Reduced order adaptive models for systems of PDEs using POD

In this work we propose a method to accelerate time dependent numerical solvers of systems of PDEs that require a high cost in computational time and memory. The method is based on the combined use of such numerical solver with a proper orthogonal decomposition, from which we identify modes, a Galerkin projection (that provides a reduced system of equations) and the integration of the reduced system, studying the evolution of the modal amplitudes. We integrate the reduced model until our a priori error estimator indicates that our approximation in not accurate. At this point we use again our original numerical code in a short time interval to adapt the POD manifold and continue then with the integration of the reduced model. Application will be made to two model problems: the Ginzburg-Landau equation in transient chaos conditions and the two-dimensional pulsating cavity problem, which describes the motion of liquid in a box whose upper wall is moving back and forth in a quasi-periodic fashion. Finally, we will discuss a way of improving the performance of the method using experimental data or information from numerical simulations

Mixing Snapshots and Fast Time Integration of PDEs

A local proper orthogonal decomposition (POD) plus Galerkin projection method was recently developed to accelerate time dependent numerical solvers of PDEs. This method is based on the combined use of a numerical code (NC) and a Galerkin sys- tem (GS) in a sequence of interspersed time intervals, INC and IGS, respectively. POD is performed on some sets of snapshots calculated by the numerical solver in the INC inter- vals. The governing equations are Galerkin projected onto the most energetic POD modes and the resulting GS is time integrated in the next IGS interval. The major computa- tional e®ort is associated with the snapshots calculation in the ¯rst INC interval, where the POD manifold needs to be completely constructed (it is only updated in subsequent INC intervals, which can thus be quite small). As the POD manifold depends only weakly on the particular values of the parameters of the problem, a suitable library can be con- structed adapting the snapshots calculated in other runs to drastically reduce the size of the ¯rst INC interval and thus the involved computational cost. The strategy is success- fully tested in (i) the one-dimensional complex Ginzburg-Landau equation, including the case in which it exhibits transient chaos, and (ii) the two-dimensional unsteady lid-driven cavity problem

Modelling of chloride transport in non-saturated concrete : from microscale to macroscale

