The modelling of the processes of advection and dispersion-diffusion is the most crucial factor in solute transport simulations. It is generally appreciated that the first order upwind difference scheme gives rise to excessive numerical diffusion, whereas the conventional second order central difference scheme exhibits severe oscillations for advection dominated transport, especially in regions of high solute gradients or discontinuities. Higher order schemes have therefore become increasingly used for improved accuracy and for reducing grid scale oscillations. Two such schemes are the QUICK (Quadratic Upwind Interpolation for Convective Kinematics) and TOASOD (Third Order Advection Second Order Diffusion) schemes, which are similar in formulation but different in accuracy, with the two schemes being second and third order accurate in space respectively for finite difference models. These two schemes can be written in various finite difference forms for transient solute transport models, with the different representations having different numerical properties and computational efficiencies. Although these two schemes are advectively (or convectively) stable, it has been shown that the originally proposed explicit QUICK and TOASOD schemes become numerically unstable for the case of pure advection. The stability constraints have been established for each scheme representation based upon the von Neumann stability analysis. All the derived schemes have been tested for various initial solute distributions and for a number of continuous discharge cases, with both constant and time varying velocity fields. The 1-D QUICKEST (QUICK with Estimated Streaming Term) scheme is third order accurate both in time and space. It has been shown analytically and numerically that a previously derived quasi 2-D explicit QUICKEST scheme, with a reduced accuracy in time, is unstable for the case of pure advection. The modified 2-D explicit QUICKEST, ADI-TOASOD and ADI-QUICK schemes have been developed herein and proved to be numerically stable, with the bility sta- region of each derived 2-D scheme having also been established. All these derived 2-D schemesh ave been tested in a 2-D domain for various initial solute distributions with both uniform and rotational flow fields. They were further tested for a number of 2-D continuous discharge cases, with the corresponding exact solutions having also been derived herein. All the numerical tests in both the 1-D and 2-D cases were compared with the corresponding exact solutions and the results obtained using various other difference schemes, with the higher order schemes generally producing more accurate predictions, except for the characteristic based schemes which failed to conserve mass for the 2-D rotational flow tests. The ADI-TOASOD scheme has also been applied to two water quality studies in the U. K., simulating nitrate and faecal coliform distributions respectively, with the results showing a marked improvement in comparison with the results obtained by the second order central difference scheme. Details are also given of a refined numerical representation of flooding and drying of tidal flood plains for hydrodynamic modelling, with the results showing considerable improvements in comparison with a number of existing models and in good agreement with the field measured data in a natural harbour study.

A novel parallel block-based anisotropic adaptive mesh refinement (AMR) technique for multi-block body-fitted grids is proposed and described. Rather than adopting the more usual isotropic approach to mesh refinement, an anisotropic refinement procedure is proposed which allows refinement of grid blocks in each coordinate direction in an independent fashion. This allows for more efficient and accurate treatment of narrow layers and/or discontinuities which occur, for example, in the boundary and mixing layers of viscous flows, and in regions of strong non-linear wave interactions with shocks. The anisotropic AMR technique is implemented within an existing finite-volume framework, which encompasses both explicit and implicit solution methods, and is capable of performing calculations with second- and higher-order spatial accuracy. To clearly demonstrate the feasibility of the proposed technique, it is applied to the unsteady and steady-state solutions of both the advection diffusion equation, as well as the Euler equations, in two space dimensions.

A novel parallel block-based anisotropic adaptive mesh refinement (AMR) technique for multi-block body-fitted grids is proposed and described. Rather than adopting the more usual isotropic approach to mesh refinement, an anisotropic refinement procedure is proposed which allows refinement of grid blocks in each coordinate direction in an independent fashion. This allows for more efficient and accurate treatment of narrow layers and/or discontinuities which occur, for example, in the boundary and mixing layers of viscous flows, and in regions of strong non-linear wave interactions with shocks. The anisotropic AMR technique is implemented within an existing finite-volume framework, which encompasses both explicit and implicit solution methods, and is capable of performing calculations with second- and higher-order spatial accuracy. To clearly demonstrate the feasibility of the proposed technique, it is applied to the unsteady and steady-state solutions of both the advection diffusion equation, as well as the Euler equations, in two space dimensions.

