Análise Matemática do Método SPH via Estudo do Modelo de Ruptura de Barragens
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Data
2017-11-17
Autores
Dias, Neylan Leal
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Universidade Estadual Paulista (Unesp)
Resumo
O estudo dos métodos sem malha tem sido muito atrativo nos últimos anos, devido a suas capacidades de melhor resolver deficiências enfrentadas pelos métodos tradicionais que usam malha. O SPH é um dos primeiros métodos sem malha, por isso vários estudos têm sido feitos para seu melhor desenvolvimento. Uma das aplicações clássicas em dinâmica dos fluidos é a ruptura de barragens. Uma das problemáticas enfrentadas na aplicação da ruptura de barragem é a recuperação do campo de velocidades e de pressão. O objetivo deste trabalho é analisar as correções aplicadas ao SPH a m de suavizar as oscilações dos campos de velocidades e do campo de pressões, usando a viscosidade artificial e as correções dos filtros de densidade Shepard e MLS, por meio do software SPHysics. Além disso, foi feita uma comparação dos resultados simulados com resultados de laboratório. As correções aplicadas se mostraram eficientes na recuperação dos campos propostos. Quando comparados os resultados simulados para o escoamento do fluido com os resultados laboratoriais, foram obtidas boas aproximações, com diferenças percentuais baixas.
The study of the meshless methods have been very attractive in recent years due to their ability to better address shortcomings faced by traditional mesh based methods. SPH is one of the first meshless methods, so several studies have been done for its best development. One of the classic applications in fluid dynamics is the dam break problem, which has been the subject of much research using the SPH method. One of the difficulties faced in the application of dam break is the recovery of velocity and pressure fields. The objective of this work is to analyze the corrections applied to SPH in order to smooth and better recover the velocity and pressure fields, using artificial viscosity and the corrections of the Shepard and MLS density filters, through the SPHysics software. In addition, a comparison between simulated and available experimental results is made in order to validate the study. The applied corrections were efficient for recovering the mentioned fields. The comparisons showed very good agreement, that is, very low percentage differences.
The study of the meshless methods have been very attractive in recent years due to their ability to better address shortcomings faced by traditional mesh based methods. SPH is one of the first meshless methods, so several studies have been done for its best development. One of the classic applications in fluid dynamics is the dam break problem, which has been the subject of much research using the SPH method. One of the difficulties faced in the application of dam break is the recovery of velocity and pressure fields. The objective of this work is to analyze the corrections applied to SPH in order to smooth and better recover the velocity and pressure fields, using artificial viscosity and the corrections of the Shepard and MLS density filters, through the SPHysics software. In addition, a comparison between simulated and available experimental results is made in order to validate the study. The applied corrections were efficient for recovering the mentioned fields. The comparisons showed very good agreement, that is, very low percentage differences.
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Palavras-chave
Smoothed Particle Hydrodynamicsen, Filtro de densidade Shepard e Moving Least Squares, Ruptura de barragem, SPHysics, Shepard density filters and Moving Least Squares, Dam Break