The objective of this PhD research programme is to investigate the effectiveness of a finite volume method incorporating radial basis functions for simulating nonlinear transport processes. The finite volume method is the favoured numerical technique for solving the advection-diffusion equations that arise in transport simulation. The method transforms the original problem into a system of nonlinear, algebraic equations through the process of discretisation. The accuracy of this discretisation determines to a large extent the accuracy of the final solution. A new method of discretisation is presented that employs radial basis functions (rbfs) as a means of local interpolation. When combined with Gaussian quadrature integration methods, the resulting finite volume discretisation leads to accurate numerical solutions without the need for very fine meshes, and the additional overheads they entail. The resulting nonlinear, algebraic system is solved efficiently using a Jacobian-free Newton-Krylov method. By employing the new method as an extension of existing shape function-based approaches, the number of nonlinear iterations required to obtain convergence can be reduced. Furthermore, information obtained from these iterations can be used to increase the efficiency of subsequent rbf-based iterations, as well as to construct an effective parallel reconditioner to further reduce the number of nonlinear iterations required. Results are presented that demonstrate the improved accuracy offered by the new method when applied to several test problems. By successively refining the meshes, it is also possible to demonstrate the increased order of the new method, when compared to a traditional shape function basedmethod. Comparing the resources required for both methods reveals that the new approach can be many times more efficient at producing a solution of a given accuracy.

This study presents a new Lagrangian model for predicting dynamics and transport in rivers and shallow water flows. A hydrostatic model is developed for the prediction of rivers and floodplain flow and lateral interactions between them. The model is extended to the Boussinesq weakly non-linear, non-hydrostatic model for the simulation of solitary waves and undular bores. A model for advection-diffusion transport of tracers in open channel flow is also presented. The simulation results are compared against an analytical solution and published laboratory data, field data and theoretical results. It is demonstrated that the Lagrangian moving grid eliminates numerical diffusion and oscillations; the model is dynamically adaptive, providing higher resolution under the wave by compressing the parcels (grid). It also allows flow over dry beds and moving boundaries to be handled efficiently. The hydrostatic model results have shown that the model accurately simulates wave propagation and non-linear steepening until wave breaking. The model is successfully applied to simulate flow and lateral interactions in a compound channel and flood wave movement in a natural river. The non-hydrostatic model has successfully reproduced the general features of solitary waves such as the balance between non-linearity and wave dispersion and non-linear interactions of two solitary waves by phase-shift. Also, the model successfully reproduced undular bores (high frequency short waves) from a long wave and the predicted maximum height of the leading wave agreed very well with the published results. It is shown that the simple second order accurate Lagrangian scheme efficiently simulates dispersive waves without any numerical diffusion. Lagrangian modeling of advection-diffusion transport of Gaussian tracer distributions, top hat tracer distributions and steep fronts (step function) in steady, uniform flow has provided exact results and has shown that the scheme allows the use of a large time step without any numerical diffusion and oscillations, including for the advection of steep fronts. The scheme can handle large Courant numbers (results are presented for Cr = 0 to 20) and the entire range of grid Peclet numbers from zero to infinity. The model is successfully applied to tracer transport due to flow induced by simple waves, solitary waves and undular bores

Na presente tese é apresentada uma nova solução analítica para a equação de ad-vecção-difusão bidimensional transiente para simular a dispersão de poluentes na atmosfera. Para tanto, a equação de advecção-difusão é resolvida pela combinação da transformada de Laplace e da técnica GILTT (Generalized Integral Laplace Transform Technique). O fechamento da turbulência para os casos Fickiano e não-Fickiano é considerado. É investigado o problema de modelagem da dispersão de poluentes em condições de ventos fortes e fracos considerando, para o caso de ventos fracos, a difusão longitudinal na equação de advecção-difusão. Além disso, foi incluída no modelo a velocidade vertical e avaliada sua influência considerando-se o campo de velocidades constante e também geradas via LES (Large Eddy Simulation), para poder simular uma camada limite turbulenta mais realística. Os resultados obtidos por essa metodologia são validados com resultados experimentais disponíveis na literatura. / In the present thesis it is presented a new analytical solution for the transient two- dimensional advection-diffusion equation to simulate the pollutant dispersion in atmosphere. For that, the advection-diffusion equation is solved combining the Laplace transform and the GILTT (Generalized Integral Laplace Transform Technique) techniques. The turbulence closure for Fickian and non-Fickian cases is considered. It is investigated the problem of modeling the pollutant dispersion in strong and weak winds considering, for the case of low wind conditions, the longitudinal diffusion in the advection-diffusion equation. Moreover, it was considered in the model the vertical velocity and its influence was evaluated considering velocities field constant and also generated by means of LES (Large Eddy Simulation), to simulate a more realistic turbulent boundary layer. The results attained by this methodology are validated with experimental results available in literature.

