Parameterization Of Turbulence Models Using 3DVAR Data Assimilation

In this research the 3DVAR data assimilation scheme is implemented in the numerical model DIVAST in order to optimize the performance of the numerical model by selecting an appropriate turbulence scheme and tuning its parameters. Two turbulence closure schemes: the Prandtl mixing length model and the two-equation k-ε model were incorporated into DIVAST and examined with respect to their universality of application, complexity of solutions, computational efficiency and numerical stability. A square harbour with one symmetrical entrance subject to tide-induced flows was selected to investigate the structure of turbulent flows. The experimental part of the research was conducted in a tidal basin. A significant advantage of such laboratory experiment is a fully controlled environment where domain setup and forcing are user-defined. The research shows that the Prandtl mixing length model and the two-equation k-ε model, with default parameterization predefined according to literature recommendations, overestimate eddy viscosity which in turn results in a significant underestimation of velocity magnitudes in the harbour. The data assimilation of the model-predicted velocity and laboratory observations significantly improves model predictions for both turbulence models by adjusting modelled flows in the harbour to match de-errored observations. 3DVAR allows also to identify and quantify shortcomings of the numerical model. Such comprehensive analysis gives an optimal solution based on which numerical model parameters can be estimated. The process of turbulence model optimization by reparameterization and tuning towards optimal state led to new constants that may be potentially applied to complex turbulent flows, such as rapidly developing flows or recirculating flows.

Numerical Simulation Of Sediment Transport And Bedmorphology Around A Hydraulic Structure On A River

Scour around hydraulic structures is a critical problem in hydraulic engineering. Under prediction of scour depth may lead to costly failures of the structure, while over prediction might result in unnecessary costs. Unfortunately, up-to-date empirical scour prediction formulas are based on laboratory experiments that are not always able to reproduce field conditions due to complicated geometry of rivers and temporal and spatial scales of a physical model. However, computational fluid dynamics (CFD) tools can perform using real field dimensions and operating conditions to predict sediment scour around hydraulic structures. In Korea, after completing the Four Major Rivers Restoration Project, several new weirs have been built across Han, Nakdong, Geum and Yeongsan Rivers. Consequently, sediment deposition and bed erosion around such structures have became a major issue in these four rivers. In this study, an application of an open source CFD software package, the TELEMAC-MASCARET, to simulate sediment transport and bed morphology around Gangjeong weir, which is the largest multipurpose weir built on Nakdong River. A real bathymetry of the river and a geometry of the weir have been implemented into the numerical model. The numerical simulation is carried out with a real hydrograph at the upstream boundary. The bedmorphology obtained from the numerical results has been validated against field observation data, and a maximum of simulated scour depth is compared with the results obtained by empirical formulas of Hoffmans. Agreement between numerical computations, observed data and empirical formulas is judged to be satisfactory on all major comparisons. The outcome of this study does not only point out the locations where deposition and erosion might take place depending on the weir gate operation, but also analyzes the mechanism of formation and evolution of scour holes after the weir gates.

Combined Vertical And Lateral Channel Evolution Numerical Modeling

Vertical stream bed erosion has been studied routinely and its modeling is getting widespread acceptance. The same cannot be said with lateral stream bank erosion since its measurement or numerical modeling is very challenging. Bank erosion, however, can be important to channel morphology. It may contribute significantly to the overall sediment budget of a stream, is a leading cause of channel migration, and is the cause of major channel maintenance. However, combined vertical and lateral channel evolution is seldom addressed. In this study, a new geofluival numerical model is developed to simulate combined vertical and lateral channel evolution. Vertical erosion is predicted with a 2D depth-averaged model SRH-2D, while lateral erosion is simulated with a linear retreat bank erosion model developed in this study. SRH-2D and the bank erosion model are coupled together both spatially and temporally through a common mesh and the same time advancement. The new geofluvial model is first tested and verified using laboratory meander channels; good agreement are obtained between predicted bank retreat and measured data. The model is then applied to a 16-kilometer reach of Chosui River, Taiwan. Vertical and lateral channel evolution during a three-year period (2004 to 2007) is simulated and results are compared with the field data. It is shown that the geofluvial model correctly captures all major erosion and deposition patterns. The new model is shown to be useful for identifying potential erosion sites and providing information for river maintenance planning.

