A 2.5D BEM-FEM using a spectral approach to study scattered waves in fluid–solid interaction problems

42nd International Conference on Boundary Elements and other Mesh Reduction Methods, BEM/MRM 2019; ITeCons-University of Coimbra, Coimbra; Portugal; 2 July 2019 through 4 July 2019. - Publicado en WIT Transactions on Engineering Sciences, Volume 126, 2019, Pages 111-123This work presents a two-and-a-half dimensional (2.5D) spectral formulation based on the finite element method (FEM) and the boundary element method (BEM) to study wave propagation in acoustic and elastic waveguides. The analysis involved superposing two dimensional (2D) problems with different longitudinal wavenumbers. A spectral finite element (SFEM) is proposed to represent waveguides in solids with arbitrary cross-section. Moreover, the BEM is extended to its spectral formulation (SBEM) to study unbounded fluid media and acoustic enclosures. Both approaches use Lagrange polynomials as element shape functions at the Legendre–Gauss–Lobatto (LGL) points. The fluid and solid subdomains are coupled by applying the appropriate boundary conditions at the limiting interface. The proposed method is verified by means of a benchmark problem regarding the scattering of waves by an elastic inclusion. The convergence and the computational effort are evaluated for different h-p strategies. Numerical results show good agreement with the reference solution. Finally, the proposed method is used to study the pressure field generated by an array of elastic fluid-filled scatterers immersed in an acoustic mediumMinisterio de Economía y Competitividad BIA2016-75042-C2-1-

Joint PDF modelling of turbulent flow and dispersion in an urban street canyon

The joint probability density function (PDF) of turbulent velocity and concentration of a passive scalar in an urban street canyon is computed using a newly developed particle-in-cell Monte Carlo method. Compared to moment closures, the PDF methodology provides the full one-point one-time PDF of the underlying fields containing all higher moments and correlations. The small-scale mixing of the scalar released from a concentrated source at the street level is modelled by the interaction by exchange with the conditional mean (IECM) model, with a micro-mixing time scale designed for geometrically complex settings. The boundary layer along no-slip walls (building sides and tops) is fully resolved using an elliptic relaxation technique, which captures the high anisotropy and inhomogeneity of the Reynolds stress tensor in these regions. A less computationally intensive technique based on wall functions to represent boundary layers and its effect on the solution are also explored. The calculated statistics are compared to experimental data and large-eddy simulation. The present work can be considered as the first example of computation of the full joint PDF of velocity and a transported passive scalar in an urban setting. The methodology proves successful in providing high level statistical information on the turbulence and pollutant concentration fields in complex urban scenarios.Comment: Accepted in Boundary-Layer Meteorology, Feb. 19, 200

Numerical methods and tangible interfaces for pollutant dispersion simulation

Dissertação apresentada para obtenção do Grau de Doutor em Engenharia do Ambiente, pela Universidade Nova de Lisboa, Faculdade de Ciências e TecnologiaThe first main objective of this thesis is to reduce numerical errors in advection-diffusion modelling. This is accomplished by presenting DisPar methods, a class of numerical schemes for advection-diffusion or transport problems, based on a particle displacement distribution for Markov processes. The development and analyses of explicit and implicit DisPar formulations applied to one and two dimensional uniform grids are presented. The first explicit method, called DisPar-1, is based on the development of a discrete probability distribution for a particle displacement, whose numerical values are evaluated by analysing average and variance. These two statistical parameters depend on the physical conditions (velocity, dispersion coefficients and flows). The second explicit method,DisPar-k, is an extension of the previous one and it is developed for one and two dimensions. Besides average and variance, this method is also based on a specific number of particle displacement moments. These moments are obtained by the relation between the advection-diffusion and the Fokker-Planck equation, assuming a Gaussian distribution for the particle displacement distribution. The number of particle displacement moments directly affects the spatial accuracy of the method, and it is possible to achieve good results for pure-advection situations. The comparison with other methods showed that the main DisPar disadvantage is the presence of oscillations in the vicinity of step concentration profiles. However, the models that avoid those oscillations generally require complex and expensive computational techniques, and do not perform so well as DisPar in Gaussian plume transport. The application of the 2-D DisPar to the Tagus estuary demonstrates the model capacity of representing mass transport under complex flows. Finally, an implicit version of DisPar is also developed and tested in linear conditions, and similar results were obtained in terms of truncation error and particle transport methods. The second main objective of this thesis, to contribute to modelling cost reduction, is accomplished by presenting TangiTable, a tangible interface for pollutant dispersion simulation composed by a personal computer, a camera, a video projector and a table. In this system, a virtual environment is projected on the table, where the users place objects representing infrastructures that affect the water of an existent river and the air quality. The environment and the pollution dispersion along the river are then projected on the table. TangiTable usability was tested in a public exhibition and the feedback was very positive. Future uses include public participation and collaborative work applications.Fundação para a Ciência e Tecnologia - scholarship contract BD/5064/2001 and the research contract MGS/33998/99-0