Na presente tese é apresentada uma nova solução analítica para a equação de ad-vecção-difusão bidimensional transiente para simular a dispersão de poluentes na atmosfera. Para tanto, a equação de advecção-difusão é resolvida pela combinação da transformada de Laplace e da técnica GILTT (Generalized Integral Laplace Transform Technique). O fechamento da turbulência para os casos Fickiano e não-Fickiano é considerado. É investigado o problema de modelagem da dispersão de poluentes em condições de ventos fortes e fracos considerando, para o caso de ventos fracos, a difusão longitudinal na equação de advecção-difusão. Além disso, foi incluída no modelo a velocidade vertical e avaliada sua influência considerando-se o campo de velocidades constante e também geradas via LES (Large Eddy Simulation), para poder simular uma camada limite turbulenta mais realística. Os resultados obtidos por essa metodologia são validados com resultados experimentais disponíveis na literatura. / In the present thesis it is presented a new analytical solution for the transient two- dimensional advection-diffusion equation to simulate the pollutant dispersion in atmosphere. For that, the advection-diffusion equation is solved combining the Laplace transform and the GILTT (Generalized Integral Laplace Transform Technique) techniques. The turbulence closure for Fickian and non-Fickian cases is considered. It is investigated the problem of modeling the pollutant dispersion in strong and weak winds considering, for the case of low wind conditions, the longitudinal diffusion in the advection-diffusion equation. Moreover, it was considered in the model the vertical velocity and its influence was evaluated considering velocities field constant and also generated by means of LES (Large Eddy Simulation), to simulate a more realistic turbulent boundary layer. The results attained by this methodology are validated with experimental results available in literature.

No description available.

Na presente tese é apresentada uma nova solução analítica para a equação de ad-vecção-difusão bidimensional transiente para simular a dispersão de poluentes na atmosfera. Para tanto, a equação de advecção-difusão é resolvida pela combinação da transformada de Laplace e da técnica GILTT (Generalized Integral Laplace Transform Technique). O fechamento da turbulência para os casos Fickiano e não-Fickiano é considerado. É investigado o problema de modelagem da dispersão de poluentes em condições de ventos fortes e fracos considerando, para o caso de ventos fracos, a difusão longitudinal na equação de advecção-difusão. Além disso, foi incluída no modelo a velocidade vertical e avaliada sua influência considerando-se o campo de velocidades constante e também geradas via LES (Large Eddy Simulation), para poder simular uma camada limite turbulenta mais realística. Os resultados obtidos por essa metodologia são validados com resultados experimentais disponíveis na literatura. / In the present thesis it is presented a new analytical solution for the transient two- dimensional advection-diffusion equation to simulate the pollutant dispersion in atmosphere. For that, the advection-diffusion equation is solved combining the Laplace transform and the GILTT (Generalized Integral Laplace Transform Technique) techniques. The turbulence closure for Fickian and non-Fickian cases is considered. It is investigated the problem of modeling the pollutant dispersion in strong and weak winds considering, for the case of low wind conditions, the longitudinal diffusion in the advection-diffusion equation. Moreover, it was considered in the model the vertical velocity and its influence was evaluated considering velocities field constant and also generated by means of LES (Large Eddy Simulation), to simulate a more realistic turbulent boundary layer. The results attained by this methodology are validated with experimental results available in literature.

