Métodos tradicionais de animação de fluidos têm dificuldade em resolver escoamentos que envolvem aberturas estreitas e geometrias finas. Abordagens anteriores artificialmente inflaram ou voxelizaram geometrias de objetos finos, sacrificando a geometria e topologias corretas do domínio de simulação, impedindo que o escoamento interaja corretamente com regiões estreitas. No trabalho desenvolvido, apresentamos uma técnica de simulação de fluidos que respeita geometrias complexas de maneira precisa e supera obstáculos comuns em ambientes com aberturas estreitas e geometrias finas. A nossa solução baseia-se no recorte preciso de células do grid regular, gerando uma malha conformal à geometria e topologicamente correta. Nós utilizamos uma abordagem de bordas incorporadas (cut-cells): em cada passo do tempo, a malha de triângulos representando a superfície sólida de um objeto no domínio de simulação é recortada pelas células que intercepta, potencialmente gerando múltiplas sub-células distintas. A malha resultante é conformal ao objeto incorporado e se reduz ao grid regular em regiões que não estão em contato com a superfície. Nós estendemos as abordagens tradicionais de advecção de velocidade e projeção da pressão para dar suporte a essa estrutura de malha aprimorada. Em geral, nossa abordagem é capaz de representar melhor detalhes de geometrias que são menores que uma célula do grid, corretamente recuperando condições de contorno no-slip e free-slip, enquanto mantém uma convergência para a solução da pressão de segunda ordem no espaço. Para melhorar a advecção em regiões próximas às bordas irregulares, introduzimos um método de interpolação que funciona em células poliédricas arbitrárias, utilizando-se do método de interpolação spherical barycentric coordinates (SBC). Essa abordagem possibilita que as linhas características do escoamento respeitem a geometria sem penetrá-la, em contraste com métodos tradicionais de interpolação lineares ou cúbicos. Finalmente, nós melhoramos os métodos de advecção com um método FLIP modificado. Nosso método resolve uma dificuldade inerente a advecção Semi-Lagrangiana no contexto de geometrias deslocando-se através do domínio de simulação: as células que são varridas por sólidos em locomoção perdem sua informação de velocidade e tem de ser preenchidas com velocidades extrapoladas de células vizinhas. Nosso esquema FLIP garante que a informação de velocidade viaje corretamente com as superfícies, não necessitando de nenhum método de extrapolação. / Fluid animation methods based on Eulerian grids have long struggled to resolve flows involving narrow gaps and thin solid features. Past approaches have artificially inflated or voxelized boundaries, although this sacrifices the correct geometry and topology of the fluid domain and prevents flow through narrow regions. We present a boundary-respecting fluid simulator that overcomes these challenges. Our solution is to intersect the solid boundary geometry with the cells of a background regular grid to generate a topologically correct, boundary-conforming cut-cell mesh. We extend both pressure projection and velocity advection to support this enhanced grid structure. For pressure projection, we introduce a general graph-based scheme that properly preserves discrete incompressibility even in thin and topologically complex flow regions, while nevertheless yielding symmetric positive definite linear systems. For advection, we exploit polyhedral interpolation to improve the degree to which the flow conforms to irregular and possibly non-convex cell boundaries, and propose a modified PIC/FLIP advection scheme to eliminate the need to inaccurately reinitialize invalid cells that are swept over by moving boundaries. The method naturally extends the standard Eulerian fluid simulation framework, and while we focus on thin boundaries, our contributions are beneficial for volumetric solids as well. Our results demonstrate successful one-way fluid-solid coupling in the presence of thin objects and narrow flow regions even on very coarse grids.

An Eulerian approach to fluid flow provides an efficient, stable paradigm for realistic fluid simulation. However, its traditional reliance on a fixed-resolution grid is not ideal for simulations that simultaneously exhibit both large and small-scale fluid phenomena. Octree-based fluid simulation approaches have provided the needed adaptivity, but the inherent weakness of a pointer-based tree structure has limited their effectiveness. We present a linear octree structure that provides a significant runtime speedup using these octree-based simulation algorithms. As memory prices continue to decline, we leverage additional memory when compared to traditional octree structures to provide this improvement. In addition to reducing the level of indirection in the data, because our linear octree is stored contiguously in memory as a simple C array rather than a recursive set of pointers, we provide a more cache-friendly data layout than a traditional octree. In our testing, our approach yielded run-times that were 1.5 to nearly 5 times faster than the same simulations running on a traditional octree implementation.