Inflation and debt indexation : the equivalence of two alternative schemes for the case of periodic payments

The presence of inflation has induced the financial institutions to implement procedures devised to protect the real values of theirs loans. Two of such procedurcs, the floaaing rale scheme and the monetary correction mechanism, tend to lead to very different streams of payments. However, whenever the floating rate scheme follows the rule of Strict adhercnce to lhe Fisher equation, lhe two procedures are financially equivalent.

Collateral avoids Ponzi schemes in incomplete markets

Without introducing neither debt constraints nor transversality conditions to avoid the possibility of Ponzi schemes, we show existence of equilibrium in an incomplete markets economy with a collateral structure.

On Ponzi schemes in infinite horizon collateralized economies with default penalties

Araujo, Páscoa and Torres-Martínez (2002) showed that, without imposing any debt constraint, Ponzi schemes are ruled out in infinite horizon economies with limited commitment when collateral is the only mechanism that partially secures loans. Páscoa and Seghir (2009) presented two examples in which they argued that Ponzi schemes may reappear if, additionally to the seizure of the collateral, there are sufficiently harsh default penalties assessed (directly in terms of utility) against the defaulters. Moreover, they claimed that if default penalties are moderate then Ponzi schemes are ruled out and existence of a competitive equilibrium is restored. This paper questions the validity of the claims made in Páscoa and Seghir (2009). First, we show that it is not true that harsh default penalties lead to Ponzi schemes in the examples they have proposed. A competitive equilibrium with no trade can be supported due to unduly pessimistic expectations on asset deliveries. We subsequently refine the equilibrium concept in the spirit of Dubey, Geanakoplos and Shubik (2005) in order to rule out spurious inactivity on asset markets due to irrational expectations. Our second contribution is to provide a specific example of an economy with moderate default penalties in which Ponzi schemes reappear when overpessimistic beliefs on asset deliveries are ruled out. Our finding shows that, contrary to what is claimed by Páscoa and Seghir (2009), moderate default penalties do not always prevent agents to run a Ponzi scheme.

Essays on economic regulation

It is known that stock prices of public listed regulated companies react to price revisions by the regulator, and that the information conveyed by this price reaction might be used by the regulator on the contract design. This paper builds on Laffont and Tirole's (1986) regulation model with observable costs to better understand the effects the inclusion of the stock market can have on the regulator-regulated firm relationship. Our numerical simulations show that the inclusion of the market induce more powerful incentive schemes, with higher cost-reducing efforts, smaller informational rent by the firms and higher overall social welfare. In particular, we find that when the regulator is committed, the presence of short-term investors can make the first-best contract feasible, and that in the non-commitment case the market affects the firm's strategy by making it reveal more information about its cost than it normally would.

Um método de linearização local com passo adaptativo para solução numérica de equações diferenciais estocásticas com ruído aditivo

Neste trabalho apresentamos um novo método numérico com passo adaptativo baseado na abordagem de linearização local, para a integração de equações diferenciais estocásticas com ruído aditivo. Propomos, também, um esquema computacional que permite a implementação eficiente deste método, adaptando adequadamente o algorítimo de Padé com a estratégia “scaling-squaring” para o cálculo das exponenciais de matrizes envolvidas. Antes de introduzirmos a construção deste método, apresentaremos de forma breve o que são equações diferenciais estocásticas, a matemática que as fundamenta, a sua relevância para a modelagem dos mais diversos fenômenos, e a importância da utilização de métodos numéricos para avaliar tais equações. Também é feito um breve estudo sobre estabilidade numérica. Com isto, pretendemos introduzir as bases necessárias para a construção do novo método/esquema. Ao final, vários experimentos numéricos são realizados para mostrar, de forma prática, a eficácia do método proposto, e compará-lo com outros métodos usualmente utilizados.