Solution of the advection equation using finite difference schemes and the method of characteristics

Numerical models are important engineering tools when considering the prediction of pollution transport in a body of water. Such a prediction is achieved by the solution of the advection-diffusion equation. At present, there exist many numerical techniques which can be used to solve the advection-diffusion equation. The major difficulty when considering undertaking such a simulation, is what method should be used to calculate the advection term. It is now accepted that the appropriate method to follow would involve, splitting up this water quality equation into two separate terms, advection and diffusion. By using this process, each term can be solved individually and the numerical difficulties associated with each term, treated separately. This work discusses the various numerical modelling techniques which can be used to solve the advection term. Two-dimensional finite difference schemes, including QUICKEST, are compared with multi-point method of characteristics techniques. These are analysed in terms of solving advection for various distributions of concentration. The adaptation of these schemes to allow for the use of Courant numbers exceeding unity is also explored. The ultimate aim is to develop a numerical scheme which can be implemented in an industrial model

Locating and quantifying gas emission sources using remotely obtained concentration data

We describe a method for detecting, locating and quantifying sources of gas emissions to the atmosphere using remotely obtained gas concentration data; the method is applicable to gases of environmental concern. We demonstrate its performance using methane data collected from aircraft. Atmospheric point concentration measurements are modelled as the sum of a spatially and temporally smooth atmospheric background concentration, augmented by concentrations due to local sources. We model source emission rates with a Gaussian mixture model and use a Markov random field to represent the atmospheric background concentration component of the measurements. A Gaussian plume atmospheric eddy dispersion model represents gas dispersion between sources and measurement locations. Initial point estimates of background concentrations and source emission rates are obtained using mixed L2-L1 optimisation over a discretised grid of potential source locations. Subsequent reversible jump Markov chain Monte Carlo inference provides estimated values and uncertainties for the number, emission rates and locations of sources unconstrained by a grid. Source area, atmospheric background concentrations and other model parameters are also estimated. We investigate the performance of the approach first using a synthetic problem, then apply the method to real data collected from an aircraft flying over: a 1600 km^2 area containing two landfills, then a 225 km^2 area containing a gas flare stack

Multifractal concentrations of inertial particles in smooth random flows

Collisionless suspensions of inertial particles (finite-size impurities) are studied in 2D and 3D spatially smooth flows. Tools borrowed from the study of random dynamical systems are used to identify and to characterise in full generality the mechanisms leading to the formation of strong inhomogeneities in the particle concentration. Phenomenological arguments are used to show that in 2D, heavy particles form dynamical fractal clusters when their Stokes number (non-dimensional viscous friction time) is below some critical value. Numerical simulations provide strong evidence for this threshold in both 2D and 3D and for particles not only heavier but also lighter than the carrier fluid. In 2D, light particles are found to cluster at discrete (time-dependent) positions and velocities in some range of the dynamical parameters (the Stokes number and the mass density ratio between fluid and particles). This regime is absent in 3D, where evidence is that the Hausdorff dimension of clusters in phase space (position-velocity) remains always above two. After relaxation of transients, the phase-space density of particles becomes a singular random measure with non-trivial multiscaling properties. Theoretical results about the projection of fractal sets are used to relate the distribution in phase space to the distribution of the particle positions. Multifractality in phase space implies also multiscaling of the spatial distribution of the mass of particles. Two-dimensional simulations, using simple random flows and heavy particles, allow the accurate determination of the scaling exponents: anomalous deviations from self-similar scaling are already observed for Stokes numbers as small as $10^{-4}$.Comment: 21 pages, 13 figure

Data assimilation for micrometeorological applications with the fluid dynamics model Code_Saturne

