthetic test cases are used to validate the theoretical results as well as more experimental properties of the solver. The results show the importance of taking into full consideration the bottom geometry even for relatively mild and slowly varying curvatures. The low-order discretization method is subsequently extended to the Discontinuous Galerkin framework. We implement a linear version of the DG scheme defined intrinsically on the surface and we start from the resolution of the scalar transport equation. We test the scheme for convergence and then we move towards the intrinsic shallow water model. Simulations on synthetic test cases are reported and the improvement with respect to the first order finite volume discretization is clearly visible. Finally, we consider a finite element method for advection-diffusion-reaction equations on surfaces. Unlike many previous techniques, this approach is based on the geometrically intrinsic formulation and the resulting finite element method is fully intrinsic to the surface. In the last part of this work, we lay out in detail the formulation and compare it to a well-established finite element scheme for surface PDEs. We then evaluate the method for several steady and transient problems involving both diffusion and advection-dominated regime. The experimental results show the theoretically expected convergence rates and good performance of the established finite element methods.

Curve and surface primitives have an important role in conveying an object shape and their recognition finds significant applications in manufacturing, art, design and medical applications. When 3D models are acquired by scanning real objects, the resulting geometry does not explicitly encode these curves and surfaces, especially in the presence of noise or missing data. Then, the knowledge of the parts that compose a 3D model allows the reconstruction of the model itself. The problem of recognising curves and surfaces and providing a mathematical representation of them can be addressed using the Hough transform technique (HT), which in literature is mainly used to recognise curves in the plane and planes in space. Only in the last few years, it has been explored for the fitting of space curves and extended to different families of surfaces. Such a technique is robust to noise, does not suffer from missing parts and benefits from the flexibility of the template curve or surface. For these reasons, our approach is inspired by a generalisation of the Hough transform defined for algebraic curves. In this thesis, we present the methods we implemented and the results we obtained about the recognition, extraction, and representation of feature parts that compose a 3D model (both meshes and point clouds). Specifically, we first study the recognition of plane curves, simple and compound, expressed both in implicit and parametric form, with a focus on the application of cultural heritage and geometric motifs. Then, we analyse the extension of the method to space curves, concentrating on the improvement of the model through the insertion of the recognised curves directly on its surface. To overcome the limitation of knowing in advance the family of curves to be used with the HT, we introduce a piece-wise curve approximation using specific parametric, low-degree polynomial curves. Finally, we analyse how to recognise simple and complex geometric surface primitives on both pre-segmented and entire point clouds, and we show a comparison with state-of-the-art approaches on two benchmarks specifically created to evaluate existing and our methods.

This thesis focuses on solutions of reactive transport problems in porous media. The principle mechanisms of flow and reactive mass transport in porous media are investigated. Global implicit approach (GIA), where transport and reaction are fully coupled, and sequential noniterative approach (SNIA) are implemented into the software OpenGeoSys (OGS6) to couple chemical reaction and mass transport. The reduction scheme proposed by Kräutle is used in GIA to reduce the number of coupled nonlinear differential equations. The reduction scheme takes linear combinations within mobile species and immobile species and effectively separates the reaction-independent linear differential equations from coupled nonlinear ones (i.e. reducing the number of primary variables in the nonlinear system). A chemical solver is implemented using semi-smooth Newton iteration which employs complementarity condition to solve for equilibrium mineral reactions. The results of three benchmarks are used for code verification. Based on the solutions of these benchmarks, it is shown that GIA with the reduction scheme is faster (ca. 6.7 times) than SNIA in simulating homogeneous equilibrium reactions and (ca. 24 times) in simulating kinetic reaction. In simulating heterogeneous equilibrium mineral reactions, SNIA outperforms GIA with the reduction scheme by 4.7 times
Diese Arbeit konzentriert sich auf die numerische Berechnung reaktiver Transportprobleme in porösen Medien. Es werden prinzipielle Mechanismen von Fluidströmung und reaktive Stofftransport in porösen Medien untersucht. Um chemische Reaktionen und Stofftransport zu koppeln, wurden die Ansätze Global Implicit Approach (GIA) sowie Sequential Non-Iterative Approach (SNIA) in die Software OpenGeoSys (OGS6) implementiert. Das von Kräutle vorgeschlagene Reduzierungsschema wird in GIA verwendet, um die Anzahl der gekoppelten nichtlinearen Differentialgleichungen zu reduzieren. Das Reduzierungsschema verwendet Linearkombinationen von mobilen und immobile Spezies und trennt die reaktionsunabhngigen linearen Differentialgleichungen von den gekoppelten nichtlinearen Gleichungen (dh Verringerung der Anzahl der Primärvariablen des nicht-linearen Gleichungssystems). Um die Gleichgewichtsreaktionen der Mineralien zu berechnen, wurde ein chemischer Gleichungslaser auf Basis von ”semi-smooth Newton-Iterations” implementiert. Ergebnisse von drei Benchmarks wurden zur Code-Verifikation verwendet. Diese Ergebnisse zeigen, dass die Simulation homogener Equilibriumreaktionen mit GIA 6,7 mal schneller und bei kinetischen Reaktionen 24 mal schneller als SNIA sind. Bei Simulationen heterogener Equilibriumreaktionen ist SNIA 4,7 mal schneller als der GIA Ansatz

