Fluid simulations for computer graphics applications have attracted the attention of many researchers and practitioners due to the enhanced realism that natural phenomena simulation adds to graphical applications. Vortex methods are receiving increasing attention from the computer graphics community for simple and direct modeling of complex flow phenomena such as turbulence. However, vortex methods have not been developed yet to the level of other techniques for fluid simulation in computer graphics. In this work we present a novel simulation framework to model inviscid flows using Lagrangian vortex particle methods. We introduce novel stable methods to solve the vorticity flow equations that produce highly detailed visual fluid simulations. We incorporate the full interplay of solids and fluids in our framework. The coupling between free-form solids, represented by arbitrary surface meshes and fluids simulated with vortex methods, leads to visually rich simulations. Previous vortex simulators only focus on modeling the solid as a boundary for the flow. We model solid boundaries using an extended potential flow at the solid surface coupled with a boundary layer simulation. This allows the accurate simulation of two processes of visual interest. The first is the introduction of surface vorticity in the main flow as turbulence (vortex shedding). The second is the motion of the solid induced by fluid forces, which is calculated from the dynamics of vorticity in the flow and the rate of vorticity creation at solid surfaces. We demonstrate high quality results of our methods simulating flows around solid objects and solid object propulsion due to flows. This work ameliorates one of the important omissions in the development of vortex methods for computer graphics, which is the simulation of two-way coupling of solids and fluids.

Fluid simulations for computer graphics applications have attracted the attention of many researchers and practitioners due to the enhanced realism that natural phenomena simulation adds to graphical applications. Vortex methods are receiving increasing attention from the computer graphics community for simple and direct modeling of complex flow phenomena such as turbulence. However, vortex methods have not been developed yet to the level of other techniques for fluid simulation in computer graphics. In this work we present a novel simulation framework to model inviscid flows using Lagrangian vortex particle methods. We introduce novel stable methods to solve the vorticity flow equations that produce highly detailed visual fluid simulations. We incorporate the full interplay of solids and fluids in our framework. The coupling between free-form solids, represented by arbitrary surface meshes and fluids simulated with vortex methods, leads to visually rich simulations. Previous vortex simulators only focus on modeling the solid as a boundary for the flow. We model solid boundaries using an extended potential flow at the solid surface coupled with a boundary layer simulation. This allows the accurate simulation of two processes of visual interest. The first is the introduction of surface vorticity in the main flow as turbulence (vortex shedding). The second is the motion of the solid induced by fluid forces, which is calculated from the dynamics of vorticity in the flow and the rate of vorticity creation at solid surfaces. We demonstrate high quality results of our methods simulating flows around solid objects and solid object propulsion due to flows. This work ameliorates one of the important omissions in the development of vortex methods for computer graphics, which is the simulation of two-way coupling of solids and fluids.

Fluid simulations for computer graphics applications have attracted the attention of many researchers and practitioners due to the enhanced realism that natural phenomena simulation adds to graphical applications. Vortex methods are receiving increasing attention from the computer graphics community for simple and direct modeling of complex flow phenomena such as turbulence. However, vortex methods have not been developed yet to the level of other techniques for fluid simulation in computer graphics. In this work we present a novel simulation framework to model inviscid flows using Lagrangian vortex particle methods. We introduce novel stable methods to solve the vorticity flow equations that produce highly detailed visual fluid simulations. We incorporate the full interplay of solids and fluids in our framework. The coupling between free-form solids, represented by arbitrary surface meshes and fluids simulated with vortex methods, leads to visually rich simulations. Previous vortex simulators only focus on modeling the solid as a boundary for the flow. We model solid boundaries using an extended potential flow at the solid surface coupled with a boundary layer simulation. This allows the accurate simulation of two processes of visual interest. The first is the introduction of surface vorticity in the main flow as turbulence (vortex shedding). The second is the motion of the solid induced by fluid forces, which is calculated from the dynamics of vorticity in the flow and the rate of vorticity creation at solid surfaces. We demonstrate high quality results of our methods simulating flows around solid objects and solid object propulsion due to flows. This work ameliorates one of the important omissions in the development of vortex methods for computer graphics, which is the simulation of two-way coupling of solids and fluids.