<p>Simulating fluid behavior has proven to be a demanding challenge which requires complex computational models and highly efficient data structures. Smoothed Particle Hydrodynamics (SPH) is a particle based computational model used to simulate fluid behavior that has been found capable of producing convincing results. However, the SPH algorithm is computational heavy which makes it cumbersome to work with.</p><p>This master thesis describes how the SPH algorithm can be accelerated by utilizing the GPU’s computational resources. It describes a model for how to distribute the work load on the GPU and presents a suitable data structure. In addition, it proposes a method to represent and handle moving objects in the fluids surroundings. Finally, the performance gain due to the GPU is evaluated by comparing processing times with an identical implementation running solely on the CPU.</p>

<p>Fluid simulation is today a hot topic in computer graphics. New highly optimized algorithms have allowed complex systems to be simulated in high speed. This master thesis describes how the graphics processing unit, found in most computer workstations, can be used to optimize the rendering of volumetric fluids. The main aim of the work has been to develop a software that is capable of rendering fluids in high quality and with high performance using OpenGL. The software was developed at Filmgate, a digital effects company in Göteborg, and much time was spent making the interface and the workflow easy to use for people familiar with Autodesk Maya. The project resulted in a standalone rendering application, together with a set of plugins to exchange data between Maya and our renderer.</p><p>Most of the goals have been reached when it comes to rendering features. The performance bottleneck turned out to be reading data from disc and this is an area suitable for future development of the software.</p>

The steam generator plays a primary role in the safety and performance of a pressurized water reactor nuclear power plant. The cost to utilities is in the order of millions of Rands a year as a direct result of damage to steam generators. The damage results in lower efficiency or even plant shutdown. It is necessary for the utility and for academia to have models of nuclear components by which research and analysis may be performed. It must be possible to analyse steam generator performance for both day-to-day operational analysis as well as in the case of extreme accident scenarios. The homogeneous model for two-phase flow is simpler in its implementation than the two-fluid model, and therefore suffers in accuracy. Its advantage lies in its quick turnover time for development of models and subsequent analysis. It is often beneficial for a modeller to be able to quickly set up and analyse a model of a system, and a trade-off between accuracy and time-management is thus required. Searches through available literature failed to provide answers to how the homogeneous model compares with the two-fluid model for operational and safety analysis. It is expected to see variations between the models, from the analysis of the mathematics, but it remains to be shown what these differences are. The purpose of this study was to determine how the homogeneous model for two-phase flow compares with the two-fluid model when applied to a u-tube steam generator of a typical pressurized water reactor. The steam generator was modelled in both RELAP5 and in Flownex. A custom script was written for Flownex in order to implement the Chen correlation for boiling heat transfer. This was significantly less detailed than RELAP5’s solution of a matrix of flow regimes and heat transfer correlations. The geometry of the models were based on technical drawings from Koeberg Nuclear Power Plant, and were simplified to a one-dimensional model. Plant data obtained from Koeberg was used to validate the models at 100%, 80% and 60% power output. It was found that the overall heat transfer rate predicted with the RELAP5 two-fluid model was within 1.5% of the measured data from the Koeberg plant. The results generated by the homogeneous model for the overall heat transfer were within 4.5% of the measured values. However, the differences in the detailed temperature distributions and heat transfer coefficient values were quite significant at the inlet and outlet ends of the tube bundle, at the bottom tube sheet of the steam generator. In this area the water-level was not accurately modelled by the homogeneous model, and therefore there was an under-prediction in heat transfer in that region. Large differences arose between the Flownex and RELAP5 solutions due to difference in the heat transfer correlations used. The Flownex model exclusively implemented the Chen correlation, while RELAP5 implements a flow regime map correlated to a table of heat transfer correlations. It was concluded that the results from the homogeneous model for two-phase flow do not differ significantly when compared with the two-fluid model when applied to the u-tube steam generator at the normal operating conditions. Significant differences do, however, occur in lower regions of the boiler where the quality is lower. We conclude that the homogeneous model offers significant advantage in simplicity over the two-fluid model for normal operational analysis. This may not be the case for detailed accident analysis, which was beyond the scope of this study. / Thesis (MIng (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013.

