177 research outputs found

    Mixed finite element approximation of porous media flows

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    The reliable simulation of flow in fractured porous media is a key aspect in the decision making process of stakeholders within politics and the geosciences, for example when assessing the suitability of burial sites for storage of high–level radioactive waste. This thesis aims to tackle the challenge that is the accurate simulation of these flows and does so via three computational developments. That is, suitable models for porous media flow with fractures; obtaining rigorous and reliable estimates of errors generated through these models; and the accurate simulation of the times–of–flight for particles transported by groundwater within the porous medium. Firstly, an expansion procedure for fractures in porous media is developed so that physical fluid laws are still retained when tracking particles across fracture–bulk interfaces. Moreover, the second contribution of this work is the utilisation of the dual–weighted–residual method to define suitable elementwise indicators for generic quantities of interest. The third contribution of this thesis is the attainment of accurate simulations of travel times for particles in porous media, achieved through linearising the functional representing the time–of–flight; in practice, numerical examples, including one inspired by the Sellafield site in Cumbria, UK, validate the performance of the proposed error estimator, and hence are useful in the safety assessment of storage facilities intended for radioactive waste

    CVEM-BEM Coupling with Decoupled Orders for 2D Exterior Poisson Problems

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    For the solution of 2D exterior Dirichlet Poisson problems, we propose the coupling of a Curved Virtual Element Method (CVEM) with a Boundary Element Method (BEM), by using decoupled approximation orders. We provide optimal convergence error estimates, in the energy and in the weaker L-2-norm, in which the CVEM and BEM contributions to the error are separated. This allows for taking advantage of the high order flexibility of the CVEM to retrieve an accurate discrete solution by using a low order BEM. The numerical results confirm the a priori estimates and show the effectiveness of the proposed approach

    A posteriori error estimation and modeling of unsaturated flow in fractured porous media

