Šiame darbe nagrinėjamas parametrinių tiesinio programavimo uždavinių sprendimas. Tuo tikslu buvo sukurti Solver ir AMPL taikomieji projektai. Aprašomi projektų realizavimo algoritmai, aptariamos problemos, su kuriomis buvo susidurta kuriant šiuos projektus. Remiantis įvairių parametrinių uždavinių sprendimais lyginami projektų rezultatai bei įvertinamos projektų galimybės. / In this work is analysing parametric linear programming solution of tasks. On this purpose has been created Solver and AMPL projects.There has been described algorithms of the project realization also all the problems has been discussed which came creating these projects. The results of the projects is based on a various tasks of solution of parametric and all projects opportunities has been positive rated.

Em um ambiente de competição e escassez de recursos, sistemas estruturais devem ser projetados levando-se em conta, além da funcionalidade, o custo total de construção e de operação da estrutura, bem como sua capacidade de geração de lucro. Verifica-se, portanto, que a minimização do custo total de um sistema estrutural passa, necessariamente, por uma otimização de parâmetros para o qual o sistema é projetado. Na análise de estruturas destacam-se as vigas, elementos em que a solicitação predominante em geral é a flexão. Além de uma revisão de conceitos de otimização e de seus métodos, este trabalho trata de flexão simples, programação linear e não-linear. São consideradas duas implementações de projeto ótimo para vigas: um exemplo em balanço, com material dado e seção escalonada, e outro para uma viga de concreto armado contínua. No decorrer do trabalho, as aplicações permitiram a utilização dos métodos Simplex e do Gradiente Reduzido Generalizado, conforme o tipo de problema de otimização. Para tanto, foram utilizadas as ferramentas computacionais Solver e Ftool, para otimização e análise estrutural, respectivamente. O trabalho apontou que o uso da otimização mostrou-se vantajoso, dado o vasto campo de aplicações na engenharia de estruturas. As conclusões firmadas propõem sugestões de trabalhos futuros, visando diminuir as simplificações adotadas para o cálculo e estudar modelos que incluam o efeito do cisalhamento, no sentido de torná-los mais próximos da realidade / In an environment of competition and shortage of resources, structural systems must be projected taking into account, over the functionality, the operation and the construction total cost of the structure, besides its capacity of generating profit. There is, therefore, that minimizing the total cost is for, necessarily, an optimization of parameters for which the system is designed. In the structural analysis there are the beams, elements that are subject to bending generally. Above a comprehensive review of concepts and methods of optimization, this work focuses on simple bending, linear and non-linear programming. There are two implementations considered for optimal design of beams: an example of cantilever beam with material given and discontinuous section and another of continuous beam with reinforced concrete. In this work, the applications permitted the use of the Simplex and Generalized Reduced Gradient methods in compliance with the type of optimization problem. Thus, the computational tools Solver and Ftoll were used, for optimization and structural analysis, respectively. The work showed that the use of optimization was beneficial, opening an wide field of applications in structures engineering. The conclusion proposes suggestions for future works in order to reduce the simplifications adopted and shear effect included for become the models closer to reality