The steam generator plays a primary role in the safety and performance of a pressurized water reactor nuclear power plant. The cost to utilities is in the order of millions of Rands a year as a direct result of damage to steam generators. The damage results in lower efficiency or even plant shutdown. It is necessary for the utility and for academia to have models of nuclear components by which research and analysis may be performed. It must be possible to analyse steam generator performance for both day-to-day operational analysis as well as in the case of extreme accident scenarios. The homogeneous model for two-phase flow is simpler in its implementation than the two-fluid model, and therefore suffers in accuracy. Its advantage lies in its quick turnover time for development of models and subsequent analysis. It is often beneficial for a modeller to be able to quickly set up and analyse a model of a system, and a trade-off between accuracy and time-management is thus required. Searches through available literature failed to provide answers to how the homogeneous model compares with the two-fluid model for operational and safety analysis. It is expected to see variations between the models, from the analysis of the mathematics, but it remains to be shown what these differences are. The purpose of this study was to determine how the homogeneous model for two-phase flow compares with the two-fluid model when applied to a u-tube steam generator of a typical pressurized water reactor. The steam generator was modelled in both RELAP5 and in Flownex. A custom script was written for Flownex in order to implement the Chen correlation for boiling heat transfer. This was significantly less detailed than RELAP5’s solution of a matrix of flow regimes and heat transfer correlations. The geometry of the models were based on technical drawings from Koeberg Nuclear Power Plant, and were simplified to a one-dimensional model. Plant data obtained from Koeberg was used to validate the models at 100%, 80% and 60% power output. It was found that the overall heat transfer rate predicted with the RELAP5 two-fluid model was within 1.5% of the measured data from the Koeberg plant. The results generated by the homogeneous model for the overall heat transfer were within 4.5% of the measured values. However, the differences in the detailed temperature distributions and heat transfer coefficient values were quite significant at the inlet and outlet ends of the tube bundle, at the bottom tube sheet of the steam generator. In this area the water-level was not accurately modelled by the homogeneous model, and therefore there was an under-prediction in heat transfer in that region. Large differences arose between the Flownex and RELAP5 solutions due to difference in the heat transfer correlations used. The Flownex model exclusively implemented the Chen correlation, while RELAP5 implements a flow regime map correlated to a table of heat transfer correlations. It was concluded that the results from the homogeneous model for two-phase flow do not differ significantly when compared with the two-fluid model when applied to the u-tube steam generator at the normal operating conditions. Significant differences do, however, occur in lower regions of the boiler where the quality is lower. We conclude that the homogeneous model offers significant advantage in simplicity over the two-fluid model for normal operational analysis. This may not be the case for detailed accident analysis, which was beyond the scope of this study. / Thesis (MIng (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013.

[pt] Fluxos de partículas em suspensão ainda são um desafio importante em muitas aplicações, tais como sedimentação, reologia e suspensões em leitos fluidizados. O acoplamento entre o fluxo da fase líquida e o movimento das partículas é o ponto central para a compreensão completa deste fenômeno. Além disso, o estudo da evolução da disposição das partículas na interface entre duas fases de fluido imiscíveis é também uma área de pesquisa muito importante, pois tal fenômeno ocorre em engenharia em muitos processos industriais, tais como transporte de pastas e a secagem de micro e nanocoberturas. Este trabalho propõe uma nova formulação baseada em domínios fictícios e multiplicadores de Lagrange que resolve as equações de Navier–Stokes e de corpo rígido para realizar a simulação do fluxo e da flutuação de partículas submersas em uma ou mais fases de fluidos imiscíveis. Para obtermos a solução discreta das equações utilizamos o método dos elementos finitos e uma abordagem totalmente implícita e acoplada. Esta formulação foi validada usando diferentes problemas de teste. Os resultados obtidos foram comparados com trabalhos anteriores e a concordância foi excelente. / [en] Flows with particles in suspension is still a challenging task important in many applications such as sedimentation, rheology and fluidized suspensions. The coupling between the suspending liquid flow and the particles’ motion is the central point in the complete understanding of these phenomena. Moreover, the study of the evolution of the configuration of particles at an interface between two immisible fluid phases is also a very important research area, since it occurs in many engineering and industrial processes like slurries transport and drying processes of micro and nano suspension coating. This work proposes a new fictitious domain formulation based on Lagrange multipliers that solves the Navier–Stokes and rigid body equations to perform the simulation of the flow and of the flotation of particles embedded on one or more immiscible fluid phases that we numerically discretize using a fully implicit and coupled finite element approach. The method is validated using different test problems. The results obtained are compared with previous works, and the agreement is excellent.