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    This doctoral thesis focuses on three topics: (1) modeling of unsaturated flow in fractured porous media, (2) a posteriori error estimation for mixed-dimensional elliptic equations, and (3) contributions to open-source software for complex multiphysics processes in porous media. In our first contribution, following a Discrete-Fracture Matrix (DFM) approach, we propose a model where Richards' equation governs the water flow in the matrix, whereas fractures are represented as lower-dimensional open channels, naturally providing a capillary barrier to the water flow. Therefore, water in the matrix is only allowed to imbibe the fracture if the capillary barrier is overcome. When this occurs, we assume that the water inside the fracture flows downwards without resistance and, therefore, is instantaneously at hydrostatic equilibrium. This assumption can be justifiable for fractures with sufficiently large apertures, where capillary forces play no role. Mathematically, our model can be classified as a coupled PDE-ODE system of equations with variational inequalities, in which each fracture is considered a potential seepage face. Our second contribution deals with error estimation for mixed-dimensional (mD) elliptic equations, which, in particular, model single-phase flow in fractured porous media. Here, based on the theory of functional a posteriori error estimates, we derive guaranteed upper bounds for the mD primal and mD dual variables, and two-sided bounds for the mD primal-dual pair. Moreover, we improve the standard results of the functional approach by proposing four ways of estimating the residual errors based on the conservation properties of the approximations, that is, (1) no conservation, (2) subdomain conservation, (3) local conservation, and (4) pointwise conservation. This results in sharper and fully-computable bounds when mass is conserved either locally or exactly. To our knowledge, to date, no error estimates have been available for fracture networks, including fracture intersections and floating subdomains. Our last contribution is related to the development of open-source software. First, we present the implementation of a new multipoint finite-volume-based module for unsaturated poroelasticity, compatible with the Matlab Reservoir Simulation Toolbox (MRST). Second, we present a new Python-based simulation framework for multiphysics processes in fractured porous media, named PorePy. PorePy, by design, is particularly well-suited for handling mixed-dimensional geometries, and thus optimal for DFM models. The first two contributions discussed above were implemented in PorePy.Denne avhandlingen tar for seg tre emner: (1) modellering av flyt i umettet porøst medium med sprekker, (2) a posteriori feilestimater for blandet-dimensjonale elliptiske ligninger, og (3) bidrag til åpen kildekode for komplekse multifysikk-prosesser i porøse medier. I det første bidraget anvender vi en Discrete-Fracture Matrix (DFM) (Diskret-Sprekk Matrise) metode til å sette opp en modell hvor Richard's ligning modellerer vann-flyt i matrisen, og sprekkene representeres som lavere-dimensjonale åpne kanaler, som naturlig virker som kapillærbarrierer til vann-flyten. Derfor vil vann i matrisen kun få tilgang til sprekken når kapillærbarrieren blir brutt. Når det inntreffer, antar vi at vannet i sprekken flyter nedover uten motstand, og at hydrostatisk ekvilibrium derfor inntreffer øyeblikkelig. Slike antakelser kan rettferdiggjøres for sprekker med tilstrekkelig stor apertur (åpning), hvor kapillærkrefter ikke har noen innvirkning. Fra et matematisk standpunkt kan modellen klassifiseres som en sammenkoblet PDE-ODE med variasjonelle ulikheter hvor hver sprekk behandles som en filtreringsfase. Det andre bidraget tar for seg feilestimater for blandet-dimensjonale elliptiske ligninger, som modellerer en-fase flyt i porøse medier med sprekker. Her anvender vi teorien for "funksjonal a posteriori feilestimater" til å finne øvre skranker for primær og dual variablene, samt øvre og nedre skranker for primær-dual paret. Dessuten viser vi at vi kan forbedre standardresultatene fra "funksjonal a posteriori feilestimater" ved å foreslå fire måte å estimere residualfeilen basert på bevaringsegenskapene til diskretiseringen. De fire forskjellige bevaringsegenskapene er; ingen bevaringsegenskap, under- domene bevaring, lokal bevaring og punktvis bevaring. Dette fører til skarpere skranker som er mulige å beregne når masse er bevart enten lokalt, eller eksakt. Vi kjenner ikke til andre tilgjengelige feilestimater for sprekknettverk som inkluderer snitt av sprekker og sprekkrender som ligger innenfor domenets rand. Det siste bidraget omhandler utvikling av åpen kildekode. Først presenterer vi imple- menteringen av en multipunktfluks-basert modul for flyt i umettet deformerbart porøst medium som er kompatibelt med "Matlab Reservoir Simulation Toolbox"(MRST). I tillegg presenterer vi et nytt Python-basert rammeverk for simulering av multifysikkprosesser i porøse medier med sprekker, som heter PorePy. Dette rammeverket er designet for å håndtere geometrier med blandede dimensjoner og er derfor optimalt for DFM modeller. De to første bidragene i avhandlingen (nevnt over) er implementert i PorePy.Doktorgradsavhandlin

    HERITAGE 2022. International Conference on Vernacular Heritage: Culture, People and Sustainability

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    Vernacular architecture, tangible and intangible heritage of great importance to European and global culture, represents the response of a society culturally linked to its territory, in terms of climate and landscape. Its construction features are born from the practical experience of the inhabitants, making use of local materials, taking into consideration geographical conditions and cultural, social and constructive traditions, based on the conditions of the surrounding nature and habitat. Above all, it plays an essential role in contemporary society as it is able to teach us important principles and lessons for a respectful sustainable architecture. Vernacular Heritage: Culture, People and Sustainability will be a valuable source of information for academics and professionals in the fields of Environmental Science, Civil Engineering, Construction and Building Engineering and ArchitectureMileto, C.; Vegas López-Manzanares, F.; Cristini, V.; García Soriano, L. (2022). HERITAGE 2022. International Conference on Vernacular Heritage: Culture, People and Sustainability. Editorial Universitat Politècnica de València. https://doi.org/10.4995/HERITAGE2022.2022.15942EDITORIA

    Materiality in Roman Art and Architecture

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    Material is the substance of the world of things. Literary sources suggest that materiality was part of aesthetic perception, loaded with meaning and bound to function even in antiquity. To date, this complex reading of material has not been adequately represented in archaeological research. The present volume addresses this oversight by examining the decorative use of material in Roman Italy between the Late Republic and Early Imperial period

    Optimising Stable Radicals for the Electrochemical Generation of Reactive Intermediates