Tendo em vista o aumento considerável da poltúção do ar provocado em grande parte pela industrialização e o aumento da emissão de poluentes resultantes da queima de combustíveis fósseis por veículos automotores, o presente trabalho tem como objetivo melhorar a previsão e o entendimento da dispersão turbulenta atmosférica. Para tanto, apresenta-se, pela primeira vez, uma representação analít ica para a equação de advecção-difusão-reação tridimensional transiente, com perfil de vento e coeficientes de difusão tmbulenta dependentes da altura, que modelam a dispersão de poluentes na atmosfera. A solução da equação é obtida pela combinação do método GILTT ( Generalized Integral Laplace Transform Technique) com o método da Decomposição de Adomian modificado. Consideram-se dois casos para a aplicação do modelo: no primeiro modela-se a dispersão de um poluente secundário formado por uma reação fotoquímica e no segundo caso, utiliza-se o modelo para determinar o campo de concentração de um poluente que sofre perdas e ganhos devido a influência da radiação solar. Para poder realizar essas análises propôs-se uma parametrização para o termo de reação fotoquímica. São apresentados os resultados numéricos e estatísticos, comparandose com os dados da campanha experimental da Usina Termelétrica de Candiota e com os dados de medições realizadas pela Fundação Estadual de Proteção Ambiental Henrique Luiz Roessler (FEPAM). / In view of the considerable increase of air pollution caused largely by industrialization and the increase of emission pollutants resulting from burning of fossil fuels by motor vehicles, the present work aims to improve the prediction and understanding of atmospheric turbu- lent dispersion. Therefore, is presented, for the rst time, an analytical representation to the transient three-dimensional advection-diffusion-reaction equation, with wind pro le and turbulent diffusion coefficients dependent of height, modeling the dispersion of pollutants in the atmosphere. The solution of the equation is obtained by combining of the GILTT method (Generalized Integral Laplace Transform Technique) with the modi ed Adomian Decomposition method. It is considered two cases for the application of the model: in the rst is modeled the dispersion of a secondary pollutant formed by a photochemical reaction, and in the second case the model is used to determine the concentration eld of a pollutant that suffers losses and gains due to the in uence of solar radiation. To realise these analisis a parameterization for the photochemical reaction term is proposed. Numerical and statistical results are presented, comparing with the experimental campaign data of the thermoelectric plant of Candiota and with data from measurements performed by the \Funda c~ao Estadual de Prote c~ao Ambiental Henrique Luiz Roessler" (FEPAM).

Tendo em vista o aumento considerável da poltúção do ar provocado em grande parte pela industrialização e o aumento da emissão de poluentes resultantes da queima de combustíveis fósseis por veículos automotores, o presente trabalho tem como objetivo melhorar a previsão e o entendimento da dispersão turbulenta atmosférica. Para tanto, apresenta-se, pela primeira vez, uma representação analít ica para a equação de advecção-difusão-reação tridimensional transiente, com perfil de vento e coeficientes de difusão tmbulenta dependentes da altura, que modelam a dispersão de poluentes na atmosfera. A solução da equação é obtida pela combinação do método GILTT ( Generalized Integral Laplace Transform Technique) com o método da Decomposição de Adomian modificado. Consideram-se dois casos para a aplicação do modelo: no primeiro modela-se a dispersão de um poluente secundário formado por uma reação fotoquímica e no segundo caso, utiliza-se o modelo para determinar o campo de concentração de um poluente que sofre perdas e ganhos devido a influência da radiação solar. Para poder realizar essas análises propôs-se uma parametrização para o termo de reação fotoquímica. São apresentados os resultados numéricos e estatísticos, comparandose com os dados da campanha experimental da Usina Termelétrica de Candiota e com os dados de medições realizadas pela Fundação Estadual de Proteção Ambiental Henrique Luiz Roessler (FEPAM). / In view of the considerable increase of air pollution caused largely by industrialization and the increase of emission pollutants resulting from burning of fossil fuels by motor vehicles, the present work aims to improve the prediction and understanding of atmospheric turbu- lent dispersion. Therefore, is presented, for the rst time, an analytical representation to the transient three-dimensional advection-diffusion-reaction equation, with wind pro le and turbulent diffusion coefficients dependent of height, modeling the dispersion of pollutants in the atmosphere. The solution of the equation is obtained by combining of the GILTT method (Generalized Integral Laplace Transform Technique) with the modi ed Adomian Decomposition method. It is considered two cases for the application of the model: in the rst is modeled the dispersion of a secondary pollutant formed by a photochemical reaction, and in the second case the model is used to determine the concentration eld of a pollutant that suffers losses and gains due to the in uence of solar radiation. To realise these analisis a parameterization for the photochemical reaction term is proposed. Numerical and statistical results are presented, comparing with the experimental campaign data of the thermoelectric plant of Candiota and with data from measurements performed by the \Funda c~ao Estadual de Prote c~ao Ambiental Henrique Luiz Roessler" (FEPAM).