One of the most conspicuous problems in space physics for the last decades has been to theoretically describe how the large parallel electric fields on auroral field lines can be generated. There is strong observational evidence of such electric fields, and stationary theory supports the need for electric fields accelerating electrons to the ionosphere where they generate auroras. However, dynamic models have not been able to reproduce these electric fields. This thesis sheds some light on this incompatibility and shows that the missing ingredient in previous dynamic models is a correct description of the electron temperature. As the electrons accelerate towards the ionosphere, their velocity along the magnetic field line will increase. In the converging magnetic field lines, the mirror force will convert much of the parallel velocity into perpendicular velocity. The result of the acceleration and mirroring will be a velocity distribution with a significantly higher temperature in the auroral acceleration region than above. The enhanced temperature corresponds to strong electron pressure gradients that balance the parallel electric fields. Thus, in regions with electron acceleration along converging magnetic field lines, the electron temperature increase is a fundamental process and must be included in any model that aims to describe the build up of parallel electric fields. The development of such a model has been hampered by the difficulty to describe the temperature variation. This thesis shows that a local equation of state cannot be used, but the electron temperature variations must be descibed as a nonlocal response to the state of the auroral flux tube. The nonlocal response can be accomplished by the particle-fluid model presented in this thesis. This new dynamic model is a combination of a fluid model and a Particle-In-Cell (PIC) model and results in large parallel electric fields consistent with in-situ observations.

This thesis provides a synthetic understanding and an extensive analysis on megathrust earthquake generated tsunamis, with emphasis on the application of numerical modeling. In the present thesis, the tsunami characteristics are first depicted as a special hydrodynamic phenomenon. Further, a detailed literature review on the recent developments in tsunami numerical modeling techniques and on their applications is presented. A common approach in modeling the generation, propagation and inundation of tsunamis is discussed and used in the thesis. Based on the assumption of a vertical displacement of ocean water that is analogous to the ocean bottom displacement during a submarine earthquake, and the use of a non-dispersive long-wave model to simulate its physical transformation as it radiates outward from the source region. A general analysis of the Indian Ocean Tsunami of December 26th, 2004 is provided; and tsunami generation and propagation is conducted for this tsunami, as well as for tsunamis occurring in the Arabian Sea and Northwest Pacific Ocean, near the coast of the Vancouver Island. The analyses are based on geological and seismological parameters collected by the author. In this paper the author uses the collected bathymetry and earthquake information, plus tide gauge records and field survey results, and focuses on the theoretical assumptions, validation and limitation of the existing numerical models. Numerical simulations are performed using MIRONE, a tsunami modelling software developed based on the nonlinear shallow water theory. Through numerical modeling of three tsunami scenarios, e.g. December 26, 2004 Indian Ocean Tsunami, November 28, 1945 Arabian Sea Tsunami and the potential Cascadia Tsunami, a vivid overview of the tsunami features is provided as discussed. Generally, the results fairly agree with the observed data. The GEOWARE software is used to compute the tsunami travel time necessary to calibrate the results from MIRONE, using different numerical techniques. Several sensitivity analyses are conducted so that one can understand how oceanic topography affects tsunami wave propagation, determine how smoothing the topography affects the simulated tsunami travel time, and interpret the tsunami wave-height patterns as seen in the model simulations. The model can predict reasonably the tsunami behaviour, and are thus useful for tsunami warning system (tsunami mitigation and preparedness); and coastal population and industry can prepare for such possible catastrophic events.