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    This thesis concentrates on the electrochemical activation of stable-radical adducts to generate reactive intermediates for small molecule and polymer chemistry. The majority of this work concerns the computational modelling and design of such compounds using high-level, ab inito quantum chemistry methods. The main findings are as follows. It is first shown that adducts based on highly-stable Blatter and Kuhn-type radicals undergo mesolytic cleavage upon one-electron oxidation, generating reactive carbocations or carbon-centred radicals. Substituent effects are employed to optimise this chemistry, either to reduce the oxidation potential of the adduct to favour the production of radicals, or by altering the bond-dissociation free energy of mesolytic cleavage to control the rate of fragmentation. Computational chemistry is then used to explore the scope for stable-radical adducts as electrochemically activated alkylating agents. SN2-type methylations of pyridine are studied over a broad range of nitroxide, triazinyl, and verdazyl-based adducts (X-Me). Here, high oxidation potentials are found to render low SN2 barriers to methylation and thus more reactive agents, highlighting the suitability of commercially available, (2,2,6,6-tetramethylpiperidin-1-yl)oxyl (TEMPO), in this role. Modelling is also applied to study the triboelectrification of polymeric insulators. Here, material-specific charging properties and dissipation rates are found to be connected to the stability of anionic polymer fragments to oxidation, and cationic fragments to reduction. Computational methods are then used to study the low-frequency (Terahertz) vibrations in molecular crystals. A method benchmark is presented - identifying parameters that reliably produce accurate simulated spectra - along with several new analytical tools built for the assessment of spectral data

    The Hybrid Practitioner

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    The practice of architecture manifests in myriad forms and engagements. Overcoming false divides, this volume frames the fertile relationship between the cultural and scholarly production of academia and the process of designing and building in the material world. It proposes the concept of the hybrid practitioner, who bridges the gap between academia and practice by considering how different aspects of architectural practice, theory, and history intersect, opening up a fascinating array of possibilities for an active engagement with the present. The book explores different, interrelated roles for practicing architects and researchers, from the reproductive activities of teaching, consulting and publishing, through the reflective activities of drawing and writing, to the practice of building. The notion of the hybrid practitioner will appeal strongly to students, teachers and architectural practitioners as part of a multifaceted professional environment. By connecting academic interests with those of the professional realm, The Hybrid Practitioner addresses a wider readership embracing landscape design, art theory and aesthetics, European history, and the history and sociology of professions

    A Multigrid Multilevel Monte Carlo Method for Stokes–Darcy Model with Random Hydraulic Conductivity and Beavers–Joseph Condition

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    A multigrid multilevel Monte Carlo (MGMLMC) method is developed for the stochastic Stokes–Darcy interface model with random hydraulic conductivity both in the porous media domain and on the interface. Three interface conditions with randomness are considered on the interface between Stokes and Darcy equations, especially the Beavers–Joesph interface condition with random hydraulic conductivity. Because the randomness through the interface affects the flow in the Stokes domain, we investigate the coupled stochastic Stokes–Darcy model to improve the fidelity. Under suitable assumptions on the random coefficient, we prove the existence and uniqueness of the weak solution of the variational form. To construct the numerical method, we first adopt the Monte Carlo (MC) method and finite element method, for the discretization in the probability space and physical space, respectively. In order to improve the efficiency of the classical single-level Monte Carlo (SLMC) method, we adopt the multilevel Monte Carlo (MLMC) method to dramatically reduce the computational cost in the probability space. A strategy is developed to calculate the number of samples needed in MLMC method for the stochastic Stokes–Darcy model. In order to accomplish the strategy for MLMC method, we also present a practical method to determine the variance convergence rate for the stochastic Stokes–Darcy model with Beavers–Joseph interface condition. Furthermore, MLMC method naturally provides the hierarchical grids and sufficient information on these grids for multigrid (MG) method, which can in turn improve the efficiency of MLMC method. In order to fully make use of the dynamical interaction between these two methods, we propose a multigrid multilevel Monte Carlo (MGMLMC) method with finite element discretization for more efficiently solving the stochastic model, while additional attention is paid to the interface and the random Beavers–Joesph interface condition. The computational cost of the proposed MGMLMC method is rigorously analyzed and compared with the SLMC method. Numerical examples are provided to verify and illustrate the proposed method and the theoretical conclusions
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