This thesis is concerned with three-dimensional vortex dynamics, in particular the modelling of vortex structures in an inviscid context. We are motivated by the open problem of regularity of the inviscid equations, i.e. whether or not these equations possess solutions. This problem is manifest in small scales, where vortex filaments are stretched and intensify as they are drawn into increasingly thin tendrils. This creates great difficulty in the investigation of such flows. Our only means of experimentation is to perform numerical simulations, which require exceptionally high resolution to capture the small scale vortex structures. A new numerical method to solve the inviscid Euler equations for three-dimensional, incompressible fluids is presented, with special emphasis on spatial adaptivity to resolve as broad a range of scales as possible in a completely self-similar fashion. We present a hybrid vortex method whereby we discretise the vorticity in Lagrangian filaments and perform and inversion to compute velocity on an arbitrary unstructured finite-volume grid. This allows for a two-fold adaptivity strategy. First, although naturally spatially adaptive by definition, the vorticity filaments undergo ‘renoding'. We redistribute nodes along the filament to concentrate their density in regions of high curvature. Secondly the Eulerian mesh is adapted to follow high strain by increasing resolution based on local filament dimensions. These features allow vortex stretching and folding to be resolved in a completely automatic and self-similar way. The method is validated via well known vortex rings and newly discovered helical vortex equilibria are also used to test the method. We begin by presenting this new class of three-dimensional vortex equilibria which possess helical symmetry. Such vortices are observed in propeller and wind turbine wakes, and their equilibria shapes have until now been unknown. These vortices are described by contours bounding regions of uniform axial vorticity. Material conservation of axial vorticity enables equilibria to be calculated simply by a restriction on the helical stream function. The states are parameterised by their mean radius and centroid position. In the case of a single vortex, the parameter space cannot be fully filled by our numerical approach. We conjecture that multiply connected contours will characterise equilibria where the algorithm fails. We also consider multiple vortices, evenly azimuthally spaced about the origin. In such cases instabilities often lead to a single helical vortex.

Este trabalho aborda o escoamento ao redor de cilindros flexíveis com grande razão de aspecto, representando os riser utilizados na indústria petrolífera. O escoamento foi dividido em seções bidimensionais ao longo do comprimento do riser. O método dos vórtices discretos foi utilizado para estimativa dos coeficientes hidrodinâmicos nas seções correspondentes e o acoplamento se dá através da dinâmica estrutural. Esta dinâmica é resolvida pelo método dos elementos finitos implementado no código Anflex (Mourelle et al. (2001)). Processamento paralelo é utilizado para acelerar o desempenho do método numérico. Um esquema master-slave (\"mestre-escravo\") utilizando MPI (Message Passing Interface1) é utilizado para que seja explorado o paralelismo da modelagem. As seções hidrodinâmicas são igualmente divididas ao longo dos nós de um cluster de computadores utilizado nos cálculos. Cada nó do cluster (núcleo de processamento) resolve o escoamento nas seções hidrodinâmicas necessárias. As forças hidrodinâmicas atuando nas seções correspondentes são enviadas ao processo mestre que também é responsável pela resolução da dinâmica estrutural. Uma das contribuições do presente trabalho é a possibilidade de análise de risers em regime pós-crítico, através da imposição do ponto de separação da camada-limite baseado em resultados experimentais, e da modelagem de casos com risers em tandem. O Método dos Vórtices Discretos (MVD) está detalhado de forma a facilitar a implementação computacional, levando em consideração a possibilidade de estudo de interferência entre esteiras de múltiplos corpos. Como primeira aproximação, foram simulados, casos de cilindros rígidos fixos e em base elástica para os quais foram examinadas as amplitudes máximas de oscilação e os coeficientes de arrasto e sustentação. Posteriormente, o