Generalized Discontinuous Multiscale Methods for Flows in Highly Heterogeneous Porous Media

This dissertation is devoted to the development, study and testing of numerical methods for elliptic and parabolic equations with heterogeneous coefficients. The motivation for this study is to meet the need for fast and robust methods for numerical upscaling and simulation of single and multi-phase fluid flow in highly heterogeneous porous media. We consider the multiscale model reduction technique in the framework of the discontinuous Galerkin (DG) and the hybridizable discontinuous Galerkin (HDG) finite element methods. First, we design multiscale finite element methods for second order elliptic equations by applying the symmetric interior penalty discontinuous Galekin finite element method. We propose two different types of finite element spaces on the coarse mesh within DG framework. The first type of spaces is based on a local spectral problem that uses an interior weighted L²-norm and a boundary weighted L²-norm for computing the mass matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. Second, we develop multiscale model reduction methods within the HDG framework. We provide construction of several multiscale finite element spaces (related to the coarse-mesh edges) that guarantee a reasonable approximation on a reduced dimensional space of the numerical traces. In these approaches, we use local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We also provide a general framework for systematic construction of multiscale spaces. By using local snapshots we were able to add local features to the solution space and to avoid high dimensional representation of trace spaces. Further, we extend multiscale finite element methods within HDG method to nonlinear and/or time-dependent problems. These extensions demonstrate the potential of the proposed constructions for some advanced and more practical applications. For most of the proposed methods, we investigate their stability and derive error estimates for the approximate solutions. Furthermore we study the performance of all proposed methods on a representative number of numerical examples. In the numerical tests, we use various permeability data of highly heterogeneous porous media and contrasts ranging from 10³ to 10^6. Since the exact solution is in general unknown, we first generate solutions on a very fine mesh and use them as reference solutions in our tests. The numerical results confirm the theoretical study of the accuracy of the proposed methods and their robustness with respect to the media contrast. Our numerical experiments also show that the proposed methods could be implemented in a practical and efficient way

Error Estimates on Hybridizable Discontinuous Galerkin Methods for Parabolic Equations with Nonlinear Coefficients

HDG method has been widely used as an effective numerical technique to obtain physically relevant solutions for PDE. In a practical setting, PDE comes with nonlinear coefficients. Hence, it is inevitable to consider how to obtain an approximate solution for PDE with nonlinear coefficients. Research on using HDG method for PDE with nonlinear coefficients has been conducted along with results obtained from computer simulations. However, error analysis on HDG method for such settings has been limited. In this research, we give error estimations of the hybridizable discontinuous Galerkin (HDG) method for parabolic equations with nonlinear coefficients. We first review the classical HDG method and define notions that will be used throughout the paper. Then, we will give bounds for our estimates when nonlinear coefficients obey “Lipschitz” condition. We will then prove our main result that the errors for our estimations are bounded

Condições de conservação pós-colheita de frutos de pimentão (Capsicum annum L.)

Two packing types and exponsure to ethylene, in room and refrigerator conditions, were studied for fruits of sweet pepper Agronomico 10G. After 5 day intervals the fruits were weighed. It was concluded that the best temperature range for sweet pepper preservation is 7 to 9°C; at these temperatures, the best packaging was aluminium trays covered with 0,0165 mm PVC film. Potassium permanganate in perforated capsules showed no evident effect as ethylene absorbent. After 30 days fruit losses were very high due to senescence and/or disease incidence.Com o objetivo de verificar a conservação de frutos de pimentão, foi estudada a utilização de dois tipos de embalagem e um seqüestrador de etileno, em condições ambientais e em geladeira. As avaliações foram realizadas a cada cinco dias, obtendo-se as seguintes conclusões: a melhor temperatura para conservação de pimentões situa-se entre 7 e 9°C; o armazenamento de pimentões em bandejas envolvidas com filme de PVC, constitui-se na melhor alternativa para sua conservação, naquela faixa de temperatura. O permanganato de potássio, colocado em cápsulas perfuradas no interior das embalagens, não apresentou efeito evidente como absorvente de etileno. Após 30 dias, foram verificadas perdas de frutos por senescência e/ou pela incidência de doenças

Arsenic in Peruvian rice cultivated in the major rice growing region of Tumbes river basin

Arsenic (As) exposure from surface and groundwater in Peru is being recognised as a 16 potential threat but there are limited studies on As in the food-chain and none on As in 17 Peruvian rice. In this study, we have determined the As content in rice cultivated in the 18 Tumbes river basin located in the northern province of Peru, an area known for extensive rice 19 cultivation. We collected rice and soil samples from agricultural fields, soil was collected 20 using grid sampling technique while rice was collected from the heaps of harvested crop 21 placed across the fields. The average total As concentration in rice was 167.94 ± 71 μg kg-1 22 (n=29; range 68.39-345.31 μg kg-1). While the rice As levels were not highly elevated, the As 23 content of few samples (n=7) greater than 200 μg kg-1 could contribute negatively to human health upon chronic exposure. Average concentration of As in soil was 8.63 ± 7.8 mg kg-1 25 (n=30) and soil to grain transfer factor was 0.025 ± 0.018 for 12 matched samples. Compared 26 to our previous pilot study in 2006 (samples collected from the same agricultural fields but 27 not from exact locations) there was a 41% decrease in As soil concentration in this study. 28 Rice samples collected in 2006 (n=5) had a mean concentration of 420 ± 109 μg kg-1. Our 29 data provides a baseline of rice grain As concentrations in Peruvian province of Tumbes and 30 warrants further studies on factors affecting uptake of As by the rice varieties cultivated in 31 Peru and any potential human health risks

Ley General del Ambiente: Ley Nº 28611. Ley del Marco del Sistema Nacional de Gestión Ambiental: Ley Nº 28245. Reglamento de la Ley Marco del Sistema Nacional de Gestión Ambiental: Decreto Supremo Nº 008 - 2005 - PCM. Ley de creación, organización y funciones del Ministerio del Ambiente: Decreto Legislativo Nº 1013

Principales leyes que enmarcan la gestión, protección y educación ambiental en el ámbito o contexto peruano

Error Estimates on Hybridizable Discontinuous Galerkin Methods for Parabolic Equations with Nonlinear Coefficients

HDG method has been widely used as an effective numerical technique to obtain physically relevant solutions for PDE. In a practical setting, PDE comes with nonlinear coefficients. Hence, it is inevitable to consider how to obtain an approximate solution for PDE with nonlinear coefficients. Research on using HDG method for PDE with nonlinear coefficients has been conducted along with results obtained from computer simulations. However, error analysis on HDG method for such settings has been limited. In this research, we give error estimations of the hybridizable discontinuous Galerkin (HDG) method for parabolic equations with nonlinear coefficients. We first review the classical HDG method and define notions that will be used throughout the paper. Then, we will give bounds for our estimates when nonlinear coefficients obey "Lipschitz" condition. We will then prove our main result that the errors for our estimations are bounded

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