Doctorado en Ingeniería Matemática (tesis)
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Ítem A Class of Conservative Lagrangian-Eulerian Methods on Triangular Grids for Hyperbolic Problems : Design, Analysis and Applications(Universidad EAFIT, 2024) Agudelo Quiceno, Jorge Eliécer; Pérez Sepúlveda, John Alexander; Cano Sánchez, José AlbeiroIn this thesis, we construct, analyze and implement a class of fully-discrete and semi-discrete schemes on triangular grids intended to numerically solve initial value problems involving multidimensional hyperbolic conservation and balance laws, both scalar and systems. The construction of this novel class of schemes is based on the no-flow surface/curve concept and introduces an effective class of numerical fluxes that do not require constructing or evaluating the Jacobian matrix of the respective flux functions. The implementation of the new fully-discrete and semi-discrete Lagrangian-Eulerian schemes, , in the solution of nontrivial scalar and systems problems, is performed using a weak CFL-type stability condition that is independent of the eigenvalues (exact and approximate values) of the relevant Jacobian of the numerical flux functions, and without the need for high-resolution reconstruction procedures.Ítem Data assimilation in a lotos-euros chemical transport model for Colombia using satellite measurements(Universidad EAFIT, 2023) Yarce Botero, Andrés; Quintero Montoya, Olga Lucía; Heemink, ArnoldWhen considering air quality, notably in South America, it seems that we are falling behind more developed regions in exacerbating the issue. This shortfall serves not just as observation, but as a warning, as air quality problems here are rapidly escalating. Nevertheless, by examining how other countries have addressed similar issues, we can prepare ourselves to tackle our own challenges. In this thesis we demonstrate how utilizing Data Assimilation DA we can reduce the uncertainty in some model uncertain parameters in an air quality model such as the LOTOS-EUROS Chemical Transport Model (CTM). CTMs are critical for representing reality through numerical simulations of concentrations of atmospheric constituents. These models incorporate various processes, including emissions, transportation, chemical reactions, and deposition. It is imperative to use accurate models as they enable us to understand atmospheric processes better and develop effective solutions to environmental problems, more in regions with scarce measurenments. The LOTOS-EUROS model is employed, whereby the portrayal of reality accounts for uncertainty from multiple sources. To enhance model output, it is crucial to maximise the representativeness of the input information. From a measurement perspective in Colombia, there is an evident scarcity of ground-level equipment to monitor air quality in a comprehensive manner. The principal urban areas are monitored but extensive regions remain unobserved. This is precisely where satellite data, together with cost-effective sensors, prove advantageous by offering a more comprehensive range. Satellite air quality data has become increasingly available and its temporal and spatial resolution improves. However, cloud coverage, particularly around the Andean mountains, often obstructs satellite observations. This dissertation uses TROPOMI satellite-derived NO$_2$ concentrations as the primary data source for assessing air quality in tropical regions. Furthermore, this thesis involved the development of a customised electronic hardware device specifically designed to collect in-situ measurements in a mountainous region, to compare models and perform remote data assimilation experiments. Data assimilation (DA) methods can be divided into two main categories: sequential and variational methods. Sequential methods introduce observations progressively as they become available. On the contrary, variational methods adopt a wider perspective by assimilating observations over a predetermined time frame and refining model accuracy through optimizing a cost function. The 4D Var method is a noteworthy variational method that finds application in atmospheric sciences. The method employs an adjoint model that is a crucial component in enabling the optimization process through the computation of gradients that are vital for minimizing the cost function. The implementation of adjoint models, however, poses significant challenges, involving complex coding and maintenance requirements. These challenges are more pronounced when working in the area of Chemical Transport Model (CTM), where the goal is to significantly improve the physical modelling system based on an adjoint model that is not always available. To overcome the hurdles related to adjoint models, this study explored adjoint-free data assimilation techniques. Adjoint-free methods, such as the 4DEnVar and the Local Ensemble Kalman Filter (LEnKF), employ ensemble propagation within the model to estimate variables, presenting a practical substitute. The research explored parameters that modulate emission model uncertainties as a means to reduce CTM-related uncertainties, given the focus on emissions as a significant contributing factor. Conducting experiments in various urban and rural locations in Colombia enabled a more nuanced comprehension of emission parameters. The innovative use of ensemble-based data assimilation techniques, including the 4DEnVar and LEnKF, along with the incorporation of satellite observations, has substantially enhanced the refinement of emission parameters. The combination of chemical transport models (CTMs), satellite data, low-cost sensors, and data assimilation (DA) has led to significant progress in measuring atmospheric pollutants and forecasting emissions in Colombia. The integration of the LOTOS-EUROS model, improvements in satellite data processing, and alignment of sensors has substantially enhanced the region's atmospheric chemistry modelling capabilities in the region. Moreover, the implemented data assimilation techniques have proven effective in improving the precision of air quality models, strengthening the correlation between model projections and real-world observations.Ítem Vehicle routing optimization in bicycle sharing systems(Universidad EAFIT, 2022) Palacio Domínguez, Juan David; Rivera Agudelo, Juan CarlosÍtem Ensemble-based Data Assimilation For High-uncertainty systems: a case of study with Particulate Matter in the Aburrá Valley(TU Delft, 2021) López Restrepo, Santiago; Quintero Montoya, Olga LucíaÍtem Interval analysis for handling uncertainty in epidemiological models based on ODEs that simulate the transmission of infectious diseases with application to Dengue transmission(Universidad EAFIT, 2021) Lizarralde Bejarano, Diana Paola; Puerta Yepes, Maria Eugenia; Arboleda Sánchez, Sair OrietaÍtem Entropy-based graph construction methods for unsupervised data structure detection(Universidad EAFIT, 2021) Ariza Jiménez, Leandro Fabio; Quintero Montoya, Olga Lucía; Pinel Peláez, Nicolás