Desde o importante trabalho de Barth e Frederickson (1990), um certo número de pesquisadores têm estudado o método de Volumes Finitos de alta-ordem k-exato, por exemplo o grupo do Prof. Ollivier-Gooch: Ollivier-Gooch e van Altena (2002), Nejat (2007), Michalak (2009), etc. Outras discretizações espaciais de alta-ordem bastante populares são o método Galerkin Descontínuo e o método de Diferença Espectral; processos iterativos que involucram estes esquemas tem sido acelerados, nos últimos anos, por métodos p-multigrid. Porém, esta aceleração não tem sido aplicada no contexto do método de Volumes Finitos de alta-ordem, pelo menos para conhecimento do autor desta tese. Por isso, o objetivo desta pesquisa é adaptar o p-multigrid desenvolvido por Liang et al. (2009b) no contexto da Diferença Espectral, para o ambiente dos Volumes Finitos estudado pelo Prof. Ollivier-Gooch. A pesquisa começa implementando o solver VF-RK, de Volumes Finitos com avanço Runge-Kutta, para resolver as equações de advecção-difusão e de Euler aplicados a problemas estacionários, por exemplo, o escoamento transônico ao redor do NACA 0012. Depois, estuda-se o método p-multigrid no contexto da Diferença Espectral; o p-multigrid acelera o processo iterativo comutando níveis polinomiais de alta e de baixa-ordem. Após esse estudo, a adaptação ao âmbito dos Volumes Finitos é realizada resultando num p-multigrid relativamente mais simples porque, em contraposição com o p-multigrid para Diferença Espectral, não precisa de operadores de restrição e prolongação para a comunicação entre diferentes níveis polinomiais. A pesquisa conclui com uma comparação com o método de Volumes Finitos de 4a ordem sem p-multigrid (solver VF-RK). Nesse sentido, implementa-se o solver pMG, baseado no p-multigrid proposto, para resolver os problemas estacionários considerados na primeira parte do trabalho; o smoother do p-multigrid é o esquema Runge-Kutta do código VF-RK, e cada problema estacionário é resolvido utilizando diferentes Vciclos procurando sempre soluções de 4a ordem. Os resultados indicam que o método p-multigrid proposto é mais eficiente que o método de Volumes Finitos de 4a ordem sem p-multigrid, isto é, os dois métodos oferecem a mesma precisão mas o primeiro pode levar menos de 50% do tempo de CPU do segundo. / Since Barth and Frederickson\'s important work (Barth e Frederickson, 1990), a number of researchers have studied high-order k-exact Finite Volume method, for example Prof. Ollivier-Gooch\'s group: Ollivier-Gooch e van Altena (2002), Nejat (2007), Michalak (2009), etc. Other quite popular high-order spatial discretizations are the Discontinuous Galerkin methods and the Spectral Difference methods; the iterative processes involving these schemes have been accelerated in recent years by p-multigrid methods. However, this acceleration has not been applied in the context of the high-order Finite Volume method, at least for the knowledge of the author of this thesis. Therefore, the objective of this research is to adapt the p-multigrid developed by Liang et al. (2009b) in the context of Spectral Difference methods, to the environment of Finite Volume studied by Prof. Ollivier-Gooch. This research begins by implementing the solver VF-RK, Finite Volume solver with Runge-Kutta advance, to compute the advection-diffusion equation and Euler equations applied to steady state problems, for example, the transonic flow around NACA 0012. Then, it is studied the p-multigrid method in the context of Spectral Difference schemes; p-multigrid accelerates the iterative process by switching polynomial levels of high- and low-order. After this study, the adaptation to the context of the Finite Volume scheme is performed resulting in a relatively simple p-multigrid because, in contrast to the p-multigrid for Spectral Difference schemes, it doesn\'t need restriction and prolongation operators for communication between different polynomial levels. The research concludes with a comparison with 4th order Finite Volume method without p-multigrid (solver VF-RK). Accordingly, the solver pMG, based on the proposed p-multigrid, is implemented to resolve the steady state problems considered in the first part of the work; the p-multigrid smoother is the Runge-Kutta scheme from VF-RK code, and each steady state problem is solved using different Vcycles, looking for 4th order solutions ever. The results indicate that the proposed p-multigrid method is more efficient than the 4th order Finite Volume method without p-multigrid: the two methods give the same accuracy but the first one can take less than 50% of second one\'s CPU time.

