Immersed boundary methods are a class of techniques in computational fluid dynamics where the Navier-Stokes equations are simulated on a computational grid that does not conform to the interfaces in the domain of interest. This facilitates the simulation of flows with complex moving and deforming geometries without considerable effort wasted in generating the mesh. The first part of this dissertation is concerned with the aerodynamics of the cross-section of a species of flying snake, Chrysopelea paradisi (paradise tree snake). Past experiments have shown that the unique cross-section of this snake, which can be described as a lifting bluff body, produces an unusual lift curve--with a pronounced peak in lift coefficient at an angle of attack of 35 degrees for Reynolds numbers 9000 and beyond. We studied the aerodynamics of the cross-section using a 2-D immersed boundary method code. We were able to qualitatively reproduce the spike in the lift coefficient at the same angle of attack for flows beyond a Reynolds number of 2000. This phenomenon was associated with flow separation at the leading edge of the body that did not result in a stall. This produced a stronger vortex and an associated reduction in pressure on the dorsal surface of the snake cross-section, which resulted in higher lift. The second part of this work deals with the analysis of the direct forcing method, which is a popular immersed boundary method for flows with rigid boundaries. We begin with the fully discretized Navier-Stokes equations along with the appropriate boundary conditions applied at the solid boundary, and derive the fractional step method as an approximate block LU decomposition of this system. This results in an alternate formulation of the direct forcing method that takes into consideration mass conservation at the immersed boundaries and also handles the pressure boundary conditions more consistently. We demonstrate that this method is between first and second-order accurate in space when linear interpolation is used to enforce the boundary conditions on velocity. We then develop a theory for the order of accuracy of the direct forcing method with linear interpolation. For a simple 1-D case, we show that the method can converge at a range of rates for different locations of the solid body with respect to the mesh. But this effect averages out in higher dimensions and results in a scheme that has the same order of accuracy as the expected order of accuracy of the interpolation at the boundary. The discrete direct forcing method for the Navier-Stokes equations exhibits an order of accuracy between 1 and 2 because the velocities at the boundary are linearly interpolated, but the resulting boundary conditions on the pressure gradient turn out to be only first-order accurate. We recommend linearly interpolating the pressure gradient as well to make the method fully second-order accurate. We have also developed two open source codes in the course of these studies. The first, cuIBM, is a two-dimensional immersed boundary method code that runs on a single GPU. It can simulate incompressible flow around rigid bodies with prescribed motion. It is based on the general idea of a fractional step method as an approximate block LU decomposition, and can incorporate any type of immersed boundary method that can be made to fit within this framework. The second code, PetIBM, can simulate both two and three-dimensional incompressible flow and runs in parallel on multiple CPUs. Both codes have been validated using well-known test cases.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work, the combined multi-direct forcing and immersed boundary method (IBM) were presented to simulate uid-structure interaction problems. The multi-direct forcing is used aim at satisfying the no-slip condition in the immersed boundary. For the numerical simulations was used a multi-purpose computer code that is being developed in the MFlab - Fluid Mechanics Laboratory of Federal University of Uberl^andia. Tests are made to validate the numerical schemes and routines were implemented to simulate uid-structures interaction problems. Furthermore, computational tools are developed to construct and manage and optimize the use of a Beowulf cluster where all the parallel simulations presented in this work were done. The Method of Manufactured Solutions has been used for order-of-accuracy verication in the computational uid dynamics code. Two uid-structure interaction problems were studied using this methodology. The rst is a ow over a sphere for some Reynolds numbers. The results were compared to empirical results, obtaining satisfactory approximations. The second one is a immersed simple pendulum. For this problem the results are in agreement with physics. Indeed, these are preliminar results. New tests must be done to make progress in the methodology. Improvements are proposed in the IBM, in the uid-structure model, in the turbulence model, in the method used to discretize the uid domain. It is also proposed to apply the methodology to real problems as risers and valves. / O presente trabalho tem como principal objetivo a aplicação do método multifoçagem (MMF) para solução numérica tridimensional de problemas de interação uidoestrutura, buscando-se garantir a condição de não-escorregamento na região da fronteira imersa. Para as simulações numéricas foi utilizado um código computacional multipropósito em desenvolvimento no MFlab - Laboratório de Mecânica dos Fluidos da Universidade Federal de Uberlândia. Foram feitas modificações nesse código para que se pudesse validá-lo para solução de problemas com fronteira imersa e foi implementada uma rotina para solução de um problema de interação uido-estrutura total. Além disso, foi desenvolvido um pacote de ferramentas computacionais que possibilitou instalar e melhorar o desempenho de um cluster do tipo Beowulf utilizado para o desenvolvimento das simulações num eriças em paralelo do presente trabalho. Utilizando o Método das Soluções Manufaturadas foram obtidas soluções sintetizadas para as equações de Navier-Stokes, o que possibilitou obter a ordem de convergência numérica do código computacional para problemas contínuos e a validação deste código para problemas envolvendo corpos imersos ao combinar a o método das soluções manufaturadas com a metodologia de fronteira imersa. Na sequência foi solucionado o problema de escoamento ao redor de uma esfera parada, cujos resultados foram comparados com referencias empíricas, obtendo-se boa aproximação. Ainda para esse caso foi feita a avalição da norma L2 para as soluções num eriças obtidas nos pontos lagrangianos verificando a garantia da condição de não-escorregamento e feita uma análise da inuência dos número de ciclos utilizados no método multi-forçagem. Foi vericado que a solução numérica obtida depende do número de ciclos o que faz com que seja necessário se estabelecer um critério de convergência para este método. Um segundo problema de interação uido-estrutura total foi estudado. Consiste em um pêndulo simples imerso em um uido que parte de uma dada posição angular inicial e oscila em torno da sua posição de equilíbrio, até parar. Para esse caso foram feitas análises quantitativas. Os resultados são preliminares mas coerentes com a física do problema, indicando que a metodologia é adequada para solução deste tipo de problema. / Mestre em Engenharia Mecânica