MVD foi integrado ao Anflex dando origem ao AnflexCFD, com capacidade de processamento paralelo da parte correspondente ao CFD. Os resultados obtidos numericamente foram comparados a resultados experimentais realizados em laboratório. A metodologia de utilização do MVD para cálculo dos coeficientes hidrodinâmicos é baseada na comparação com resultados experimentais obtidos em laboratório para cilindros rígidos fixos e em base elástica para os quais se observa uma aderência satisfatória com relação aos resultados obtidos numericamente. O resultado do presente trabalho foi a criação de uma ferramenta alternativa no projeto de risers de grande razão de aspecto, como uma forma de avaliação do comportamento dinâmico da estrutura submetida a diferentes perfis de corrente e, consequentemente, a estimativa do tempo de sua vida útil. A característica puramente Lagrangiana do MVD possibilita a simulação de centenas de ciclos de oscilação da estrutura sendo que para os métodos Eulerianos tradicionais de CFD, como o método dos volumes finitos e o método dos elementos finitos, a simulação necessita de um tempo computacional inviável para projeto. A aderência do modelo adotado em relação aos resultados experimentais, aliada a eficiência do MVD, é um indicativo da vantagem da utilização de métodos Lagrangianos na modelagem do escoamento ao redor de cilindros flexíveis com grande razão de aspecto, em relação aos métodos Eulerianos tradicionais. A metodologia apresentada neste trabalho pode ser aplicada utilizando outros métodos de CFD, lembrando que isto pode implicar num aumento significativo do tempo computacional necessário para uma análise. / In this work the dynamic response of a high aspect ratio flexible cylinder due to vortex shedding is numerically investigated. The model is divided in two-dimensional sections along the riser length. The discrete vortex method (DVM) is employed for the assessment of the hydrodynamic forces acting on these two-dimensional sections. The hydrodynamic sections are solved independently, and the coupling among the sections is taken into account by the solution of the structure in the time domain by the finite element method implemented in Anflex code (Mourelle et al. (2001)). Parallel processing is employed to improve the performance of the method. A master-slave approach via MPI (Message Passing Interface) is used to exploit the parallelism of the present code. The riser sections are equally divided among the nodes of the cluster. Each node solves the hydrodynamic sections assigned to it. The forces acting on the sections are then passed to the master processor, which is responsible for the calculation of the displacement of the whole structure. One of the main contributions of the present work is the possibility of simulating the flow around flexible cylinders in the pos-critical regime and around bundle of risers.

Este trabalho aborda o escoamento ao redor de cilindros flexíveis com grande razão de aspecto, representando os riser utilizados na indústria petrolífera. O escoamento foi dividido em seções bidimensionais ao longo do comprimento do riser. O método dos vórtices discretos foi utilizado para estimativa dos coeficientes hidrodinâmicos nas seções correspondentes e o acoplamento se dá através da dinâmica estrutural. Esta dinâmica é resolvida pelo método dos elementos finitos implementado no código Anflex (Mourelle et al. (2001)). Processamento paralelo é utilizado para acelerar o desempenho do método numérico. Um esquema master-slave (\"mestre-escravo\") utilizando MPI (Message Passing Interface1) é utilizado para que seja explorado o paralelismo da modelagem. As seções hidrodinâmicas são igualmente divididas ao longo dos nós de um cluster de computadores utilizado nos cálculos. Cada nó do cluster (núcleo de processamento) resolve o escoamento nas seções hidrodinâmicas necessárias. As forças hidrodinâmicas atuando nas seções correspondentes são enviadas ao processo mestre que também é responsável pela resolução da dinâmica estrutural. Uma das contribuições do presente trabalho é a possibilidade de análise de risers em regime pós-crítico, através da imposição do ponto de separação da camada-limite baseado em resultados experimentais, e da modelagem de casos com risers em tandem. O Método dos Vórtices Discretos (MVD) está detalhado de forma a facilitar a implementação computacional, levando