Lors d’un glissement sismique, l’énergie libérée par la décharge élastique des blocs de terre adjacente peut être séparée en trois parties principales : L’énergie qui est rayonnée à la surface de la terre (_ 5% du budget énergétique total), l’énergie de fracture pour la création de nouvelles surfaces de faille et enfin, l’énergie dissipée à l’intérieur d’une région de la faille, d’épaisseur finie, que l’on appelle le “fault gouge ". Cette région accumule la majorité du glissement sismique. Estimer correctement la largeur de fault gouge est d’une importance capitale pour calculer l’énergie dissipée pendant le séisme, le comportement frictionnel de la faille et les conditions de nucléation de la faille sous la forme d’un glissement sismique ou asismique.Dans cette thèse, approches différentes de régularisation ont été explorées pour l’estimation de la largeur de localisation de la zone de glissement principal de la faille pendant le glissement cosmique. Celles-ci comprennent l’application de la viscosité et des couplages multiphasiques dans le continuum classique de Cauchy, et l’introduction d’un continuum micromorphe de Cosserat du premier ordre. Tout d’abord, nous nous concentrons sur le rôle de la régularisation visqueuse dans le contexte des analyses dynamiques, en tant que méthode de régularisation de la localisation des déformations. Nous étudions le cas dynamique d’un continuum de Cauchy classique adoucissant à la déformation et durcissant à la vitesse de déformation. En appliquant l’analyse de stabilité de Lyapunov, nous montrons que l’introduction de la viscosité est incapable d’empêcher la localisation de la déformation sur un plan mathématique et la dépendance de du maillage des éléments finis.Nous effectuons des analyses non linéaires en utilisant le continuum de Cosserat dans le cas de grands déplacements par glissement sismique de fault gouge par rapport à sa largeur. Le continuum de Cosserat nous permet de rendre compte de l’énergie dissipée pendant un séisme et du rôle de la microstructure dans l’évolution de la friction de la faille. Nous nous concentrons sur l’influence de la vitesse de glissement sismique sur le mécanisme d’assidument frictionnel de la pressurisation thermique. Nous remarquons que l’influence des conditions aux limites dans la diffusion du fluide interstitiel à l’intérieur de fault gouge, conduit à une reprise du frottement après l’affaiblissement initial. De plus, un mode de localisation de déformation en mouvement est présent pendant le cisaillement de la couche, introduisant des oscillations dans la réponse du frottement. Ces oscillations augmentent le contenu spectral du séisme. L’introduction de la viscosité dans le mode ci-dessus, conduit à un comportement de "rate and state" sans l’introduction d’une variable interne. Nos conclusions sur le rôle de la pressurisation thermique pendant le cisaillement de fault gouge sont en accord qualitatif avec les nouveaux résultats expérimentaux disponibles. Enfin, sur la base des résultats numériques, nous étudions les hypothèses du modèle actuel de glissement sur un plan mathématique proposent à la littérature. Le rôle des conditions aux limites et du mode de localisation des déformations dans l’évolution du frottement de la faille pendant le glissement sismique. Le cas d’un domaine délimité et d’un mode de localisation de la déformation en mouvement est examiné dans le contexte d’un glissement sur un plan mathématique sous pressurisation thermique. Nos résultats étoffent le modèle original dans un contexte plus général
During coseismic slip, the energy released by the elastic unloading of the adjacent earth blocks can be separated in three main parts: The energy that is radiated to the earth’s surface (_ 5% of the whole energy budget), the fracture energy for the creation of new fault surfaces and finally, the energy dissipated inside a region of the fault, with finite thickness, which is called the fault gauge. This region accumulates the majority of the seismic slip. Estimating correctly the width of the fault gauge is of paramount importance in calculating the energy dissipated during the earthquake, the fault’s frictional response, and the conditions for nucleation of the fault in the form of seismic or aseismic slip.In this thesis different regularization approaches were explored for the estimation of the localization width of the fault’s principal slip zone during coseismic slip. These include the application of viscosity and multiphysical couplings in the classical Cauchy continuum, and the introduction of a first order micromorphic Cosserat continuum. First, we focus on the role of viscous regularization in the context of dynamical analyses, as a method for regularizing strain localization. We study the dynamic case for a strain softening strain-rate hardening classical Cauchy continuum, and by applying the Lyapunov stability analysis we show that introduction of viscosity is unable to prevent strain localization on a mathematical plane and mesh dependence.We perform fully non linear analyses using the Cosserat continuum under large seismic slip displacements of the fault gouge in comparison to its width. Cosserat continuum provides us with a proper account of the energy dissipated during an earthquake and the role of the microstructure in the evolution of the fault’s friction. We focus on the influence of the seismic slip velocity to the weakening mechanism of thermal pressurization. We notice that the influence of the boundary conditions in the diffusion of the pore fluid inside the fault gouge, leads to frictional strength regain after initial weakening. Furthermore, a traveling strain localization mode is present during shearing of the layer introducing oscillations in the frictional response. Such oscillations increase the spectral content of the earthquake. Introduction of viscosity in the above mode, leads to a rate and state behavior without the introduction of a specific internal state variable. Our conclusions about the role of thermal pressurization during shearing of the fault gouge, agree qualitatively with newly available experimental results.Finally, based on the numerical findings we investigate the assumptions of the current model of a slip on a mathematical plane, in particular the role of the boundary conditions and strain localization mode in the evolution of the fault’s friction during coseismic slip. The case of a bounded domain and a traveling strain localization mode are examined in the context of slip on a mathematical plane under thermal pressurization. Our results expand the original model in a more general context