Corrosion of steel bars embedded in concrete has a great influence on structural performance and durability of reinforced concrete. Chloride penetration is considered to be a primary cause of concrete deterioration in a vast majority of structures. Therefore, modelling of chloride penetration into concrete has become an area of great interest. The present work focuses on modelling of chloride transport in concrete. The differential macroscopic equations which govern the problem were derived from the equations at the microscopic scale by comparing the porous network with a single equivalent pore whose properties are the same as the average properties of the real porous network. The resulting transport model, which accounts for diffusion, migration, advection, chloride binding and chloride precipitation, consists of three coupled differential equations. The first equation models the transport of chloride ions, while the other two model the flow of the pore water and the heat transfer. In order to calibrate the model, the material parameters to determine experimentally were identified. The differential equations were solved by means of the finite element method. The classical Galerkin method was employed for the pore solution flow and the heat transfer equations, while the streamline upwind Petrov Galerkin method was adopted for the transport equation in order to avoid spatial instabilities for advection dominated problems. The finite element codes are implemented in Matlab® . To retrieve a good understanding of the influence of each variable and parameter, a detailed sensitivity analysis of the model was carried out. In order to determine the diffusive and hygroscopic properties of the studied concretes, as well as their chloride binding capacity, an experimental analysis was performed. The model was successfully compared with experimental data obtained from an offshore oil platform located in Brazil. Moreover, apart from the main objectives, numerous results were obtained throughout this work. For instance, several diffusion coefficients and the relation between them are discussed. It is shown how the electric field set up between the ionic species depends on the gradient of the species’ concentrations. Furthermore, the capillary hysteresis effects are illustrated by a proposed model, which leads to the determination of several microstructure properties, such as the pore size distribution and the tortuosity-connectivity of the porous network. El fenómeno de corrosión del acero de refuerzo embebido en el hormigón ha tenido gran influencia en estructuras de hormigón armado, tanto en su funcionalidad estructural como en aspectos de durabilidad. La penetración de cloruros en el interior del hormigón esta considerada como el factor principal en el deterioro de la gran mayoría de estructuras. Por lo tanto, la modelización numérica de dicho fenómeno ha generado gran interés. El presente trabajo de investigación se centra en la modelización del transporte de cloruros en el interior del hormigón. Las ecuaciones diferenciales que gobiernan los fenómenos a nivel macroscópico se deducen de ecuaciones planteadas a nivel microscópico. Esto se obtiene comparando la red porosa con un poro equivalente, el cual mantiene las mismas propiedades de la red porosa real. El modelo está constituido por tres ecuaciones diferenciales acopladas que consideran el transporte de cloruros, el flujo de la solución de poro y la transferencia de calor. Con estas ecuaciones se tienen en cuenta los fenómenos de difusión, migración, advección, combinación y precipitación de cloruros. El análisis llevado a cabo en este trabajo ha definido los parámetros necesarios para calibrar el modelo. De acuerdo con ellas, se seleccionaron los ensayos experimentales a realizar. Las ecuaciones diferenciales se resolvieron mediante el método de elementos finitos. El método clásico de Galerkin se empleó para solucionar las ecuaciones de flujo de la solución de poro y de la transferencia de calor, mientras que el método streamline upwind Petrov-Galerkin se utilizó para resolver la ecuación de transporte de cloruros con la finalidad de evitar inestabilidades espaciales en problemas con advección dominante. El código de elementos finitos está implementado en Matlab® . Con el objetivo de facilitar la comprensión del grado de influencia de cada variable y parámetro, se realizó un análisis de sensibilidad detallado del modelo. Se llevó a cabo una campaña experimental sobre los hormigones estudiados, con el objeto de obtener sus propiedades difusivas, químicas e higroscópicas. El modelo se contrastó con datos experimentales obtenidos en una plataforma petrolera localizada en Brasil. Las simulaciones numéricas corroboraron los datos experimentales. Además, durante el desarrollo de la investigación se obtuvieron resultados paralelos a los planteados inicialmente. Por ejemplo, el análisis de diferentes coeficientes de difusión y la relación entre ellos. Así como también se observó que el campo eléctrico establecido entre las especies iónicas disueltas en la solución de poro depende del gradiente de concentración de las mismas. Los efectos de histéresis capilar son expresados por el modelo propuesto, el cual conduce a la determinación de una serie de propiedades microscópicas, tales como la distribución del tamaño de poro, además de la tortuosidad y conectividad de la red porosa.

Kinetics of amorphization induced by swift heavy ions in α-quartz

The kinetics of amorphization in crystalline SiO2 (α-quartz) under irradiation with swift heavy ions (O+1 at 4 MeV, O+4 at 13 MeV, F+2 at 5 MeV, F+4 at 15 MeV, Cl+3 at 10 MeV, Cl+4 at 20 MeV, Br+5 at 15 and 25 MeV and Br+8 at 40 MeV) has been analyzed in this work with an Avrami-type law and also with a recently developed cumulative approach (track-overlap model). This latter model assumes a track morphology consisting of an amorphous core (area σ) and a surrounding defective halo (area h), both being axially symmetric. The parameters of the two approaches which provide the best fit to the experimental data have been obtained as a function of the electronic stopping power Se. The extrapolation of the σ(Se) dependence yields a threshold value for amorphization, Sth ≈ 2.1 keV/nm; a second threshold is also observed around 4.1 keV/nm. We believe that this double-threshold effect could be related to the appearance of discontinuous tracks in the region between 2.1 and 4.1 keV/nm. For stopping power values around or below the lower threshold, where the ratio h/σ is large, the track-overlap model provides a much better fit than the Avrami function. Therefore, the data show that a right modeling of the amorphization kinetics needs to take into account the contribution of the defective track halo. Finally, a short comparative discussion with the kinetic laws obtained for elastic collision damage is given.