Neste trabalho foi analisado o comportamento de um solo argiloso compactado (CCL) da Fm. Corumbataí e de um geocomposto bentonítico (GCL) composto por bentonita \'NA\', frente a gradientes hidráulicos e químicos. As propriedades físicas e mineralógicas dos solos foram avaliadas, bem como determinados em ensaios de adsorção em lote os parâmetros das isotermas de Freundlich e Langmuir. Foi desenvolvido um equipamento para avaliar o comportamento membrana e poder calcular o coeficiente de eficiência químico-osmótico (\'ômega\') em ensaio de difusão-membrana. Os ensaios de advecção foram executados com o equipamento já existente no departamento de Geotecnia. Em todos os ensaios foram utilizadas soluções monoiônicas de \'KCL\' e \'CU\'CL IND.2\' 2\'H IND.2\'O\'. O valor do factor de retardamento Rd determinado no ensaio em lote (batch test) foi maior que o Rd medido no ensaio de advecção, enquanto que, no ensaio de difusão-membrana, obteve-se o menor valor de Rd. Tanto o GCL quanto o CCL apresentaram comportamento membrana e geração de pressão osmótica para as soluções utilizadas. No entanto, com a solução de \'K POT.+\' as diferenças de pressão se mantiveram durante o ensaio, enquanto que no caso da solução de \'CU POT.+2\' a pressão induzida no corpo de prova do CCL e do GCL tem um pico e logo diminue até zero. O GCL teve um aumento na condutividade hidráulica, no ensaio de advecção, quando permeado com solução de \'CU POT.+2\'. Este comportamento é atribuído ao colapso da dupla camada difusa das partículas de argila. O CCL não apresentou este comportamento. Os resultados deste trabalho sugerem que o CCL da Fm. Corumbataí tem melhor desempenho como barreira que o GCL, nas condições de laboratório e para as soluções usadas. / In this research the behavior of a compacted clayey liner (CCL) of Corumbataí Fm. and a geosynthetic clay liner (GCL) containing \'NA\'-bentonite, was evaluated in presence of hydraulic and chemical gradients. Physical and mineralogical properties of the soils were determined and batch tests were executed to obtain the adsorption parameters of the Freundlich and Langmuir models. A laboratory apparatus was developed for assessment of the membrane behavior allowing determining the chemico-osmotic efficiency coefficient (\'ômega\') in diffusion-membrane test. The advection test was carried out with existent equipment in geotechnical department. Both tests were performed with single salt \'KCL\' and \'CU\'CL IND.2\' 2\'H IND.2\'O\' solutions. The measured value of the retardation factor (Rd) for the batch test is bigger than the Rd measured in advection test while in the diffusion-membrane test, the Rd obtained is the smallest. Both GCL and the CCL exhibit membrane behavior and they generate osmotic pressure with both solutions. However with \'KCL\' solution the difference of pressure are maintained during the test, while in the case of \'CU POT.+2\' solution the induced pressure across the specimen of CCL and GCL have a peak to after decrease to zero. The GCL had an increase in the hydraulic conductivity for a \'CU POT.+2\' solution in the advection test. This behavior is attributed to the collapse of the diffuse double layers of clay particles. The CCL did not exhibit this behavior. The results of this study suggest that the CCL of Corumbataí Fm. has a better performance as clay barrier tha the GCL, considering the solutions used and in the laboratory conditions.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Advections of shallow cloudiness from ocean toward the continent are often observed after the cold fronts and extratropical cyclones on the Southern South America. Such a process has characteristic persistence of 1-2 days and it may last for periods longer than 3 consecutive days. This study identified 108 cases over the Southern Brazil between 2005 and 2010, which were characterized using NCEP/NCAR reanalysis. A seasonal climatology determined that the higher frequencies of cases were in autumn and summer, and the lower frequencies in spring and winter. The average wind directions that occurred over the Southern Brazil (Southwesterly, Southerly, Southeasterly and Easterly) were due to positioning of the center of the transient anticyclone over three major regions. Based on these results, it was obtained three synoptic patterns at lower and middle-higher levels. A seasonal distribution of those three patterns was also performed. In such mean situations, it was remarkable the displacement of cold air from the Region of Brazil-Malvinas Confluence (BMC) toward the Southern Brazil due to the circulation of the transient high. Along the way, the stable flow suffers low levels instability due to turbulent mixing processes, and heat and moisture fluxes when it passes from cold to warm waters on the BMC. As a consequence, a shallow convection layer develops downstream in the flow with wide support for the formation of stratiform and/or cumuliform cloud cover as it top. The synoptic patterns show the large scale air