Em um ambiente de competição e escassez de recursos, sistemas estruturais devem ser projetados levando-se em conta, além da funcionalidade, o custo total de construção e de operação da estrutura, bem como sua capacidade de geração de lucro. Verifica-se, portanto, que a minimização do custo total de um sistema estrutural passa, necessariamente, por uma otimização de parâmetros para o qual o sistema é projetado. Na análise de estruturas destacam-se as vigas, elementos em que a solicitação predominante em geral é a flexão. Além de uma revisão de conceitos de otimização e de seus métodos, este trabalho trata de flexão simples, programação linear e não-linear. São consideradas duas implementações de projeto ótimo para vigas: um exemplo em balanço, com material dado e seção escalonada, e outro para uma viga de concreto armado contínua. No decorrer do trabalho, as aplicações permitiram a utilização dos métodos Simplex e do Gradiente Reduzido Generalizado, conforme o tipo de problema de otimização. Para tanto, foram utilizadas as ferramentas computacionais Solver e Ftool, para otimização e análise estrutural, respectivamente. O trabalho apontou que o uso da otimização mostrou-se vantajoso, dado o vasto campo de aplicações na engenharia de estruturas. As conclusões firmadas propõem sugestões de trabalhos futuros, visando diminuir as simplificações adotadas para o cálculo e estudar modelos que incluam o efeito do cisalhamento, no sentido de torná-los mais próximos da realidade / In an environment of competition and shortage of resources, structural systems must be projected taking into account, over the functionality, the operation and the construction total cost of the structure, besides its capacity of generating profit. There is, therefore, that minimizing the total cost is for, necessarily, an optimization of parameters for which the system is designed. In the structural analysis there are the beams, elements that are subject to bending generally. Above a comprehensive review of concepts and methods of optimization, this work focuses on simple bending, linear and non-linear programming. There are two implementations considered for optimal design of beams: an example of cantilever beam with material given and discontinuous section and another of continuous beam with reinforced concrete. In this work, the applications permitted the use of the Simplex and Generalized Reduced Gradient methods in compliance with the type of optimization problem. Thus, the computational tools Solver and Ftoll were used, for optimization and structural analysis, respectively. The work showed that the use of optimization was beneficial, opening an wide field of applications in structures engineering. The conclusion proposes suggestions for future works in order to reduce the simplifications adopted and shear effect included for become the models closer to reality

A numerical method for the simulation of compressible turbulent flows is presented. This method includes a novel hybrid grid generation for airfoil cascades and an unstructured mesh flow solver. The mesh tool incorporates a mapping technique and a grid smoothing method. The mapping technique is used to build an initial volume mesh and the grid smoothing method is used to improve the quality of the initial mesh. The grid smoothing is based on the optimization of mesh-quality parameters. The further improvement of the smoothed mesh is achieved by an edge-swapping and node-insertion technique. The unstructured flow solver is developed for a hybrid grid. This flow solver uses a rotational frame of reference. The convective and viscous fluxes are numerically solved by an upwind scheme and an averaged nodal gradient. A higher-order spatial accuracy is achieved by a piece-wise linear reconstruction. An explicit multi-stage method is employed for integration in time. The Menter’s k −τ model is implemented to simulate the turbulence effects. The flow solver is validated against the analytical and experimental results. A parametric study is performed for a high speed centrifugal compressor.

A numerical method for the simulation of compressible turbulent flows is presented. This method includes a novel hybrid grid generation for airfoil cascades and an unstructured mesh flow solver. The mesh tool incorporates a mapping technique and a grid smoothing method. The mapping technique is used to build an initial volume mesh and the grid smoothing method is used to improve the quality of the initial mesh. The grid smoothing is based on the optimization of mesh-quality parameters. The further improvement of the smoothed mesh is achieved by an edge-swapping and node-insertion technique. The unstructured flow solver is developed for a hybrid grid. This flow solver uses a rotational frame of reference. The convective and viscous fluxes are numerically solved by an upwind scheme and an averaged nodal gradient. A higher-order spatial accuracy is achieved by a piece-wise linear reconstruction. An explicit multi-stage method is employed for integration in time. The Menter’s k −τ model is implemented to simulate the turbulence effects. The flow solver is validated against the analytical and experimental results. A parametric study is performed for a high speed centrifugal compressor.

Master of Science / This project aims to develop computational tools for analyzing an underwater acoustic system designed to deter invasive fish species in the Mississippi River Basin. It leverages an established numerical framework (OpenFOAM) and deals with understanding how to model the system. The study prioritizes enhancing the accuracy of the methods developed and ways to improve its computational efficiency.

No description available.