Thesis (Ph. D.) -- University of Maryland, College Park, 2008.
Thesis research directed by: Dept. of Mechanical Engineering. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

The current work aims to make a numerical model for an engineering design of anindustrial cyclone gasifier called as the Hortlax plant with capacity of providing 2.4 (MWth)of district heating as well as 1.3 (MW) of electricity. The model is needed to be able not onlyto predict the gasifier flow field with a suitable accuracy but also to investigate a largenumber of design alternatives with limited computer resources.The time-dependent single-phase flow field in a cyclone at first was simulated by usingseveral popular turbulence models including standard k-epsilon and SST models withcurvature correction, SSG-RSM and LES Smagorinsky models. The goal was to find the mostappropriate turbulence modeling as a foundation for the further works. Averaged andfluctuating parts of the simulated velocity component profiles from different turbulencemodels were compared with each other and the LDA measurements from literature.Comparison showed that the SSG-RSM can be the best alternative for the future simulations.An isothermal time-dependent Eulerian-Lagrangian particle modeling was implemented asthe second step for simulating particle-laden cold flow in the Hortlax gasifier. The impacts ofparticle-to-gas coupling on the pressure and velocity of the flow and particles motion insidethe gasifier were studied. The model could reasonably predict the particle tracking aspresented in the experimental results from the literature. High temperature of the gas flowinside the gasifier had quite important effects on the reduction of swirl and turbulenceintensity especially in the core region, pressure and particle behaviors. However, the presenceof solid particles did not influence the swirl intensity and turbulence significantly.The Hortlax gasifier was moreover experimentally studied in order to optimize thegasification plant efficiency, and understand the effect of operating. The air stoichiometricratio was varied to find the optimal condition for the plant. Moreover, the gasification processwas modeled using adiabatic thermodynamic equilibrium to see how far the process is fromequilibrium condition. Five different commercially available fuels were also studied usingequilibrium calculations. It was found that the gasifier is needed to work under the processtemperature of 1000 °C and stoichiometric ratio of 0.3, since at higher temperature the ash ismelted that is seriously avoided in the cyclone gasifier. Accordingly, the amount of undesiredmethane in the produced gas is quite high and the gasification efficiency is relatively lowaround 56%. Although the process does not reach equilibrium, it was seen thatthermodynamic equilibrium could compare the fuels performance almost close to theexperiments.