[pt] A modelagem de fluidos é frequentemente utilizada, tanto na engenharia como na área de efeitos especiais para cinema e TV, para simular fenômenos naturais, tais como fogo, explosões, fumaça, água e ar. Basicamente, esta modelagem utiliza métodos baseados em malhas, tais como volumes finitos e elementos finitos, ou métodos independentes de malhas baseados em partículas, tais como MPS e SPH. Uma questão comum nas técnicas de partículas é o problema de fronteiras entre fluidos, já que não há uma solução geral e satisfatória. O objetivo deste trabalho é propor uma nova técnica para a visualização da fronteira entre fluidos utilizando o método SPH (Smoothed-particle Hydrodynamics) e o algoritmo Marching Cubes. Testes são realizados para averiguar os custos computacionais envolvidos na geração e renderização da malha da fronteira. / [en] In engineering and special effects for film and television, fluid modeling is frequently used to simulate natural phenomena, such as fire, explosions, smoke, water, and air. Basically, this modeling uses mesh-based methods, such as finite volumes and finite elements, or mesh-free methods based on particles, such as MPS and SPH. A common question among particle techniques is the problem of boundary between fluids, since there is no general and satisfactory solution available. The objective of this work is to propose a new technique for the visualization of the boundary between fluids using the SPH method (Smoothed-particle Hydrodynamics) and the Marching Cubes algorithm. Tests are made to investigate the computational costs involved in the generation and rendering of the boundary mesh.

Métodos tradicionais de animação de fluidos têm dificuldade em resolver escoamentos que envolvem aberturas estreitas e geometrias finas. Abordagens anteriores artificialmente inflaram ou voxelizaram geometrias de objetos finos, sacrificando a geometria e topologias corretas do domínio de simulação, impedindo que o escoamento interaja corretamente com regiões estreitas. No trabalho desenvolvido, apresentamos uma técnica de simulação de fluidos que respeita geometrias complexas de maneira precisa e supera obstáculos comuns em ambientes com aberturas estreitas e geometrias finas. A nossa solução baseia-se no recorte preciso de células do grid regular, gerando uma malha conformal à geometria e topologicamente correta. Nós utilizamos uma abordagem de bordas incorporadas (cut-cells): em cada passo do tempo, a malha de triângulos representando a superfície sólida de um objeto no domínio de simulação é recortada pelas células que intercepta, potencialmente gerando múltiplas sub-células distintas. A malha resultante é conformal ao objeto incorporado e se reduz ao grid regular em regiões que não estão em contato com a superfície. Nós estendemos as abordagens tradicionais de advecção de velocidade e projeção da pressão para dar suporte a essa estrutura de malha aprimorada. Em geral, nossa abordagem é capaz de representar melhor detalhes de geometrias que são menores que uma célula do grid, corretamente recuperando condições de contorno no-slip e free-slip, enquanto mantém uma convergência para a solução da pressão de segunda ordem no espaço. Para melhorar a advecção em regiões próximas às bordas irregulares, introduzimos um método de interpolação que funciona em células poliédricas arbitrárias, utilizando-se do método de interpolação spherical barycentric coordinates (SBC). Essa abordagem possibilita que as linhas características do escoamento respeitem a geometria sem penetrá-la, em contraste com métodos tradicionais de interpolação lineares ou cúbicos. Finalmente, nós melhoramos os métodos de advecção com um método FLIP modificado. Nosso método resolve uma dificuldade inerente a advecção Semi-Lagrangiana no contexto de geometrias deslocando-se através do domínio de simulação: as células que são varridas por sólidos em locomoção perdem sua informação de velocidade e tem de ser preenchidas com velocidades extrapoladas de células vizinhas. Nosso esquema FLIP garante que a informação de velocidade viaje corretamente com as superfícies, não necessitando de nenhum método de extrapolação. / Fluid animation methods based on Eulerian grids have long struggled to resolve flows involving narrow gaps and thin solid features. Past approaches have artificially inflated or voxelized boundaries, although this sacrifices the correct geometry and topology of the fluid domain and prevents flow through narrow regions. We present a boundary-respecting fluid simulator that overcomes these challenges. Our solution is to intersect the solid boundary geometry with the cells of a background regular grid to generate a topologically correct, boundary-conforming cut-cell mesh. We extend both pressure projection and velocity advection to support this enhanced grid structure. For pressure projection, we introduce a general graph-based scheme that properly preserves discrete incompressibility even in thin and topologically complex flow regions, while nevertheless yielding symmetric positive definite linear systems. For advection, we exploit polyhedral interpolation to improve the degree to which the flow conforms to irregular and possibly non-convex cell boundaries, and propose a modified PIC/FLIP advection scheme to eliminate the need to inaccurately reinitialize invalid cells that are swept over by moving boundaries. The method naturally extends the standard Eulerian fluid simulation framework, and while we focus on thin boundaries, our contributions are beneficial for volumetric solids as well. Our results demonstrate successful one-way fluid-solid coupling in the presence of thin objects and narrow flow regions even on very coarse grids.