Air quality is a major health and environmental issue worldwide. Similarly, the accuracy of wind resource assessment triggers significant economic and environmental repercussions. In order to study these two topics, it is necessary to accurately determine local wind fields using numerical models of micrometeorology. Such simulations are extremely sensitive to meteorological conditions at the domain borders. Up to present, the boundary conditions (BC) were estimated based on the results of larger scale simulations, which provide information that is not accurate enough, or even incomplete, for local scale purposes. As a matter of fact, the lack of knowledge about the BC represents a major source of error and uncertainty for micrometeorological studies.The potential sites for wind farm installation as well as built environments (urban areas or industrial sites) can be equipped with instruments measuring meteorological variables or pollutant concentration. The observations provided by these instruments represent a second source of information, insufficiently exploited for micrometeorological studies. Indeed, the in situ measurements are perturbed by the complex geometrical features on sites and might be difficult to exploit. In order to improve the exactitude and the accuracy of the BC, and consequently of the locale-scale atmospheric simulations, data assimilation (DA) methods, suited to this micrometeorological problem, could be applied to take benefit from the available observations.So far, DA methods have been mainly developed for large-scale meteorology and employed to correct the initial conditions (IC). In order to broaden the application scope of DA to micrometeorology, existing DA methods must be adapted to be able to correct the BC instead of IC.Two of the existing DA methods seem compatible with computational fluid dynamics (CFD) models used for micrometeorology over complex geometries: the back and forth nudging (BFN) algorithm and the iterative ensemble Kalman smoother (IEnKS). We have adapted these two methods, from a theoretical perspective, so as to include the BC in the control variables. The performances of the adapted versions of the BFN algorithm and the IEnKS have first been assessed with a simplified, 1D model of atmospheric flow with two layers, based on the shallow-water equations. The BFN algorithm and the IEnKS have then been tested in 2D and 3D with the atmospheric module of the open-source CFD model Code_Saturne.The first study case with Code_Saturne corresponds to a real application of wind resource assessment in a mountainous region with steep topography where three meteorological masts have been installed during a few months and provided in situ wind observations. The second case is a study of pollutant dispersion in an urban area, based on the measurements of wind and pollutant concentration coming from the ``Mock Urban Setting Test'' field campaign carried out in the USA. In this second case, the turbulence is also included in the BC and thus in the control variables. For both studies, some observations are assimilated and the remaining ones are used to validate the results.The experiences performed for the wind resource assessment study have revealed that the CFD models present too strong nonlinearities (flow recirculation after obstacles) for the BFN algorithm, which is based on a linearity assumption. However, both cases have shown the ability of the IEnKS to reduce the error and the uncertainty of the BC by assimilating a few observations, with operationally affordable computational costs. Consequently, the simulated wind fields with Code_Saturne are also closer to the validation observations and the confidence intervals are reduced. Eventually, the IEnKS allows, in one case to estimate the wind potential, and in the other case to build the pollution maps, with much more exactitude and accuracy.La qualité de l’air est un enjeu sanitaire et environnemental majeur. Par ailleurs, l'estimation précise des potentiels éoliens est la source d’importantes retombées économiques et environnementales. Pour étudier ces deux sujets, il est nécessaire de reconstituer précisément les champs de vent locaux grâce à des modèles numériques de micro-météorologie. Ces simulations sont extrêmement sensibles aux conditions météorologiques aux limites du domaine d’étude. Jusqu’à présent, les conditions aux limites (CL) étaient estimées à partir de simulations à plus grande échelle, qui fournissent des informations imprécises, voire incomplètes pour l’utilisation à micro-échelle. Par conséquent, la méconnaissance des CL représente une source majeure d’erreur et d’incertitude dans les études micro-météorologiques. Les sites susceptibles d’accueillir un parc éolien et les environnements bâtis (quartiers urbains ou sites industriels) peuvent être équipés d’instruments de mesures météorologiques et de concentration de polluants. Les observations fournies par ces instruments constituent une seconde source d’information, jusqu’à ce jour peu exploitée pour les études micro-météorologiques. En effet, étant à l’intérieur du domaine, les observations sont perturbées par la géométrie complexe des sites étudiés. Afin d'améliorer la précision des CL et donc des simulations atmosphériques à l'échelle locale, des méthodes d'assimilation de données (AD) adaptées à cette problématique pourraient permettre de mettre à profit les observations disponibles. Jusqu’à présent, les méthodes d’AD ont été principalement développées pour répondre aux besoins de la météorologie à grande échelle et donc utilisées pour corriger les conditions initiales (CI). Afin d'élargir le champ d'application de l’assimilation de données aux simulations à l’échelle locale, il faut adapter les méthodes d'AD pour qu'elles permettent de corriger les CL plutôt que les CI. Parmi les méthodes d'assimilation de données existantes, deux semblent compatibles avec les modèles de mécanique des fluides atmosphérique (CFD) utilisés pour la micro-météorologie en géométrie complexe : l’algorithme de nudging direct et rétrograde (BFN) et le lisseur de Kalman d’ensemble itératif (IEnKS). Nous avons adapté ces deux méthodes d’un point de vue théorique pour inclure les CL dans les variables de contrôle. Les performances des versions adaptées du BFN et de l'IEnKS ont tout d'abord été étudiées avec un modèle simplifié d’écoulement atmosphérique à deux couches en 1D, basé sur les équations de Saint-Venant. Le BFN et l’IEnKS ont ensuite été testés en deux puis trois dimensions avec le module atmosphérique du modèle open-source de CFD Code_Saturne. Le premier cas d’étude avec Code_Saturne correspond à une application réelle d’estimation de potentiel éolien dans une région montagneuse au relief très accidenté où trois mâts de mesure fournissent des observations de vent. Le second cas d’étude correspond à une étude de dispersion de polluants en milieu urbain, basé sur les observations de vent et de concentration, provenant de la campagne de mesures « Mock Urban Setting Test » aux USA. Dans ce second cas, la turbulence est également incluse dans les conditions aux limites. Dans les deux cas, une partie des observations est utilisée pour l’assimilation et le reste pour la validation des résultats. Les expériences menées sur le premier cas ont révélé que les modèles de CFD présentent des non-linéarités trop fortes (recirculations derrière les obstacles) pour l’algorithme de BFN, fondé sur une hypothèse de linéarité. Les études avec cette méthode n'ont donc pas été poursuivies. En revanche, les deux cas d'étude ont montré la capacité de l'IEnKS à réduire l'erreur et l'incertitude sur les CL grâce à l'assimilation d'une petite dizaine d'observations, en un nombre raisonnable de calculs. Par suite, l'écart entre les champs de vent simulés et les observations de validation est également réduit. De même, l'incertitudesur les simulations est plus faible. Finalement, l'IEnKS permet d'estimer le potentiel éolien dans un cas et les concentrations en polluant dans l'autre, avec beaucoup plus de précision