subsidence as an inhibiting mechanism for the development of a deep convective layer. Still, the cloud cover was enough to generate low intensity precipitation and/or drizzle over the Southern Brazil. The analysis of the precipitating cases showed that the phenomenon affected the coastal zone more frequently, and, sometimes, the inland areas. Mean vertical profiles of the 108 events, and peculiarly the precipitating ones, indicated the presence of a thick dry layer at the middle and upper levels, and a shallow moist layer at lower levels (1000-700 hPa). This study showed the importance of the Region BMC for the regional weather and climate patterns. It is shown that the circulation induced by transient anticyclone is essential for the transport of cold air from the cold to the warm waters in Confluence zone, generating and advecting shallow cloudiness and an unstable moist boundary layer over the South of Brazil. / A advecção de nebulosidade rasa em direção ao continente após a passagem de frentes frias e ciclones extratropicais, pelo Sul da América do Sul, é um fenômeno frequentemente observado, e tem persistência característica de 1-2 dias, podendo durar por períodos superiores a 3 dias consecutivos. O presente estudo identificou sobre o Sul do Brasil 108 casos entre 2005 e 2010, os quais foram caracterizados utilizando reanálises do NCEP/NCAR. Uma climatologia sazonal definiu que as ocorrências foram mais frequentes no outono e no verão, e menores na primavera e no inverno. São apresentadas as direções médias do vento sobre o Sul do Brasil (Sudoeste, Sul, Sudeste e Leste), devido aos posicionamentos do centro do anticiclone sobre três regiões preferenciais. Com base nesses resultados, foram obtidos três padrões sinóticos, bem como suas distribuições sazonais. Evidenciou-se que o deslocamento da massa de ar frio a partir da Região de Confluência Brasil-Malvinas (CBM) em direção ao Sul do Brasil deve-se à ação do anticiclone transiente. Ao longo do percurso, ao passar sobre a CBM da região de águas frias para a região de águas aquecidas, o escoamento estável sofre instabilização em baixos níveis devido à processo de mistura turbulenta, fluxos de calor e umidade. Consequentemente, uma camada rasa de convecção desenvolve-se corrente abaixo do escoamento, com amplo suporte a formação de nebulosidade rasa dos tipos estratiforme e cumuliforme. Os padrões sinóticios mostram a subsidência em grande escala como mecanismo inibidor do desenvolvimento de uma camada convectiva profunda. Mesmo assim, tal cobertura de nuvens foi suficiente para gerar precipitação de fraca intensidade e/ou chuviscos sobre o Sul do Brasil. A análise dos eventos precipitantes mostrou que o fenômeno afetou com maior frequência a zona costeira, e, por vezes, o interior do continente. Perfis termodinâmicos médios dos 108 eventos, e especialmente dos casos precipitantes, indicaram a presença de uma espessa camada de ar seco em níveis médios e superiores, e uma camada rasa de ar úmido em baixos níveis (1000-700 hPa). Neste estudo evidenciou-se a importância da CBM para os padrões de tempo e clima regionais. Mostra-se que a circulação induzida pelo anticiclone transiente é fundamental para o transporte de ar frio da zona de águas frias para as águas quentes na Confluência, gerando e advectando nebulosidade rasa e uma camada limite úmida instável sobre o Sul do Brasil.

Cette thèse a pour objectif la construction de schémas d’ordre élevé et peu diffusifs pour le transport d’un scalaire dans les écoulements à surface libre, en deux ou trois dimensions. On souhaite en particulier obtenir des schémas robustes, qui gardent au niveau discret les propriétés mathématiques de l’équation de transport avec une faible diffusion numérique, et les utiliser sur des cas industriels. Dans ce travail deux méthodes numériques sont envisagées : une méthode aux volumes finis (VF) et une méthode aux résidus distribués (RD). Dans les deux cas, l’équation de transport est résolue avec une approche découplée, qui est la solution la plus avantageuse en termes de précision et de coûts de calcul. Pour ce qui concerne la méthode aux volumes finis, les équations de Saint-Venant couplées à l’équation du transport sont d’abord résolues avec un schéma dit vertex-centred où le flux numérique est approximé avec un solveur de Riemann appelé Harten-Lax-Van Leer-Contact [135]. A partir de cette approche, une formulation découplée est proposée. Cette dernière permet de résoudre l’équation du transport avec un pas de temps plus grand que celui de la formulation couplée. Cette idée a été d’abord proposée pour d’autres schémas dans [13]. Pour augmenter l’ordre de précision en espace, la technique MUSCL [89] est utilisée en combinaison avec l’approche découplée. Finalement, la problématique des zones sèches est abordée. Dans le cas de la méthode aux résidus distribués, les équations de Saint-Venant sont résolues avec une méthode éléments finis, et la méthode RD est utilisée seulement pour discrétiser l’équation