Approach to integrate product conceptual design information into a computer-aided design system

Commercial computer-aided design systems support the geometric definition of product, but they lack utilities to support initial design stages. Typical tasks such as customer need capture, functional requirement formalization, or design parameter definition are conducted in applications that, for instance, support ?quality function deployment? and ?failure modes and effects analysis? techniques. Such applications are noninteroperable with the computer-aided design systems, leading to discontinuous design information flows. This study addresses this issue and proposes a method to enhance the integration of design information generated in the early design stages into a commercial computer-aided design system. To demonstrate the feasibility of the approach adopted, a prototype application was developed and two case studies were executed.

Hexagons and spiral defect chaos in non-Boussinesq convection at low Prandtl numbers

We study the stability and dynamics of non-Boussinesq convection in pure gases ?CO2 and SF6? with Prandtl numbers near Pr? 1 and in a H2-Xe mixture with Pr= 0.17. Focusing on the strongly nonlinear regime we employ Galerkin stability analyses and direct numerical simulations of the Navier-Stokes equations. For Pr ? 1 and intermediate non-Boussinesq effects we find reentrance of stable hexagons as the Rayleigh number is increased. For stronger non-Boussinesq effects the usual, transverse side-band instability is superseded by a longitudinal side-band instability. Moreover, the hexagons do not exhibit any amplitude instability to rolls. Seemingly, this result contradicts the experimentally observed transition from hexagons to rolls. We resolve this discrepancy by including the effect of the lateral walls. Non-Boussinesq effects modify the spiral defect chaos observed for larger Rayleigh numbers. For convection in SF6 we find that non-Boussinesq effects strongly increase the number of small, compact convection cells and with it enhance the cellular character of the patterns. In H2-Xe, closer to threshold, we find instead an enhanced tendency toward roll-like structures. In both cases the number of spirals and of targetlike components is reduced. We quantify these effects using recently developed diagnostics of the geometric properties of the patterns.

Image analysis by moment invariants using a set of step-like basis functions

Moment invariants have been thoroughly studied and repeatedly proposed as one of the most powerful tools for 2D shape identification. In this paper a set of such descriptors is proposed, being the basis functions discontinuous in a finite number of points. The goal of using discontinuous functions is to avoid the Gibbs phenomenon, and therefore to yield a better approximation capability for discontinuous signals, as images. Moreover, the proposed set of moments allows the definition of rotation invariants, being this the other main design concern. Translation and scale invariance are achieved by means of standard image normalization. Tests are conducted to evaluate the behavior of these descriptors in noisy environments, where images are corrupted with Gaussian noise up to different SNR values. Results are compared to those obtained using Zernike moments, showing that the proposed descriptor has the same performance in image retrieval tasks in noisy environments, but demanding much less computational power for every stage in the query chain.

Modelling of chloride transport in non-saturated concrete : from microscale to macroscale

A model for chloride transport in concrete is proposed. The model accounts for transport several transport mechanisms such as diffusion, advection, migration, etc. This work shows the chloride transport equations at the macroscopic scale in non-saturated concrete. The equations involve diffusion, migration, capillary suction, chloride combination and precipitation mechanisms. The material is assumed to be infinitely rigid, though the porosity can change under influence of chloride binding and precipitation. The involved microscopic and macroscopic properties of the materials are measured by standardized methods. The variables which must be imposed on the boundaries are temperature, relative humidity and chloride concentration. The output data of the model are the free, bound, precipitated and total chloride ion concentrations, as well as the pore solution content and the porosity. The proposed equations are solved by means of the finite element method (FEM) implemented in MATLAB (classical Galerkin formulation and the streamline upwind Petrov-Galerkin (SUPG) method to avoid spatial instabilities for advection dominated flows).

Numerical model for the study of hydrodynamics on bays and estuaries

A nonlinear implicit finite element model for the solution of two-dimensional (2-D) shallow water equations, based on a Galerkin formulation of the 2-D estuaries hydrodynamic equations, has been developed. Spatial discretization has been achieved by the use of isoparametric, Lagrangian elements. To obtain the different element matrices, Simpson numerical integration has been applied. For time integration of the model, several schemes in finite differences have been used: the Cranck-Nicholson iterative method supplies a superior accuracy and allows us to work with the greatest time step Δt; however, central differences time integration produces a greater velocity of calculation. The model has been tested with different examples to check its accuracy and advantages in relation to computation and handling of matrices. Finally, an application to the Bay of Santander is also presented.