Determination of characteristic turbulence length scales from large-eddy simulation of the convective planetary boundary layer

Turbulente Austauschprozesse in der atmosphärischen Grenzschicht spielen eine Schlüsselrolle beim vertikalen Impuls-, Energie- und Stofftransport in der Erdatmosphäre. In meso- und globalskaligen Atmosphärenmodellen sind turbulente Austauschprozesse jedoch subskalig und müssen unter Verwendung geeigneter Schliessungsansätze parametrisiert werden. Hierbei spielt die Spezifikation der charakteristischen Turbulenzlängenskala in Abhängigkeit vom Stabilitätszustand der Atmosphäre eine entscheidende Rolle. Gegenwärtig verwendete Ansätze, die auf der Verwendung der turbulenten Mischungslänge für neutrale Schichtung sowie dimensionsloser Stabilitätsfunktionen basieren, zeigen vor allem Defizite im oberen Bereich der konvektiven Grenzschicht sowie in der Entrainmentzone, wo starke vertikale Gradienten auftreten. In der vorliegenden Arbeit wurden hochaufgelöste dreidimensionale Grobstruktursimulationen der trockenen und feuchten Grenzschicht für ein weites Spektrum von Labilitätsbedingungen durchgeführt. Erste und zweite Momente atmosphärischer Strömungsvariablen wurden aus den simulierten hydro- und thermodynamischen Feldern berechnet und diskutiert. Die Spektraleigenschaften turbulenter Fluktuationen der Strömungsvariablen, das raumzeitliche Verhalten kohärenter Strukturen sowie charakteristische Turbulenzlängenskalen wurden abgeleitet. Eine Verifizierung der charakteristischen Turbulenzlängenskalen erfolgte durch Vergleich mit Ergebnissen früherer numerischer Simulationen, mit Turbulenzmessungen in der atmosphärischen Grenzschicht sowie mit Laborexperimenten. Mit Hilfe der nichtlinearen Datenmodellierung wurden leicht verwendbare Approximationen der charakteristischen Turbulenzlängenskalen abgeleitet und deren statistische Signifikanz diskutiert. Unter Verwendung dieser Approximationen wurde ein existierendes Parametrisierungsmodell revidiert und mit Hilfe von Grobstruktursimulationen verifiziert. Desweiteren wurde der Einfluß der turbulenten Mischungslänge auf die Prognose mesokaliger Felder untersucht. Hierzu wurde mit dem Lokal-Modell des Deutschen Wetterdienstes eine entsprechende Sensitivitätsstudie durchgeführt. Anhand von Satellitendaten und Analysedaten aus der 4D-Datenassimilation wurden die Simulationsergebnisse verifiziert

