Facultad de Ciencias Físicas y Matemáticas
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Browsing Facultad de Ciencias Físicas y Matemáticas by Subject "AGUA limpia y saneamiento"
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Item Assessment of water quality using hyperspectral and multispectral data for the characterization of eutrophication in Lake Villarrica.(Universidad de Concepción, 2026) Cartes Esquivel, Óscar David; Yépez Figueroa, Santiago Paul; Rodríguez López, LienEl lago Villarrica, situado en el sur de Chile, es un recurso vital de agua dulce cuyo estado ecológico requiere una evaluación continua. El control de la calidad de sus aguas es esencial para detectar procesos de eutrofización. La clorofilaa (Chl-a) es un indicador clave de la biomasa de fitoplancton y su estimación mediante sensores satelitales permite un control eficiente y a gran escala. En este estudio se comparó el rendimiento de diferentes modelos empíricos basados en datos de reflectancia obtenidos a partir de imágenes satelitales corregidas atmosféricamente utilizando el software ACOLITE, calibrados con mediciones in-situ de Chl-a recogidas durante las estaciones de primavera y verano entre 2014 y 2024. Para cada sensor, se seleccionó la mejor combinación de bandas espectrales y se generaron modelos utilizando un procedimiento de bootstrapping con 1000 iteraciones para obtener coeficientes de regresión robustos; los modelos finales se definieron utilizando la mediana de estos coeficientes. El modelo con mejor rendimiento para Landsat-8 y 9 se basó en una combinación de bandas azul y roja (R2= 0.79, RMSE = 2.1 μg ·L−1, MAE = 1.2 μg ·L−1, n = 74), mientras que para Sentinel-2, el modelo óptimo utilizó las bandas azul y verde (R2= 0.75, RMSE = 0.8 μg ·L−1, MAE = 0.72 μg ·L−1, n = 112).En general, los resultados obtenidos mediante teledetección revelan un aumento gradual de los niveles de Chl-a durante la última década. Esta tendencia podría estar relacionada tanto con el calentamiento climático como con el aumento de las presiones antropogénicas, lo que refuerza la necesidad de contar con sistemas de vigilancia continua basados en observaciones satelitales. Ampliar la base de datos in-situ de Chl-a, aumentar la disponibilidad de imágenes satelitales e incorporar mediciones de reflectancia in-situ y cámaras multiespectrales es esencial para mejorar la precisión de los modelos y superar los retos que plantean la cobertura nubosa y los aerosoles.Item Métodos de galerkin discontinuos para problemas de interfaz: aplicación a procesos de desalinización del agua.(Universidad de Concepción, 2024) Bermúdez Montiel, Isaac; Solano Palma, Manuel Esteban; Camaño Valenzuela, Jessika PamelaThe aim of this thesis is to develop continuous and discontinuous Galerkin-type discretizations applied to interface problems modelled by systems of partial differential equations (PDEs). The com plexity of these problems lies in the unknowns and their associated source terms arising from coupling interfaces, as well as the non-linearity of the equations. First, we consider a coupled Navier–Stokes/transport system inspired by the modeling of a reverse osmosis effect in water desalination processes when considering feed and permeate channels coupled through a semi-permeate membrane. The variational formulation consists of a set of equations where the velocities and concentrations, along with tensors and vector fields introduced as auxiliary unknowns, and two Lagrange multipliers, are the main unknowns of the system. The latter are introduced to deal with the trace of functions that do not have enough regularity to be restricted to the boundary. In addition, the pressures can be recovered afterwards by a postprocessing formula. As a consequence, we obtain a nonlinear Banach spaces-based mixed formulation, which has a perturbed saddle point struc ture. We analyze the continuous and discrete solvability of this problem by linearizing the perturbation term and applying the classical Banach fixed point theorem along with the Banach–Nečas–Babuška result. Regarding the discrete scheme, feasible choices of finite element subspaces that can be used include Raviart–Thomas spaces for the auxiliary tensor and vector unknowns, piecewise polynomials for the velocities and concentrations, and continuous polynomial space of lowest order for the traces, yielding stable discrete schemes. An optimal a priori error estimate is derived, and numerical results illustrating both, the performance of the scheme confirming the theoretical rates of convergence, and its applicability, are reported. Once we have established the theoretical foundations to ensure the solvability of the variational scheme, we take advantage of them to numerically address different approaches closely related to reverse osmosis processes by considering coupled Brinkman–Forchheimer/transport equations in addition to Navier–Stokes/transport equations. The cases of a single channel and coupled feed/permeate channels are covered. Thus, through diverse numerical simulations and a variety of configurations, we illustrate the capability of the method to accurately capture the behavior of saline water when passing through membrane-based reverse osmosis desalination channels. Onthe other hand, we present and analyze a hybridizable discontinuous Galerkin (HDG) method for coupling Stokes and Darcy equations, whose domains are discretized by two independent triangulations. This causes non-conformity at the intersection of the subdomains or originates a gap (unmeshed region) between them. In order to properly couple the two different discretizations and obtain a high order scheme, we propose suitable transmission conditions based on mass conservation, equilibrium of normal forces, and the Beavers–Joseph–Saffman law. Since the meshes do not necessarily coincide at the interface, we use the Transfer Path Method (TPM) to tie them. We establish the well-posedness of the method and provide error estimates where the influences of the non-conformity and the gap are explicit in the constants. Finally, numerical experiments that illustrate the performance of the method are shown.Item A mixed finite element method for a reverse osmosis model.(Universidad de Concepción, 2025) Burgos Villanueva, Víctor Manuel; Oyarzúa Vargas, Ricardo ElvisWe develop and analyze a numerical method to approximate the solution of a partial differential equation arising from a phenomenological model of water desalination through reverse osmosis within a channel module. The problem involves a coupled nonlinear system that accounts for the steady state of mass transport phenomena via a convection-diffusion equation and linear momentum balance through the Navier-Stokes equation. To address this problem, we introduce a mixed variational formulation based on Banach spaces for both phenomena, utilizing appropriate Lebesgue spaces to define the nonlinear terms and introducing a Lagrange multiplier that couples both phenomena at the boundary. We establish the existence and uniqueness of the solution under smallness assumptions on the physical parameters. We consider conforming subspaces, demonstrate the well-posedness of the discrete formulation, and derive the respective a priori error estimates. Finally, the model is verified against analytical solutions and compared with a related literature study under realistic conditions.