Granular materials are multi-particle systems involved in many industrial process and everyday life. The mechanical behavior of granular media such as sand, coffee beans, planetary rings and powders are current challenging tasks. In the last years, these systems have been widely examined experimentally, analytically and numerically, and they continue producing relevant and unexpected results. Despite the fact that granular media are often composed of grains with anisotropic shapes like rice, lentils or pills, most experimental and theoretical studies have concerned spherical particles. The aim of this thesis has been to examine numerically the behavior of granular media composted by spherical and non-spherical particles. Our numerical implementations have permitted the description of the macroscopic properties of mechanically stable granular assemblies, which have been experimentally examined in a framework of the projects "Estabilidad y dinámica de medios granulares anisótropos" (FIS2008- 06034-C02-02) University of Girona and "Interacciones entre partículas y emergencia de propiedades macroscópicas en medios granulares" (FIS2008-06034-C02-01) University of Navarra
Els materials granulars són sistemes de moltes partícules implicats en diversos processos industrials i en la nostra vida quotidiana. El comportament mecànic de conjunts granulars, com la sorra, grans de cafè, anells o pols planetàries, representa actualment un repte per a la ciència. En els últims anys aquests sistemes s’han estudiat àmpliament de forma experimental, analítica i numèrica. De totes maneres, avui dia es continuen obtenint resultats rellevants, i en moltes ocasions, inesperats. Malgrat el fet que els materials granulars sovint estan compostos per grans amb forma anisotròpica, com l’arròs, les llenties o les píndoles, la majoria dels estudis experimentals i teòrics se centren en partícules esfèriques. L’objectiu d’aquesta tesi ha estat analitzar numèricament el comportament dels mitjans granulars compostos per partícules esfèriques i no esfèriques. Els mètodes numèrics implementats han permès la descripció de les propietats macroscòpiques de piles i columnes granulars, que s’han estudiat experimentalment en el marc dels projectes "Estabilidad y dinámica de medios granulares anisótropos" (FIS2008-06034-C02- 02) de la Universitat de Girona i "Interacciones entre partículas y emergencia de propiedades macroscópicas en medios granulares" (FIS2008-06034-C02- 01) de la Universitat de Navarra

The behavior of jointed rock mass is very complex and is influenced by many factors such as location of joints, joint frequency, joint orientation and joint strength. A thorough review of literature on different aspects of jointed rock mass indicate that the discontinuities or planes of weakness present in rock mass significantly influence its behavior. Numerous experimental tests were conducted to study the behavior of natural as well as artificial joints in rocks. Laboratory tests are time consuming and give results applicable to specific joint fabric and confining pressure. Numerical methods are the best alternative to laboratory tests to study the behavior of jointed rock mass. With the advent of computers numerical methods of analysis have become very popular, as they are highly flexible and can represent all complex geometries and material behavior. The accuracy of a numerical model depends upon the how well constitutive relations for the jointed rock mass are defined in the analysis. Empirical relationships for describing the mechanical behavior of discontinuities obtained from scaling the laboratory data is crucial unresolved problem, which will affect the quality of results obtained. One more important aspect in the numerical model is strength criteria used for jointed rock mass. The applicability of existing strength criteria to a particular jointed rock has to be carefully examined before they are used. Equivalent continuum approach simplifies the modeling of jointed rock mass as the joints are not modeled separately. Instead in equivalent continuum approach the jointed rock mass is represented by an equivalent continuum whose properties are defined by a combination of intact rock properties and joint properties. The accuracy of this kind of modeling depends upon the relationships used to define the jointed rock mass properties as a function of intact rock properties and joint properties. In the present study, an effort has been made (i) to establish empirical relations to define the properties of jointed rock mass as a function of intact rock properties and joint factor (ii) to develop a numerical model based on equivalent continuum approach using the empirical relations derived above, for easy and efficient modeling of jointed rock mass (iii) comparison of existing strength criteria for jointed rock masses using the equivalent continuum model developed above (iv) Modeling of joints explicitly and comparing these results with the equivalent continuum model results. Empirical relationships expressing the uniaxial compressive strength and elastic modulus of jointed rock as a function of corresponding intact rock properties and joint factor have been derived based on the statistical analysis of large amount of experimental data of uniaxial and triaxial tests collected from the literature. The effect of joints in the jointed rock is taken in to account by the joint factor. A comparative study of the empirical relationships arrived by the above analysis has been made to choose the best relation for the numerical analysis. Empirical relationships thus arrived for jointed rock mass are used in the equivalent continuum approach to represent the jointed rock properties as a combination of intact rock properties and joint factor. Equivalent continuum model developed is thoroughly tested, validated and applied for single, multiple and block jointed rocks. The equivalent continuum model developed has been applied for analysis of the power cavern for Shiobara power station. Different strength criteria available for jointed rock namely Mohr-Coulomb, Hoek and Drown, Yudhbir et al. and Rarnamurthy are incorporated in the equivalent continuum model to evaluate their applicability for jointed rock masses. Ramarnurthy's strength criterion gives the best values of failure stress for almost all the test cases and hence used in the equivalent continuum model. Alternatively, the joints in jointed rock mass are represented explicitly using interface element in the nonlinear finite element analysis. The explicit finite element model has been tested and validated using the experimental stress strain curves and failure stress values. Comparison of results obtained using equivalent continuum analysis and explicit modeling of joints has been given in the form of stress strain curves and failure stress plots for jointed rock masses along with the experimental results. Some of the major conclusions from the present study are as follows. Statistical relationships arrived to express the properties of the jointed rock as a function of intact rock and joint factor give a fair estimate of jointed rock in the absence of experimental data. Equivalent continuum model developed using statistical relations arrived above simplifies the numerical modeling of jointed rock to a large extent and also gives a fair estimate of jointed rock behavior with minimum input data. From the equivalent continuum analysis of Shiobara power cavern, it can be concluded that this approach is very advantageous for modeling highly discontinuous systems provided the joint factor is estimated properly so that it represents the real fabric of the joints present in the system. Comparison of different strength criteria shows that Ramamurthy's strength criterion is the best for jointed rocks. When the rock mass has one or two major joints it is advantageous to model it explicitly so that the behavior of the joint can be studied in detail. Explicit representation of the joints in the finite element analysis gives a lair estimate of the zones most susceptible to failure in a jointed rock. From comparison of experimental values, equivalent continuum model results and the explicit joint model results, it can be concluded that results obtained using equivalent continuum model are nearest to the experimental results in almost all the cases.