Modelización de la rotura y fluidificación en geomateriales y geoestructuras

La rotura de las geoestructuras puede ser causada por cambios en las tensiones efectivas debidos bien por cargas externas (terremotos, por ejemplo), bien por variación de las presiones intersticiales (lluvia), o cambios en la geometría (erosión), así como por una disminución de las propiedades resistentes de los materiales (meteorización, ataque químico, etc). El caso particular de los deslizamientos es interesante, existiendo diversas clasificaciones que tienen en cuenta su forma, velocidad de propagación, etc. Dos de estos casos son los deslizamientos propiamente dichos y los flujos. En el primer caso, la deformación se concentra en zonas de pequeño espesor, que se idealiza como una superficie (superficie de rotura). La cinemática de esta rotura se puede considerar como el movimiento relativo de dos masas cuyas deformaciones no son grandes. Este mecanismo está usualmente asociado a materiales sobreconsolidados que presentan reblandecimiento. Los flujos se producen generalmente en materiales de baja densidad y estructura metaestable, con tendencia a compactar, de forma que se generan presiones intersticiales que aumentan el ángulo de rozamiento movilizado, pudiéndose llegar en algunos casos a la licuefacción. Este mecanismo de rotura se conoce como rotura difusa, y no ha sido tan estudiado como el de localización a pesar de se trata frecuentemente de roturas de tipo catastrófico. De hecho, el suelo pasa de un estado sólido a un estado fluidificado, con una gran movilidad. Es importante para el ingeniero predecir tanto el comportamiento de las geoestructuras bajo las cargas de cálculo como las condiciones en las que se producirá la rotura. De esta manera, en algunos casos, se podrán reforzar las zonas más débiles aumentando así su seguridad. En otros casos, no se podrá realizar este refuerzo (grandes deslizamientos como avalanchas, lahares, etc), pero sí se podrán conocer las consecuencias de la rotura: velocidad de propagación, alcance, espesores, etc. La modelización de estos problemas es compleja, ya que aparecen dificultades en los modelos matemáticos, constitutivos o reológicos y numéricos. Dado que en los geomateriales aparece una interacción fuerte entre el esqueleto sólido y los fluidos intersticiales, esto debe ser tenido en cuenta en los modelos matemáticos. En este trabajo se describirán, pues, el desarrollo y aplicación de técnicas avanzadas de modelización; matemática, constitutiva/reológica y numérica. Se dedicará especial atención a los problemas de transición entre suelos y suelos fluidificados, que hoy en día se estudian en una gran mayoría de los casos con modelos diferentes. Así por ejemplo, se emplean modelos constitutivos para el comportamiento previo a la rotura, y reológicos para los materiales fluidificados. En lo que respecta a los modelos matemáticos, existen formulaciones nuevas en velocidades (o desplazamientos), tensiones, y presiones de aire y agua intersticial, de los que se pueden obtener modelos simplificados integrados en profundidad para deslizamientos rápidos. Respecto de los modelos constitutivos, es interesante la teoría de la Plasticidad Generalizada (modelo básico de Pastor-Zienkiewicz y extensiones a suelos no saturados). Se estudiará la extensión de estos modelos elastoplásticos a la viscoplasticidad (Perzyna y consistente), explorando la posibilidad de emplearlos tanto antes como después de la rotura. Finalmente, en lo que a modelos numéricos se refiere, se describirá la implementación de los modelos matemáticos y constitutivos desarrollados en (i) modelos clásicos de elementos finitos, como el GeHoMadrid desarrollado en los grupo investigador M2i al que pertenece el autor de este trabajo, (ii) Métodos de tipo Taylor Galerkin, y (iii) métodos sin malla como el SPH y el Material Point Model. Estos modelos se aplicarán, principalmente a (i) Licuefacción de estructuras cimentadas en el fondo marino (ii) presas de residuos mineros (iii) deslizamientos rápidos de laderas.