A Numerical method for the semilinear stochastic transport equation

Trabalho apresentado no XXXV CNMAC, Natal-RN, 2014.

A Higher order and stable method for the numerical integration of Random Differential Equations

Trabalho apresentado no Congresso Nacional de Matemática Aplicada à Indústria, 18 a 21 de novembro de 2014, Caldas Novas - Goiás

Numerical integration of coupled stochastic oscillators driven by Random Forces

Trabalho apresentado no International Conference on Scientific Computation And Differential Equations 2015

Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.

Method of numerical correction of errors occasioned by delay of records during the monitoring of environmental variables of interest for animal production

As condições de ambiente térmico e aéreo, no interior de instalações para animais, alteram-se durante o dia, devido à influência do ambiente externo. Para que análises estatísticas e geoestatísticas sejam representativas, uma grande quantidade de pontos distribuídos espacialmente na área da instalação deve ser monitorada. Este trabalho propõe que a variação no tempo das variáveis ambientais de interesse para a produção animal, monitoradas no interior de instalações para animais, pode ser modelada com precisão a partir de registros discretos no tempo. O objetivo deste trabalho foi desenvolver um método numérico para corrigir as variações temporais dessas variáveis ambientais, transformando os dados para que tais observações independam do tempo gasto durante a aferição. O método proposto aproximou os valores registrados com retardos de tempo aos esperados no exato momento de interesse, caso os dados fossem medidos simultaneamente neste momento em todos os pontos distribuídos espacialmente. O modelo de correção numérica para variáveis ambientais foi validado para o parâmetro ambiental temperatura do ar, sendo que os valores corrigidos pelo método não diferiram pelo teste Tukey, a 5% de probabilidade dos valores reais registrados por meio de dataloggers.

Modulação quantizada para sistemas com codificação wavelet sujeitos ao desvanecimento rayleigh

Wavelet coding is an efficient technique to overcome the multipath fading effects, which are characterized by fluctuations in the intensity of the transmitted signals over wireless channels. Since the wavelet symbols are non-equiprobable, modulation schemes play a significant role in the overall performance of wavelet systems. Thus the development of an efficient design method is crucial to obtain modulation schemes suitable for wavelet systems, principally when these systems employ wavelet encoding matrixes of great dimensions. In this work, it is proposed a design methodology to obtain sub-optimum modulation schemes for wavelet systems over Rayleigh fading channels. In this context, novels signal constellations and quantization schemes are obtained via genetic algorithm and mathematical tools. Numerical results obtained from simulations show that the wavelet-coded systems derived here have very good performance characteristics over fading channels

Comparison of methodologies for degree-day estimation using numerical methods

O desenvolvimento de projetos relacionados ao desempenho de diversas culturas tem recebido aperfeiçoamento cada vez maior, incorporado a modelos matemáticos sendo indispensável à utilização de equações cada vez mais consistentes que possibilitem previsão e maior aproximação do comportamento real, diminuindo o erro na obtenção das estimativas. Entre as operações unitárias que demandam maior estudo estão aquelas relacionadas com o crescimento da cultura, caracterizadas pela temperatura ideal para o acréscimo de matéria seca. Pelo amplo uso dos métodos matemáticos na representação, análise e obtenção de estimativas de graus-dia, juntamente com a grande importância que a cultura da cana-de-açúcar tem para a economia brasileira, foi realizada uma avaliação dos modelos matemáticos comumente usados e dos métodos numéricos de integração na estimativa da disponibilidade de graus-dia para essa cultura, na região de Botucatu, Estado de São Paulo. Os modelos de integração, com discretização de 6 em 6 h, apresentaram resultados satisfatórios na estimativa de graus-dia. As metodologias tradicionais apresentaram desempenhos satisfatórios quanto à estimativa de grausdia com base na curva de temperatura horária para cada dia e para os agrupamentos de três, sete, 15 e 30 dias. Pelo método numérico de integração, a região de Botucatu, Estado de São Paulo, apresentou disponibilidade térmica anual média de 1.070,6 GD para a cultura da cana-de-açúcar.