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On lattice Boltzmann method for solving fluid-structure interaction problemsValdez, Andrés Ricardo 18 September 2017 (has links)
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Previous issue date: 2017-09-18 / Neste trabalho são apresentados aspectos de modelagem computacional para o estudo de Interação Fluido-Estrutura (FSI). Numericamente, o Método de Lattice Boltzmann (LBM) é usado para resolver a mecânica dos fluidos, em particular as equações de Navier-Stokes incompressíveis. Neste contexto, são abordados problemas de escoamentos complexos, caracterizado pela presença de obstáculos. A imposição das restrições na interface fluido-sólido é feita utilizando princípios variacionais, empregando o Princípio de Balanço de Potências Virtuais (PVPB) para obter as equações de Euler-Lagrange. Esta metodologia permite determinar as dependências entre carregamentos cinematicamente compatíveis e o estado mecânico adotado. Neste sentido, as condições de interface fluido-sólido são abordadas pelo Método de Fronteira Imersa (IBM) visando técnicas computacionais de baixo custo. A metodologia IBM trata o equilíbrio das equações na interface fluido-sólido através da interpolação entre os nós Lagrangianos (sólidos) e os nós Eulerianos (fluidos). Neste contexto, uma modificação desta estratégia que fornece soluções mais precisas é estudada. Para mostrar as capacidades do acoplamento LBM-IBM são apresentados vários experimentos computacionais que demonstram grande fidelidade entre as soluções obtidas e as soluções disponíveis na literatura. / This work presents computational modeling aspects for studying Fluid-Structure Interaction (FSI). The Lattice Boltzmann Method (LBM) is employed to solve the fluid mechanics considering the incompressible Navier-Stokes equations. The flows studied are complex due to the presence of arbitrary shaped obstacles. The obstacles alters the bulk flow adding complexity to the analysis. In this work the Euler-Lagrange equations are obtained employing the Principle of Virtual Power Balance (PVPB). Consequently, the functional dependencies between the mechanical state and every kinematic compatible loadings are established employing variational arguments. This modeling technique allows to study the fluid-solid boundary constraint. In this context the fluid-solid interface is handled employing the Immersed Boundary Method (IBM). The IBM deals with the fluid-solid interface equilibrium equations performing an interpolation of forces between Lagrangian nodes (solid domain) and Eulerian Lattice grid (fluid domain). In this work a different version of this methodology is studied that allows to obtain more accurate solutions. To show the capabilities of the implemented LBM-IBM solver several experiments are done showing the agreement with the benchmarks results available in literature.
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