Orientadores: Simone Andrea Pozza, Varese Salvador Timóteo / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Tecnologia / Made available in DSpace on 2018-08-26T20:52:16Z (GMT). No. of bitstreams: 1 Pereira_MatheusFernando_M.pdf: 7089543 bytes, checksum: 5e3fe7245aa3630ebca8dda3ddd08eb3 (MD5) Previous issue date: 2014 / Resumo: Diversas técnicas vêm sendo apresentadas para resolução da equação da difusão, a qual é empregada para estimativas da concentração de poluentes em função do espaço e do tempo, levando-se conta fatores como fonte emissora, condições meteorológicas, características do meio e velocidade em que o poluente é carreado. Neste estudo, foi empregado um algoritmo de passo variável para a resolução da equação da difusão unidimensional e avaliação da influência do parâmetro de heterogeneidade do meio, da velocidade do fluxo e do coeficiente de dispersão na variação da concentração de poluentes em função do espaço e do tempo. As simulações foram realizadas utilizando as mesmas condições iniciais e de contorno adotadas em dois estudos abordados recentemente na literatura, e de acordo com os resultados, verificou-se que características como meios de menor heterogeneidade, baixa velocidade inicial do fluxo e baixo coeficiente de dispersão implicam em menores valores de concentração, facilitando a dispersão de poluentes. O método utilizado é caracterizado pela rápida convergência, simplicidade do código e baixo tempo computacional, podendo ser utilizado como base para resolução da equação da difusão bi e tridimensional / Abstract: Several techniques have been employed for solving advection-diffusion equation, which is used to estimate pollutants concentration as function of time and space, taking account factors such as emission source, meteorological conditions, medium characteristics and the velocity in which pollutant is adduced. In this study, we used an adaptive-step algorithm for solving one-dimensional advection-diffusion equation, and evaluating the influence of medium inhomogeneity parameter, flow velocity and dispersion coefficient in the pollutants concentration variation as function of space and time. Simulations were performed using the same initial and boundary conditions adopted by Kumar et al. (2010) and by Savovic and Djordjevich (2012), and according to the results, it was found that characteristics such as medium of less inhomogeneity, low initial flow velocity and low dispersion coefficient imply in lower concentration and facilitate pollutants dispersion. The method is characterized by rapid convergence, simplicity of the code and low computational time, and it can be used as a basis for solving the two and the three dimensional advection-diffusion equation / Mestrado / Tecnologia e Inovação / Mestre em Tecnologia

There is a growing need to better understand the dynamics of small and medium Mediterranean low-inflow estuaries (LIEs), which is addressed here by characterizing a heat budget and associated heat transfer processes. A one-dimensional deterministic model was developed from the advection-diffusion equation and applied to Morro Bay, CA using 15-minute water property (temperature, salinity, pressure) and meteorological (wind speed and direction, air temperature, relative humidity, air pressure, irradiance) data collected over a two-year period (2020 – 2021). Seasonal variability is observed in meteorological components, water temperature, and salinity. There is strong seasonal variability in head-mouth temperature and salinity differences. Temperature differences peak in summer (daily mean 2.52 ºC, June – Sept.). Daily average salinity difference is 0.33 (hyposaline, Sept. – Apr.) with strongest gradients observed during the winter storm season following enhanced freshwater discharge. Inverse salinity develops intermittently May – Aug. Subtidal heat flux is dominated by surface heating, whose daily average is always positive (heat input). The developed model does not quantify adequate heat export from the estuary, however, a sensitivity analysis indicates that diffusive flux may be a significant heat export component. Excess heat appears to be exported to the ocean, allowing ocean-estuary temperatures to remain similar. Characterizing estuarine dynamics like these enables us to predict how Morro Bay, and other similar estuarine systems, may respond to long and short-term environmental changes, and how these responses influence estuarine circulation and environmental health.