Analysis of Meshfree Methods for Lagrangian Fluid-Structure Interaction

In this dissertation a new numerical method for solving Fluid-Structure Interaction (FSI) problems in a Lagrangian framework is developed, where solids of different constitutive laws can suffer very large deformations and fluids are considered to be newtonian and incompressible. For that, we first introduce a meshless discretization based on local maximum-entropy interpolants. This allows to discretize a spatial domain with no need of tessellation, avoiding the mesh limitations. Later, the Stokes flow problem is studied. The Galerkin meshless method based on a max-ent scheme for this problem suffers from instabilities, and therefore stabilization techniques are discussed and analyzed. An unconditionally stable method is finally formulated based on a Douglas-Wang stabilization. Then, a Langrangian expression for fluid mechanics is derived. This allows us to establish a common framework for fluid and solid domains, such that interaction can be naturally accounted. The resulting equations are also in the need of stabilization, what is corrected with an analogous technique as for the Stokes problem. The fully Lagrangian framework for fluid/solid interaction is completed with simple point-to-point and point-to-surface contact algorithms. The method is finally validated, and some numerical examples show the potential scope of applications.

Modelos sin malla en simulación numérica de estructuras aeroespaciales

La presente Tesis Doctoral aborda la introducción de la Partición de Unidad de Bernstein en la forma débil de Galerkin para la resolución de problemas de condiciones de contorno en el ámbito del análisis estructural. La familia de funciones base de Bernstein conforma un sistema generador del espacio de funciones polinómicas que permite construir aproximaciones numéricas para las que no se requiere la existencia de malla: las funciones de forma, de soporte global, dependen únicamente del orden de aproximación elegido y de la parametrización o mapping del dominio, estando las posiciones nodales implícitamente definidas. El desarrollo de la formulación está precedido por una revisión bibliográfica que, con su punto de partida en el Método de Elementos Finitos, recorre las principales técnicas de resolución sin malla de Ecuaciones Diferenciales en Derivadas Parciales, incluyendo los conocidos como Métodos Meshless y los métodos espectrales. En este contexto, en la Tesis se somete la aproximación Bernstein-Galerkin a validación en tests uni y bidimensionales clásicos de la Mecánica Estructural. Se estudian aspectos de la implementación tales como la consistencia, la capacidad de reproducción, la naturaleza no interpolante en la frontera, el planteamiento con refinamiento h-p o el acoplamiento con otras aproximaciones numéricas. Un bloque importante de la investigación se dedica al análisis de estrategias de optimización computacional, especialmente en lo referente a la reducción del tiempo de máquina asociado a la generación y operación con matrices llenas. Finalmente, se realiza aplicación a dos casos de referencia de estructuras aeronáuticas, el análisis de esfuerzos en un angular de material anisotrópico y la evaluación de factores de intensidad de esfuerzos de la Mecánica de Fractura mediante un modelo con Partición de Unidad de Bernstein acoplada a una malla de elementos finitos. ABSTRACT This Doctoral Thesis deals with the introduction of Bernstein Partition of Unity into Galerkin weak form to solve boundary value problems in the field of structural analysis. The family of Bernstein basis functions constitutes a spanning set of the space of polynomial functions that allows the construction of numerical approximations that do not require the presence of a mesh: the shape functions, which are globally-supported, are determined only by the selected approximation order and the parametrization or mapping of the domain, being the nodal positions implicitly defined. The exposition of the formulation is preceded by a revision of bibliography which begins with the review of the Finite Element Method and covers the main techniques to solve Partial Differential Equations without the use of mesh, including the so-called Meshless Methods and the spectral methods. In this context, in the Thesis the Bernstein-Galerkin approximation is subjected to validation in one- and two-dimensional classic benchmarks of Structural Mechanics. Implementation aspects such as consistency, reproduction capability, non-interpolating nature at boundaries, h-p refinement strategy or coupling with other numerical approximations are studied. An important part of the investigation focuses on the analysis and optimization of computational efficiency, mainly regarding the reduction of the CPU cost associated with the generation and handling of full matrices. Finally, application to two reference cases of aeronautic structures is performed: the stress analysis in an anisotropic angle part and the evaluation of stress intensity factors of Fracture Mechanics by means of a coupled Bernstein Partition of Unity - finite element mesh model.

