Finite-volume WENO scheme for viscous compressible multicomponent flows

We develop a shock- and interface-capturing numerical method that is suitable for the simulation of multicomponent flows governed by the compressible Navier–Stokes equations. The numerical method is high-order accurate in smooth regions of the flow, discretely conserves the mass of each component, as well as the total momentum and energy, and is oscillation-free, i.e. it does not introduce spurious oscillations at the locations of shockwaves and/or material interfaces. The method is of Godunov-type and utilizes a fifth-order, finite-volume, weighted essentially non-oscillatory (WENO) scheme for the spatial reconstruction and a Harten–Lax–van Leer contact (HLLC) approximate Riemann solver to upwind the fluxes. A third-order total variation diminishing (TVD) Runge–Kutta (RK) algorithm is employed to march the solution in time. The derivation is generalized to three dimensions and nonuniform Cartesian grids. A two-point, fourth-order, Gaussian quadrature rule is utilized to build the spatial averages of the reconstructed variables inside the cells, as well as at cell boundaries. The algorithm is therefore fourth-order accurate in space and third-order accurate in time in smooth regions of the flow. We corroborate the properties of our numerical method by considering several challenging one-, two- and three-dimensional test cases, the most complex of which is the asymmetric collapse of an air bubble submerged in a cylindrical water cavity that is embedded in 10% gelatin

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

Lagrangian and inertial transport in atmospheric and chaotic flows

This thesis presents a compendium of publications related to transport studies analyzed from the perspective of dynamical systems. The goal is to address the role that particle properties and the flow have on the organization of trajectories and hence the transport. To observe how transport is structured, we focus on the most widely used method: the Finite Time Lyapunov Exponents. These exponents measure the separation rate of the particles starting from nearby initial positions, estimating the hyperbolicity of the trajectories. This method allows us to make a first approach to the problem, obtaining the borders or frontiers between regions with different dynamics given a simplified vision of transport. The transport structures related with this method, are called Lagrangian Coherent Structures. In the first study, the Lagrangian transport in the troposphere was analyzed. The atmospheric flow is characterized by being turbulent in a continuum of spatiotemporal scales. Within these scales, it was observed that there are structures such as the Atmospheric Rivers that maintain a spatial and temporal coherence of the order of days acting as organizers of water vapor transport and therefore dominating the dynamics of the region at the moment they occur. At the same time, the persistence and repetition of these structures, together with all the other tropospheric structures, introduce mixing into the atmosphere. Those areas in middle latitudes where these structures develop have higher mixing variability. This is mainly due to seasonal changes. However, those regions with less variability, such as the equatorial zones, the mixing and its variability on day scales, are mainly associated with inter-annual variability events such as El Ni ˜no or La Ni ˜na or the Intertropical Convergence Zone (ITCZ). In addition, the mixing information of the air masses from a climatic point of view, was used as a predictor of rainfall for the Iberian region. The Atlantic margin is characterized by an intense activity of Atmospheric Rivers, being one of the main causes of precipitation. However, the problem of determining the activity of rainfall months in advance is complex, for this reason the use of new variables as potential predictors is required. It has been obtained that the mixing, in the Atlantic region, is related to the precipitation on the Iberian Peninsula. Addressing on the second study, we focus on the influence of forces on the particles motion so the resolution of motion equation is required to obtain the trajectories they describe. The particles are modeled as small spheres with mass, but the fact that their movement is decoupled from the flow makes their trajectories depend initially on other properties such as the initial velocity. It was observed that this dependence, for certain flows, is even higher than small perturbations in its position, mainly in those regions where there is a high spatial variability of the fluid such as regions with shear. The same happens for bubbles where flotation effects appear. They are very sensitive to the inertial effects and especially to the disturbances of the radius as well as the effects of merging with other bubbles, being especially relevant in the initial instants of the movement. In addition, it has been observed that particles properties and their collective motion play a key role in the synchronization of finite-size chemical oscillators. To experimentally support some of the aforementioned behaviors, experimental data are needed to measure the trajectories of the particles. Particle Tracking Velocimetry (PTV) methods, track the trajectories of individual particles in three-dimensional space. In the last part of this thesis, we present an experimental setup and some preliminary results of trajectories of the particles mentioned above in a high turbulent flow

Water Quality Modeling of Rivers and Lakes

Oxygen depletion, eutrophication, acidification, toxic pollution, poor hygienic state, salinity, and excess suspended matter are among the issues usually included in the concept of water quality problems. This report focuses on inland surface waters, namely on rivers, lakes, and reservoirs, to each of which the problem categories listed above are relevant. The variety of problems, the multidisciplinarity among water quality experts, the wide spectrum of societal water needs, together with the high diversity of computational approaches presently available contribute to the present situation in which applicable methodology is developing from a variety of fronts and directions, among which dynamical, partial differential equation models were taken here in focus. Transport, flow and reaction equations for shallow water bodies are reviewed for 1 and 2-dimensional cases, including an introduction to and illustration of a selection of numerical techniques. Four case studies on eutrophication modeling, and a review and discussion on the application of decision support systems on water quality management are presented thereafter