em consideração a possibilidade de estudo de interferência entre esteiras de múltiplos corpos. Como primeira aproximação, foram simulados, casos de cilindros rígidos fixos e em base elástica para os quais foram examinadas as amplitudes máximas de oscilação e os coeficientes de arrasto e sustentação. Posteriormente, o MVD foi integrado ao Anflex dando origem ao AnflexCFD, com capacidade de processamento paralelo da parte correspondente ao CFD. Os resultados obtidos numericamente foram comparados a resultados experimentais realizados em laboratório. A metodologia de utilização do MVD para cálculo dos coeficientes hidrodinâmicos é baseada na comparação com resultados experimentais obtidos em laboratório para cilindros rígidos fixos e em base elástica para os quais se observa uma aderência satisfatória com relação aos resultados obtidos numericamente. O resultado do presente trabalho foi a criação de uma ferramenta alternativa no projeto de risers de grande razão de aspecto, como uma forma de avaliação do comportamento dinâmico da estrutura submetida a diferentes perfis de corrente e, consequentemente, a estimativa do tempo de sua vida útil. A característica puramente Lagrangiana do MVD possibilita a simulação de centenas de ciclos de oscilação da estrutura sendo que para os métodos Eulerianos tradicionais de CFD, como o método dos volumes finitos e o método dos elementos finitos, a simulação necessita de um tempo computacional inviável para projeto. A aderência do modelo adotado em relação aos resultados experimentais, aliada a eficiência do MVD, é um indicativo da vantagem da utilização de métodos Lagrangianos na modelagem do escoamento ao redor de cilindros flexíveis com grande razão de aspecto, em relação aos métodos Eulerianos tradicionais. A metodologia apresentada neste trabalho pode ser aplicada utilizando outros métodos de CFD, lembrando que isto pode implicar num aumento significativo do tempo computacional necessário para uma análise. / In this work the dynamic response of a high aspect ratio flexible cylinder due to vortex shedding is numerically investigated. The model is divided in two-dimensional sections along the riser length. The discrete vortex method (DVM) is employed for the assessment of the hydrodynamic forces acting on these two-dimensional sections. The hydrodynamic sections are solved independently, and the coupling among the sections is taken into account by the solution of the structure in the time domain by the finite element method implemented in Anflex code (Mourelle et al. (2001)). Parallel processing is employed to improve the performance of the method. A master-slave approach via MPI (Message Passing Interface) is used to exploit the parallelism of the present code. The riser sections are equally divided among the nodes of the cluster. Each node solves the hydrodynamic sections assigned to it. The forces acting on the sections are then passed to the master processor, which is responsible for the calculation of the displacement of the whole structure. One of the main contributions of the present work is the possibility of simulating the flow around flexible cylinders in the pos-critical regime and around bundle of risers.

Potential flow simulations are a great engineering type, middle-ground approach to modeling complex aerodynamic systems, but quickly become computationally unwieldy for large domains. An N-body problem with N-squared interactions to calculate, this free wake vortex model of a wind turbine is well suited to parallel computation. This thesis discusses general trends in wind turbine modeling, a potential flow model of the rotor of the NREL 5MW reference turbine, various forms of parallel computing, current GPU hardware, and the application of ground effects to the model. In the vicinity of 200,000 points, current GPU hardware was found to be nearly 17 times faster than an OpenMP 12 core CPU parallel code, and over 280 times faster than serial MATLAB code. Convergence of the solution is found to be dependent on the direction in which the grid is refined. The "no entry" condition at the ground plane is found to have a measurable but small impact on the model outputs with a periodicity driven by the blade proximity to the ground plane. The effect of the ground panel method was found to converge to that of the "method of images" for increasing ground extent and number of panels.