Finite element simulation of dispersion in the Bay of Santander

Two mathematical models are used to simulate pollution in the Bay of Santander. The first is the hydrodynamic model that provides the velocity field and height of the water. The second gives the pollutant concentration field as a resultant. Both models are formulated in two-dimensional equations. Linear triangular finite elements are used in the Galerkin procedure for spatial discretization. A finite difference scheme is used for the time integration. At each time step the calculated results of the first model are input to the second model as field data. The efficiency and accuracy of the models are tested by their application to a simple illustrative example. Finally a case study in simulation of pollution evolution in the Bay of Santander is presented

Yield, nutrient utilization and soil properties in a melon crop amended with wine-distillery waste

In Spain, large quantities of wine are produced every year (3,339,700 tonnes in 2011) (FAO, 2011) with the consequent waste generation. During the winemaking process, solid residues like grape stalks are generated, as well as grape marc and wine lees as by-products. According to the Council Regulation (EC) 1493/1999 on the common organization of the wine market, by-products coming from the winery industry must be sent to alcohol-distilleries to generate exhausted grape marc and vinasses. With an adequate composting treatment, these wastes can be applied to soils as a source of nutrients and organic matter. A three-year field experiment (2011, 2012 and 2013) was carried out in Ciudad Real (central Spain) to study the effects of wine-distillery waste compost application in a melon crop (Cucumis melo L.). Melon crop has been traditionally cultivated in this area with high inputs of water and fertilizers, but no antecedents of application of winery wastes are known. In a randomized complete block design, four treatments were compared: three compost doses consisted of 6.7 (D1), 13.3 (D2) and 20 t compost ha-1 (D3), and a control treatment without compost addition (D0). The soil was a shallow sandy-loam (Petrocalcic Palexeralfs) with a depth of 0.60 m and a discontinuous petrocalcic horizon between 0.60 and 0.70 m, slightly basic (pH 8.4), poor in organic matter (0.24%), rich in potassium (410 ppm) and with a medium level of phosphorus (22.1 ppm). During each growing period four harvests were carried out and total and marketable yield (fruits weighting <1 kg or visually rotten were not considered), fruit average weight and fruit number per plant were determined. At the end of the crop cycle, four plants per treatment were sampled and the nutrient content (N, P and K) was determined. Soil samplings (0-30 cm depth) were carried before the application of compost and at the end of each growing season and available N and P, as well as exchangeable K content were analyzed. With this information, an integrated analysis was carried out with the aim to evaluate the suitability of this compost as organic amendment.

Vacíos urbanos en la ciudad de Zaragoza (1975-2010). Oportunidades para la estructuración y continuidad urbana