Acoustic waves scattered by elastic waveguides using a spectral approach with a 2.5D coupled boundary-finite element method

This work presents a two-and-a-half dimensional (2.5D) spectral formulation based on the finite element method (FEM) and the boundary element method (BEM) to study wave propagation in acoustic and elastic waveguides. The analysis involved superposing two dimensional (2D) problems with different longitudinal wavenumbers. A spectral finite element (SFEM) is proposed to represent waveguides in solids with arbitrary cross-section. Moreover, the BEM is extended to its spectral formulation (SBEM) to study unbounded fluid media and acoustic enclosures. Both approaches use Lagrange polynomials as element shape functions at the Legendre–Gauss–Lobatto (LGL) points. The fluid and solid subdomains are coupled by applying the appropriate boundary conditions at the limiting interface. The proposed method is verified by means of two benchmark problems: wave propagation in an unbounded acoustic medium and the scattering of waves by an elastic inclusion. The convergence and the computational effort are evaluated for different strategies. Numerical results show good agreement with the reference solution. Finally, the proposed method is used to study the pressure field generated by an array of elastic fluid-filled scatterers immersed in an acoustic mediumMinisterio de Economía y Competitividad BIA2016-75042-C2-1-RFondos FEDER POCI-01-0247-FEDER-01775

Numerical simulation of oil spills in coastal areas using shallow water equations in generalised coordinates

The pollution generated by accidental marine oil spills can cause persistent ecological disasters and lead to serious social and economical damages. Numerical simulations are a valuable tool to make proper decisions in emergency situation or to plan response actions beforehand. The main objective of this work was to improve SIMOIL, a computational model developed earlier at URV and capable of predicting the evaporation and spreading of massive oil spills in coastal areas. Specifically, a new coastal current model, based on the resolution of the shallow water equations in generalised coordinates, has been developed and validated and then coupled to SIMOIL. The model was specially designed to describe coastal oceanic flows over topography accounting for Coriolis force, eddy viscosity, seabed friction and to couple with SIMOIL in domain with complex boundaries. The equations have been discretized over generalised domains by means of finite differences of second order accuracy. The code was then implemented in FORTRAN. The code has been validated extensively against numerical and experimental flow studies of the bibliography. Finally, the new complete version of SIMOIL, coupling the shallow water model and the oil slick model, has been applied to the study of two accidental oil spills: • A massive leakage from the Repsol's floating dock in the port of Tarragona • The biggest oil spill ever occurred in the Eastern Mediterranean Sea: the 2006 Lebanon oil spill. In both cases, the new version of SIMOIL, demonstrate more accurate predictions of the behaviour of the oil spill, specially for moderate winds with complex topography.La contaminación generada por los vertidos accidentales de petróleo puede ser reducida si se actúa y si se toman las decisiones adecuadas a tiempo. Las simulaciones numéricas de vertidos de petróleo permiten predecir la evolución de las manchas de crudo. En este trabajo, el objetivo principal era de mejorar la precisión y el rango de aplicación del código SIMOIL desarrollando e integrando al código un modelo de predicción de corrientes marinas en aguas costeras. Se han derivado las ecuaciones de aguas poco profundas en coordenadas generalizadas. Se han discretizado las ecuaciones y el código se implementó en FORTRAN 90. El modelo así como los métodos numéricos han sido validados con el estudio de flujos experimentales y numéricos de la bibliografía. Finalmente, la nueva versión de SIMOIL se aplicó con éxito a dos casos físicos de vertidos de crudo: • un vertido ficticio desde la monoboya de descarga de Repsol en el puerto de Tarragona • un vertido real, el mas grande ocurrido en el Este del mar Mediterráneo, consecuencia de la guerra en Líbano en julio de 2006. En ambos casos la nueva versión de SIMOIL proporcionó predicciones más precisas, especialmente para vientos moderados y topografías complejas