Métodos tradicionais de animação de fluidos têm dificuldade em resolver escoamentos que envolvem aberturas estreitas e geometrias finas. Abordagens anteriores artificialmente inflaram ou voxelizaram geometrias de objetos finos, sacrificando a geometria e topologias corretas do domínio de simulação, impedindo que o escoamento interaja corretamente com regiões estreitas. No trabalho desenvolvido, apresentamos uma técnica de simulação de fluidos que respeita geometrias complexas de maneira precisa e supera obstáculos comuns em ambientes com aberturas estreitas e geometrias finas. A nossa solução baseia-se no recorte preciso de células do grid regular, gerando uma malha conformal à geometria e topologicamente correta. Nós utilizamos uma abordagem de bordas incorporadas (cut-cells): em cada passo do tempo, a malha de triângulos representando a superfície sólida de um objeto no domínio de simulação é recortada pelas células que intercepta, potencialmente gerando múltiplas sub-células distintas. A malha resultante é conformal ao objeto incorporado e se reduz ao grid regular em regiões que não estão em contato com a superfície. Nós estendemos as abordagens tradicionais de advecção de velocidade e projeção da pressão para dar suporte a essa estrutura de malha aprimorada. Em geral, nossa abordagem é capaz de representar melhor detalhes de geometrias que são menores que uma célula do grid, corretamente recuperando condições de contorno no-slip e free-slip, enquanto mantém uma convergência para a solução da pressão de segunda ordem no espaço. Para melhorar a advecção em regiões próximas às bordas irregulares, introduzimos um método de interpolação que funciona em células poliédricas arbitrárias, utilizando-se do método de interpolação spherical barycentric coordinates (SBC). Essa abordagem possibilita que as linhas características do escoamento respeitem a geometria sem penetrá-la, em contraste com métodos tradicionais de interpolação lineares ou cúbicos. Finalmente, nós melhoramos os métodos de advecção com um método FLIP modificado. Nosso método resolve uma dificuldade inerente a advecção Semi-Lagrangiana no contexto de geometrias deslocando-se através do domínio de simulação: as células que são varridas por sólidos em locomoção perdem sua informação de velocidade e tem de ser preenchidas com velocidades extrapoladas de células vizinhas. Nosso esquema FLIP garante que a informação de velocidade viaje corretamente com as superfícies, não necessitando de nenhum método de extrapolação. / Fluid animation methods based on Eulerian grids have long struggled to resolve flows involving narrow gaps and thin solid features. Past approaches have artificially inflated or voxelized boundaries, although this sacrifices the correct geometry and topology of the fluid domain and prevents flow through narrow regions. We present a boundary-respecting fluid simulator that overcomes these challenges. Our solution is to intersect the solid boundary geometry with the cells of a background regular grid to generate a topologically correct, boundary-conforming cut-cell mesh. We extend both pressure projection and velocity advection to support this enhanced grid structure. For pressure projection, we introduce a general graph-based scheme that properly preserves discrete incompressibility even in thin and topologically complex flow regions, while nevertheless yielding symmetric positive definite linear systems. For advection, we exploit polyhedral interpolation to improve the degree to which the flow conforms to irregular and possibly non-convex cell boundaries, and propose a modified PIC/FLIP advection scheme to eliminate the need to inaccurately reinitialize invalid cells that are swept over by moving boundaries. The method naturally extends the standard Eulerian fluid simulation framework, and while we focus on thin boundaries, our contributions are beneficial for volumetric solids as well. Our results demonstrate successful one-way fluid-solid coupling in the presence of thin objects and narrow flow regions even on very coarse grids.