Magíster en Ciencias, Mención Computación / Los tipos refinados (Refinement Types) son una técnica efectiva de verificación basada en lenguajes que extienden la expresividad de los sistemas de tipos tradicionales incluyendo la posibilidad de restringir valores usando predicados lógicos. Sin embargo, como cualquier otra disciplina de tipos expresiva, obligan a los programadores a lidiar con las estrictas restricciones impuestas por los tipos. Esto puede resultar ser demasiado tedioso para los programadores, especialmente en etapas tempranas de desarrollo donde el código cambia constantemente. Nosotros conjeturamos que esta rigidez no deseada puede obstaculizar la adopción de los tipos refinados. Los tipos graduales (Gradual Typing) permiten combinar la flexibilidad de los lenguajes dinámicamente tipados con las garantías otorgadas por los lenguajes estáticamente tipados. Usando tipos graduales, los programadores pueden comenzar un desarrollo con código chequeado completamente de forma dinámica y aprovechar la flexibilidad de las construcciones idiomáticas típicas de los lenguajes dinámicos. A medida que el código se vuelve más estable, el programador o la programadora puede escoger verificar estáticamente ciertas porciones del programa, haciendo precisos los tipos en esos puntos. Finalmente, si lo desea, también puede decidir verificar el código completamente de forma estática. Los sistemas de tipos graduales aseguran una transición suave entre estos distintos niveles de precisión. Esta tesis demuestra como los tipos graduales pueden ser extendidos para soportar los tipos refinados, permitiendo una evolución suave además de interoperabilidad entre tipos simples y tipos lógicamente refinados. Al hacer esto, se atacan dos desafíos previamente inexplorados en la literatura sobre tipos graduales: lidiar con información lógica imprecisa y con la presencia de tipos dependientes. El primer desafío condujo a una noción crucial de localidad para fórmulas, mientras que el segundo desafío terminó en la definición de novedosos operadores relacionados con substitución al nivel de tipos y términos, que identifican nuevas oportunidades para errores en tiempo de ejecución en lenguajes graduales con tipos dependientes. / Este trabajo ha sido parcialmente financiado por CONICYT - PCHA Magíster Nacional 2015-22150894

Nanoluids are colloidal solutions made up of particles of the nanometric scale suspended in a fluid. This type of solution has widespread great interest since the discovery of their particular properties. The Poisson-Nernst Planck system of equations (PNP) is one of the known models for the description of ion transport. This thesis aims to develop a method to solve the PNP equations in space and time for these nanoluids. Additionally, a simulation platform (C++) is developed using an iterative scheme to solve the nonlinear equations resulting from the discretization of the system. After an overview of the literature on the subject, a discussion on the validity of the results obtained through the simulation platform through its comparison with literature and a commercial software package, COMSOL.

It is widely accepted that the accuracy and efficiency of computational fluid dynamics (CFD) simulations is heavily influenced by the quality of the mesh upon which the solution is computed. Unfortunately, the computational tools available for assessing mesh quality remain rather limited. This report describes a methodology for rigorously investigating the interaction between a flow solver and a variety of mesh configurations for the purposes of deducing which mesh properties produce the best results from the solver. The techniques described herein permit a more detailed exploration of what constitutes a quality mesh in the context of a given solver and a desired flow regime. In the present work, these newly developed tools are used to investigate mesh quality as it pertains to a high-order accurate discontinuous Galerkin solver when it is used to compute inviscid and high-Reynolds number flows in domains possessing smoothly curving boundaries. For this purpose, two flow models have been generated and used to conduct parametric studies of mesh configurations involving curved elements. The results of these studies allow us to make some observations regarding mesh quality when the discontinuous Galerkin method is used to solve these types of problems. Briefly, we have found that for inviscid problems, the mesh elements used to resolve curved boundaries should be at least third order accurate. For viscous problems, the domain boundaries must be approximated by mesh elements that are of the same order as the polynomial approximation of the solution if the theoretical order of accuracy of the scheme is to be maintained. Increasing the accuracy of the boundary elements to at least one order higher than the solution approximation typically results in a noticeable improvement in the computed error norms. It is also noted that C1-continuity of the mesh is not required at element interfaces along the boundary.