This research is dedicated to make a foreseeing of the future state of the Kizildere Geothermal Field in order to suggest acceptable solutions to the current problems. The non-isothermal mechanism of the geothermal field is simulated for the pressure and temperature variables. For this purpose, a finite element model (696 four-nodal elements with 750 nodes) of the field is formulated by considering the geological conditions and the present wells already drilled in the area. Then the model is calibrated to the field for the natural state by using appropriate physical properties, boundary and initial conditions. Comparison of the simulated and the observed pressures and temperatures has emphasized a very successful calibration study. After the calibration, response of the field to the production and injection for the period of 1984-2006 has been simulated by applying a history matching study. History matching runs have yielded very good correlations between the observed and the computed values of the pressure and temperature variables. The calibrated and history matched model has been applied to the field to simulate the future performance of the field for different production and injection scenarios. In the first scenario the field is simulated for the next 10-year production period keeping the on-going production conditions. Then, the influence of the production of two new wells has been investigated in two different scenarios. In the forth scenario, the effect of injection from one of the production wells has been simulated.

The aim of this study is to construct a numerical reservoir model for Balç
ova geothermal field, which is located in the izmir bay area of the Aegean coast. A commercial numerical simulation program, TOUGH2 was utilized with a graphical interface, PETRASIM to model the Balç
ova geothermal field. Natural state modeling of the field was carried out based on the conceptual model of the field, then history matching of production &ndash
injection practices of the field was established for the period of 1996 &ndash
2008. The final stage of modeling was the future performance prediction of the field by using three different Scenarios. In Scenario-1, production and injection rates in year 2008 were repeated for 20 years. In Scenario-2, production and injection rates in year 2008 were repeated for the first 3 years, then they were increased at every 3 years. In Scenario-3, a new well (BT-1) that is assumed to be drilled to 1000 m depth is added for injecting some portion of water that was injected through BD-8 well. In that scenario, similar to Scenario-2, production and injection rates in year 2008 were repeated during the first 3 years, and then the rates of these wells (except the new well) were increased every three years. Analysis of the results indicated that in Scenario-2, compared to Scenario-1, both the temperatures of deep wells located at the eastern portion of the field (BD-6, BD-2, BD-14, BD-9, BD-11, BD-12) and the temperatures of deep wells located at the western portion (BD-4, BD-15, BD-7, BD-5) decreased more. In Scenario-3, compared to Scenario-1, the deep wells located at the eastern side experienced less temperature drops while the deep wells located at the western side experienced higher temperature drops. Such temperature differences were not encountered in shallow wells. No significant changes in bottom hole pressures of deep wells occurred in all three scenarios. On the other hand, shallow wells, especially B-10 and B-5, responded to Scenario-2 and Scenario-3 as decrease in bottom hole pressures.