du transport, en focalisant l’attention sur les problèmes non stationnaires. L’équation de continuité du fluide discrétisée est employée pour garantir la conservation de la masse et le principe du maximum. Pour obtenir des schémas d’ordre deux dans les problèmes non stationnaires, un schéma prédicteur-correcteur [112] est utilisé, en l’adaptant au cas de concentration moyennée sur la verticale. Une version d’ordre 1 mais peu diffusive, est aussi présentée dans ce travail. De plus, un schéma localement implicite, complètement nouveau, est aussi formulé pour pouvoir traiter le problème des bancs découvrant. Les deux techniques sont validées d’abord sur des cas simples, pour évaluer l’ordre de précision des schémas et ensuite sur des cas plus complexes pour vérifier aussi les autres propriétés numériques. Les résultats montrent que les nouveaux schémas sont à la fois précis et conservatifs, tout en gardant la monotonie comme le prévoient les démonstrations. Un cas d’application industriel est aussi présenté en conclusion. Le schéma prédicteur-correcteur RD est adapté aussi au cas 3D, sans aucun problème théorique nouveau, par rapport au cas 2D. Les propriétés de base des schémas sont validées sur des cas test préliminaires / The purpose of this thesis is to build higher order and less diffusive schemes for pollutant transport in shallow water flows or 3D free surface flows. We want robust schemes which respect the main mathematical properties of the advection equation with relatively low numerical diffusion and apply them to environmental industrial applications. Two techniques are tested in this work: a classical finite volume method and a residual distribution technique combined with a finite element method. For both methods we propose a decoupled approach since it is the most advantageous in terms of accuracy and CPU time. Concerning the first technique, a vertex-centred finite volume method is used to solve the augmented shallow water system where the numerical flux is computed through an Harten-Lax-Van Leer-Contact Riemannsolver [135]. Starting from this solution, a decoupled approach is formulated and is preferred since it allows to compute with a larger time step the advection of a tracer. This idea was inspired by [13]. The Monotonic Upwind Scheme for Conservation Law [89], combined with the decoupled approach, is then used for the second order extension in space. The wetting and drying problem is also analysed and a possible solution is presented. In the second case, the shallow water system is entirely solved using the finite element technique and the residual distribution method is applied to the solution of the tracer equation, focusing on the case of time-dependent problems. However, for consistency reasons the resolution of the continuity equation must be considered in the numerical discretization of the tracer. In order to get second order schemes for unsteady cases a predictor-corrector scheme [112] is used in this work. A first order but less diffusive version of the predictor-corrector scheme is also introduced. Moreover, we also present a new locally semi-implicit version of the residual distribution method which, in addition to good properties in terms of accuracy and stability, has the advantage to cope with dry zones. The two methods are first validated on academical test cases with analytical solution in order to assess the order of the schemes. Then more complex cases are addressed to test the robustness of the schemes and their performance under different flow conditions. Finally a real test case for which real data are available is carried out. An extension of the predictor-corrector residual distribution schemes to the 3D case is presented as final contribution. Even in this case the RD technique is completely compatible with the finite element framework used for the Navier-Stokes equations, thus its extension to the 3D case does not present any extra theoretical problem. The method is tested on preliminary cases

The linear Barotropic Non-Divergent simulation of a vortex on a beta plane is consistent with Willoughby’s earlier shallow-water divergent results in that it produced an unbounded accelerating westward and poleward motion without an asymptotic limit. However, Montgomery’s work which yielded finite linear drift speeds for his completely cyclonic vortex was inconsistent with ours. The nonlinearly-forced streamfunction exhibited a beta-gyre like structure, but with opposite polarity phase to the linear gyres. Utilization of the linear model with time-dependent, but otherwise beta-like, forcing revealed increasing magnitude and phase reversal in the neighborhood of a low cyclonic frequency. Here, the mean bounded vortex has an outer waveguide that supports Vortex Rossby Wave propagation that is faster than the mean flow and confined to a very narrow band of frequencies between zero and the Vortex Rossby Wave cutoff. The low frequency waves constitute the beta-gyre mode described previously by Willoughby.