La expansión de las ciudades hacia la periferia en las últimas décadas ha generado una serie de tejidos en colisión, donde los intersticios y los espacios residuales muestran la realidad de una ciudad dispersa. A esta serie de espacios intermedios los denominaremos “vacíos urbanos” y determinaremos una serie de factores que hagan posible su identificación Los vacíos urbanos son el objeto de la Tesis. El concepto “vacío urbano” adquiere un determinado significado para la investigación y se acota formulando una serie de parámetros para su definición. Definiremos los “vacíos urbanos” como espacios que han aparecido en el extrarradio de las ciudades, fruto de una expansión sin precedentes de las áreas urbanas. Han surgido como lugares residuales condicionados por elementos naturales o por infraestructuras, ligados a una temporalidad incierta, no inmersos en la dinámicas urbanas o habiendo perdido su funcionalidad. El objetivo de esta investigación es localizar y clasificar los vacíos existentes en la ciudad partiendo de la hipótesis de que es posible establecer una metodología para su reconocimiento y comprobación de los parámetros que los definen. La investigación centra su estudio en la ciudad de Zaragoza, como un ejemplo paradigmático, confirmando que la nueva fenomenología territorial, no sólo se manifiesta en dicha ciudad y en las áreas en concreto donde se ha estudiado, sino que más bien se trata de observarla como una serie de modelos tipológicos que respondan a un proceso de análisis. La propuesta metodológica de loa tesis pasa por reconocerlos, mostrarlos y darles una visibilidad que permita su clasificación, el desarrollo de un estudio de Áreas de la ciudad donde se localizan y un análisis de cada tipología de vacío urbano. Como instrumento metodológico se ha elaborado una detallada cartografía a diferentes escalas. La realización de los planos ha sido el medio de análisis que ha permitido localizar e interpretar los vacíos, complementado con unas escogidas fotografías de estos entornos. La metodología se convierte en un modo de descubrir y analizar los vacíos, el proceso conlleva la comprobación y la clasificación en una tipología. Según se han ido analizando nuevas áreas, se confirma como un hecho repetitivo exitoso y se observa que es aplicable a otras áreas urbanas de similares características, donde se den las condiciones principales de cada tipo. En general, deberán ser espacios localizados en la periferia de núcleos urbanos donde aparezcan fenómenos ligados a una expansión discontinua. Parece probable que el futuro de la ciudad se tenga que resolver en las próximas décadas sobre su actual extensión; bajo este supuesto, es trascendente la función que los vacíos puedan desempeñar en el futuro desarrollo urbano. Toda posibilidad de intervención precisará de una necesaria reinterpretación, puestas las miras en su potencial como elementos capaces de generar una rehabilitación urbana. A su vez se hace conveniente plantear una reflexión sobre estos espacios cargados de una dimensión social y cultural, como lugares capaces de articular y dotar de identidad al medio urbano. Los vacíos deberían protagonizar un papel relevante en la estructuración urbana, abriendo posibilidades para el tramado de la ciudad desde nuevas perspectivas. Una apuesta para que estos espacios libres pasen de ser el objetivo de procesos urbanizadores tradicionales, a ser considerados como oportunos elementos vertebradores de los entornos periurbanos, colaborando en el objetivo de una ciudad contemporánea sostenible. ABSTRACT In the last decades the city periphary expansion has provoked a series of matters to collide, where interstices and waste lands show the reality of a divided city. We shall determine a number of factors allowing us to treat these “in between” spaces, also called "urban voids" as identifiable elements. We will consider them the subject of the thesis and establish them as a "concept", delimiting the meaning of the research specifically acquired, defining, and formulating a set of parameters. "Urban voids" are defined as spaces that have appeared on the outskirts of cities, the result of an unprecedented expansion of urban areas. They have emerged as waste lands, conditioned by natural elements or infrastructure, related to uncertain temporality, not immersed in the urban dynamics, or having lost their functionality. It seems likely that in the upcoming decades, the future of the city will have to resolve its current way of expanding . It is under this assumption that urban voids, as intermediate spaces, will play an important role in future urban developments. Any possible intervention will require a necessary reinterpretation, closely watching their potential as elements capable of generating an urban rehabilitation. At the same time, we wish to reflect on these spaces, in many cases loaded with a social and cultural dimension, as places able to articulate and give identity to the urban environment. Based on the hypothesis that it is possible to establish a methodology for recognition and verification, the purpose of this research is to locate and classify the existing urban voids in the city. The research focuses its study on the city of Saragossa which can be seen as a paradigmatic example. The objective is to confirm that this new territorial phenomenology, not only manifests itself in Saragossa and specific areas under study, but also, can be observed as a series of typological models that respond to a review process. The methodological proposal will recognize, demonstrate, and exhibit these urban voids, in a light that will allow us to classify them, examine the different areas where they can be found, and develop a tipology analysis of each type of urban void found. The technical tool used in this research is a detailed mapping at different scales. A realization of plans, as a mean of analysis, supplemented with a few selected pictures of these environments, will facilitate the location and interpretation of these voids. This scholarly approach to discover and analyze urban voids will involve checking and classifying them in a typology. It has been confirmed as a successful constant regulator while exploring new areas. It will be apply to other urban areas with similar characteristics, that is, spaces located on the periphery of urban areas where expansion is linked to the appearence of discontinuous phenomena. The urban voids play a fundamental role within the urban structure, providing the city a weaving scheme with opportunities of fresh perspectives. The challenge for these free spaces is to move from being the consequence of traditional urban development processes, to being considered opportune backbone elements of peri-urban environments, and to finally contribute to the objectives of a sustainable contemporary city.