Dans cette thèse, nous analysons une méthode de Galerkine discontinue (GD) et deux estimateurs d'erreur a posteriori pour l'équation d'advection-diffusion-réaction linéaire et stationnaire avec diffusion hétérogène. La méthode GD considérée, la méthode SWIP, utilise des moyennes pondérées dont les poids dépendent de la diffusion. L'analyse a priori montre que la convergence est optimale en le pas du maillage et robuste par rapport aux hétérogénéités de la diffusion, ce qui est confirmé par les tests numériques. Les deux estimateurs d'erreur a posteriori sont obtenus par une analyse par résidus et contrôlent la (semi-)norme d'énergie de l'erreur. L'analyse d'efficacité locale montre que presque tous les estimateurs sont indépendants des hétérogénéités. Le deuxième estimateur d'erreur est plus précis que le premier, mais son coût de calcul est légèrement plus élevé. Cet estimateur est basé sur la construction d'un flux H(div)-conforme dans l'espace de Raviart-Thomas-Nédéléc.

O estudo do transporte de partículas tem uma importância fundamental em diversas áreas de pesquisas como, por exemplo, na formação de gelo em uma aeronave pois pode afetar a sua sustentação e estabilidade. Tamanha é a preocupação com a segurança de vôo que diversos estudos têm sido realizados, resultando em códigos computacionais como o LEWICE nos Estados Unidos, TRAJICE no Reino Unido, ONERA na França e CANICE no Canadá. No Brasil, um dos estudo é feito pela EMBRAER em parceria com algumas instituições. O objetivo deste trabalho é desenvolver um algoritmo que possa ser empregado na trajetória das partículas, utilizando uma formulação euleriana que elimina a dificuldade da semeadura de partículas específica da formulação lagrangiana na determinação da fração de volume da partícula. O método empregado é dos volumes finitos em malhas não-estruturadas cuja principal chave está na reconstrução mínimos quadrados de alta ordem com restrição nos contornos. O desenvolvimento do trabalho engloba 3 etapas: definição da geometria e geração das malhas; utilização de um solver para o tratamento do escoamento do ar e obtenção do campo de velocidade; implementação e utilização do esquema numérico com reconstrução mínimos quadrados de alta ordem para simular o cálculo da fração de volume com imposição de condições limites apropriadas no contorno do corpo. Os resultados dos testes realizados mostram que o esquema numérico com reconstrução mínimos quadrados pode ser empregado na resolução de equações que apresentam uma região de descontinuidade, como é o caso da região de sombra, reduzindo a largura da banda de difusão numérica e overshoots. / The particle transport study has a fundamental importance in diverse research area like in the icing accretion on an aircraft because that can affect its sustentation and stability. The concern is so big that many researches have been carried through, resulting in computational codes like the LEWICE in the United States, TRAJICE in the United Kingdom, ONERA in France and CANICE in Canada. In Brazil, one of the study has been made by the EMBRAER with some institutes. The goal of this work is to develop an algorithm that can be used in the particles trajectory study, using an Eulerian method that eliminates the difficulty particle sowing, particular of the Lagrangian method, in the determination of the droplet fraction volume. This is made by the finite volume method on unstructured meshes whose main key is the high order reconstruction with restriction on the boundary. The development of the work involves 3 stages: geometry definition and mesh generation; using code for the treatment of the air flow and obtained flow velocity; use of the high order numerical scheme least square reconstruction to simulate the droplet fraction volume result with imposition of appropriate limit conditions in the body contour. The realized simulations shown that Least Square method can be used in problem resolution that present descontinuos region like is shadow region reducing numerical diffusion and overshoots.