Análise de aspectos fundamentais de métodos de partículas
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Data
2017-04-10
Autores
Silva, Luciano Pereira da [UNESP]
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Editor
Universidade Estadual Paulista (Unesp)
Resumo
Atualmente, devido ao grande avanço tecnológico, o uso dos métodos de partículas (Meshfree Particle Methods), vem ganhando espaço nas simulações numéricas de escoamentos. O marco inicial foi o método Smoothed Particle Hydrodynamics (SPH) que se mostrou bastante eficiente para problemas de escoamento compressível, mas nem tanto para escoamento incompressível. Rapidamente surgiram estratégias para problemas incompressíveis, como o Incompressible Smoothed Particle Hydrodynamics (ISPH) e o Moving Particle Semi-Implicit (MPS): em ambos os métodos a pressão é atualizada por uma equação de Poisson. Assim, para se obter uma boa aproximação das equações de Navier- Stokes é necessário resolver bem a equação de Poisson. Os métodos de partículas (MPM) estão sendo usados nas mais diversas áreas e seu desenvolvimento e adequação são objetos de pesquisas no momento. O estudo desta dissertação visa uma análise comparativa dos aspectos teóricos do SPH: abordagem euleriana e lagrangiana; o formalismo, que tem como base a representação integral de uma função; discretização por duas aproximações fundamentais que são da função núcleo e por partículas e as respectivas consistências; tratamento de fronteiras e, também, um estudo detalhado sobre a influência da desordem das partículas, preocupação esta bastante recente na literatura e cujo entendimento não está ainda bem sistematizado. Um estudo comparativo, será efetuado por meio da equação de Poisson, que é objeto principal desta dissertação. A análise será feita inicialmente com as partículas fixas, uniformemente distribuídas e comparadas com distribuições perturbadas sem correção de auto ajuste. Além disso, foram desenvolvidos os códigos em Matlab® para e geração das soluções numéricas utilizando partículas desordenadas.
Currently, due to technological advances, the use of meshfree particle methods has high importance in flow numerical simulations. The milestone was the Smoothed Particle Hydrodynamics (SPH) method, which proved quite efficient for problems of compressible flow, but less so for incompressible one. Quickly emerged strategies for incompressible problems, such as Incompressible Smoothed Particle Hydrodynamics (ISPH) and Moving Particle Semi-Implicit (MPS): in both methods the pressure is updated by a Poisson equation. Thus, to obtain a good approximation of the Navier-Stokes equations it is necessary to solve the Poisson equation. Meshfree Particle Methods (MPM) are being used in several areas and their development and adaptation are research matter at the moment. This study will provide a solid expertise in MPM, since it seeks a comparative analysis of theoretical aspects of MPM: Eulerian and Lagrangian approaches; formalism of MPMs that is based on integral representation of a function; discretization by two fundamental approximations that are of the kernel and by particles as well as the respective consistencies; boundary treatment and also a detailed study on the influence of particle disorder, a concern that is quite recent in the literature and whose understanding is not yet well systematized. A comparative study will be carried out through the Poisson equation, which is the main object of this dissertation. The analysis will be done initially with the fixed particles, uniformly distributed and compared with disturbed distributions without correction of self-adjustment. In addition, the codes in Matlab® were developed for the generation of numerical solutions using disordered particles.
Currently, due to technological advances, the use of meshfree particle methods has high importance in flow numerical simulations. The milestone was the Smoothed Particle Hydrodynamics (SPH) method, which proved quite efficient for problems of compressible flow, but less so for incompressible one. Quickly emerged strategies for incompressible problems, such as Incompressible Smoothed Particle Hydrodynamics (ISPH) and Moving Particle Semi-Implicit (MPS): in both methods the pressure is updated by a Poisson equation. Thus, to obtain a good approximation of the Navier-Stokes equations it is necessary to solve the Poisson equation. Meshfree Particle Methods (MPM) are being used in several areas and their development and adaptation are research matter at the moment. This study will provide a solid expertise in MPM, since it seeks a comparative analysis of theoretical aspects of MPM: Eulerian and Lagrangian approaches; formalism of MPMs that is based on integral representation of a function; discretization by two fundamental approximations that are of the kernel and by particles as well as the respective consistencies; boundary treatment and also a detailed study on the influence of particle disorder, a concern that is quite recent in the literature and whose understanding is not yet well systematized. A comparative study will be carried out through the Poisson equation, which is the main object of this dissertation. The analysis will be done initially with the fixed particles, uniformly distributed and compared with disturbed distributions without correction of self-adjustment. In addition, the codes in Matlab® were developed for the generation of numerical solutions using disordered particles.
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Palavras-chave
Simulação, Método de partículas, Smoothed particle hydrodynamics, Desordem das partículas, Consistência, Equação de Poisson, Simulation, Meshfree particle method, Particle disorder, Consistency, Poisson equation