Numerical modelling of mesoscale atmospheric dispersion

Fall 1992.Includes bibliographical references

Prostorna distribucija koncentracije zagađenja kao rezultat pronosa u ušćima rijeka : disertacija

When addressing water quality issues in coastal zone management, rivers are considered to be among the most significant pathways for waterborne solute transport. On the other hand, estuaries are some of the most productive environments on Earth and multiple interests from different stakeholders put additional pressure on such an ecosystem. Estuaries are thus among the most critical areas for pollution hazard and a lot of research is being conducted in order to ensure their sustainable development. The flow in an estuary is characterized by a mixing process, which results from a combination of small-scale turbulent diffusion and larger-scale variation of mean advective velocities. Scalar concentration in such turbulent flows is a random variable, which requires a statistical approach. This thesis focuses on the development of two analytical methodologies for obtaining concentration statistics of a conservative contaminant generated by a steady river flow in a salt-wedge estuary. Analytically obtained concentration statistics, which include concentration moments, probability density function defined in point, spatially integrated moments, and expected mass fraction, significantly reduce the costs and time needed for obtaining the measured data. Although these analytical models lack the level of detail possessed by sophisticated numerical models, they can generate results within seconds and with little preprocessing. Therefore, the developed analytical models represent screening tools for obtaining concentration statistics of pollution in estuaries, and can be used by stakeholders of different backgrounds. While investigating various validation procedures for the developed analytical models, and using the case study of the Žrnovnica River estuary, near Split, Croatia, several new findings were obtained. For instance, a new model for mean velocity attenuation was proposed and verified. Furthermore, a new proxy concentration was tested and, combined with numerical modeling, it delivered qualitative verification of analytically obtained concentration statistics. The analytical model for point concentration statistics was implemented in a user-friendly computer application (CPoRT) and presented to different stakeholders as a screening tool. Finally, the most important scientific contributions of this thesis are the development of the semi-analytical approach for obtaining concentration statistics in a river-dominated estuary, application of proxy concentration using the salinity data and the introduction of the expected mass fraction as a significant novelty to address the pollution loading to coastal waters.Prilikom analize kakvoće vode u okviru upravljanja obalnim područjima, rijeke se smatraju jednim od najznačajnijih izvora zagađenja. Nadalje, ušća pripadaju najbogatijim ekosustavima na Zemlji, što ih čini podložnima dodatnim pritiscima različitih interesa. Stoga su ušća iznimno osjetljiva područja te se brojna istraživanja provode radi osiguravanja njihova održivog razvoja. Tok u ušćima obilježen je procesom miješanja koje predstavlja rezultat djelovanja turbulentne difuzije na maloj skali te varijabilnosti advektivne srednje brzine na većoj skali. U takvim turbulentnim tokovima skalarna koncentracija jest slučajna varijabla, što zahtijeva odgovarajući statistički pristup. Ova disertacija usredotočena je na razvoj dviju analitičkih metodologija za izračun statističkih parametara koncentracije zagađenja koje je nastalo uslijed konzervativnog i stacionarnog pronosa u stratificiranom u šću. Tako dobiveni parametri uključuju statističke momente koncentracije, pripadajuće funkcije gustoće vjerojatnosti, prostorno integrirane momente koncentracije te funkcije očekivanog udjela mase. Ako se izračunaju analitički, navedene veličine znatno smanjuju moguće troškove mjerenja. Razvijeni analitički modeli nemaju razlučivost poput sofisticiranih numeričkih modela, ali mogu brzo pružiti tražene vrijednosti uz malo pretprocesiranja. Zaključno, navedeni analitički modeli predstavljaju alate za brzu procjenu zagađenja u nekom ušću, te ih kao takve mogu upotrebljavati dionici s različitim predznanjem. Prilikom validacijskih postupaka za razvijene metodologije na pilot-području ušća rijeke Žrnovnice, pored Splita (Hrvatska), došlo je do novih spoznaja. Predložen je i verificiran novi model smanjenja srednje brzine toka. Uz navedeno, predložena je i nova proxy koncentracija (zamjena za koncentraciju zagađenja), koja je u kombinaciji s rezultatima numeričkog modeliranja omogućila kvalitativnu verifikaciju statističkih parametara dobivenih analitičkim modelima. Naknadno je analitički model za izračun točkastih statističkih parametara ugrađen u računalnu aplikaciju (CPoRT), a ista je predstavljena različitim dionicima upravo kao alat za brzu procjenu potencijalnog zagađenja u ušćima. Zaključno, najvažniji znanstveni doprinosi ove disertacije su razvoj polu-analitičkog pristupa za izračun statističkih parametara koncentracije u ušću dominiranom tokom rijeke, primjena proxy koncentracije korištenjem podataka o slanosti, primjena koncepta očekivanog udjela mase kao značajne novine prilikom analize opterećenja zagađenjem na priobalne vode

Modelling the Eddy Pattern in the harbour of Zeebrugge

Hydrodynamic