The purpose of this study is to examine the geothermal potential, sustainability, and reinjection possibility of Edremit geothermal field. In order to investigate this, a numerical model consisting of a hot and cold water aquifer system is established. A two dimensional cross sectional model is set to simulate this geothermal system. Different pressure and temperature values are applied to the nodes at the boundaries to perform a steady state calibration which minimizes the computed results and observed values obtained from the near well logs. After the calibration, three alternative scenarios are proposed and the response of the pressure and temperature to these conditions is evaluated. At first the water is pumped from the wells of Yagci, Derman, Entur and ED-3 seperately at a mass rate of 5 kg/s and energy rate of 4.182 x 105 J/s. Then, in scenario 2 the water is pumped at the same rate from all the wells mentioned in the first scenario together. For the third scenario another well is opened to the geothermal system and 80% of the pumped water (temperature being 200C) is injected to the system from the wells while all the wells mentioned are working. The results of these scenarios are utilized to evaluate the reservoir in terms of its response to different production and reinjection conditions. Interpretation of the reservoir response in view of the pressure and temperature declines emphasize that such a simulation study can be applied to assess potential and sustainability of the geothermal systems.

Thesis (M.S.)--West Virginia University, 2007.
Title from document title page. Document formatted into pages; contains xii, 94 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 93-94).

Pressure tests on wood have been conducted to determine its properties. The resultswere not as expected, and it is therefore difficult to obtain the parameters of thewood. This project examines how a specific defect in the wood sample affects theresult.The pressure test is simulated with numerical modeling. In the numerical model thecube’s top side is non-parallel with the bottom side, it is in other words somewhattilted.The results from the model agreed with the findings from some pressure tests. Withthose we can easily calculate the wood's properties. For other pressure tests, otherfactors might need to be examined before we can draw any conclusions.
Tryckprover på trä har utförts för att ta reda dess egenskaper. Resultaten blev intevad som förväntades, och det blir därför svårt att få fram träets egenskaper. Dettaprojekt undersöker hur en viss defekt i träprovet påverkar resultatet.Tryckprovet simuleras med numerisk modellering. I modellen är kubens toppsida inteparallell med bottensidan, den är med andra ord något sned.Resultatet från modellen stämde med resultat från vissa tryckprover. Då kan man fåfram träets egenskaper. För andra tryckprover kan andra faktorer behöva undersökasinnan man kan dra några slutsatser.

CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
FUNDAÇÃO DE APOIO À PESQUISA DO ESTADO DO RIO DE JANEIRO
É apresentado um modelo não-linear para estruturas unidimensionais em equilíbrio, onde não são feitas restrições de caráter geométrico. Este modelo é capaz de descrever movimentos que envolvam flexão, torção, cilhamento e extensão. As configurações de referência e deformada têm sua geometria descrita através da posição espacial de uma curva e da orientação de uma base ortonormal associada a cada ponto dessa curva. O uso dos ângulos de Euler na descrição das rotações, o que pode implicar em instabilidades numéricas, é evitado através do uso de uma nova parametrização para o problema. O problema de equilíbrio que envolve o comportamento não-linear de uma estrutura unidimensional é formulado de diferentes maneiras. São apresentados dois métodos numéricos para a solução desse problema. Um deles é baseado numa decomposição via lagrangeano aumentado e outro é um método de Newton não convencional. São discutidos detalhes acerca da implementação computacional desses métodos. A validade das formulações é atestada através de alguns exemplos numéricos. Em particular. São analisadas algumas aplicações relacionadas com operações de cabos umbilicais em prospecção petrolífera, que envolvem carregamentos estáticos complicados como aqueles ocasionados por flutuadores e pela atração gravitacional.
It is presented a model of the static geometrically non-linear behavior of an elastic rod which considers flexion, torsion, shear and tension. The geometry of the body, in the reference and deformed configurations, is described given the position of the centerline and the geometry of a rigid frame attached to each point of the line. A particular parametrization that avoids the difficulties associated with the use of Euler angles is employed simplifying the numerical treatment. The equilibrium problem for a nonlinear rod is formulated in several different ways and two numerical methods for solution of these problems are presented. One is based on augmented Lagrangian splitting and the second is a non-standard Newton’s method. Details pertaining to the implementation of that method are discussed. A number of numerical simulations have been documented to demonstrate the robustness of the formulations. In particular, some applications in connection with Off shore pipe lines operations, which involves complicated static loading conditions that includes floaters and gravitational forces, are analysed.