Many computational applications involve multiple physical components, each having its own computational domain discretized by a mesh. An integrated simulation of these physical systems require transferring data across these boundaries, which are typically represented by surface meshes composed of triangles or quadrilaterals and are non-matching with differing connectivities and geometry. It is necessary to constructa common refinement (or common tessellation) of the surface meshes to transfer data between different domains accurately and conservatively. For large-scale problems that involve moving boundary, the common tessellation must be updated frequently within the integrated simulations running on parallel computers. Previously, Jiao and Heath developed an algorithm for constructing a common tessellation by overlaying the surface meshes. The original algorithm is efficient and robust, but unfortunately, it is complex and difficult to parallelize. In this thesis, we develop a modified algorithm for overlaying surface meshes. Our algorithm employs a high-level primitive, face-intersection, which combines the low-level point-projection and edge-intersection primitives of the original algorithm. A main advantage of our modified algorithm is its ease of implementation and parallelization. Our implementation utilizes flexible data structures for efficient computation and query of the common tessellation and avoids potential redundancy in computations to achieve high efficiency. To achieve robustness, we pay special attention to avoid potential topological inconsistencies due to numerical errors, and introduce a preprocessing step to project a far-apart surface mesh onto other before computing the common tessellation. We present numerical examples to demonstrate the robustness and efficiency of our method on parallel computers.

No description available.

Surfaces in 3D are often represented by polygonal meshes and point clouds obtained from 3D modeling tools or acquisition processes such as laser range scanning. While these formats are very flexible and allow the representation of a wide variety of shapes, they are rarely appropriate in their raw form for the range of applications that benefit from their use. Their decomposition into simpler constituting parts is referred to as shape segmentation, and its automation remains a challenging area within computer science. We will present and analyze different aspects of shape segmentation. We begin by looking at useful segmentation criteria and present a categorization of current methods according to which type of criteria they address, dividing them into affinity-based, model-fitting, and property-based approaches. We then present two algorithmic contributions in the form of a model-based and a property-based segmentation approaches. These share the goals of automatically finding redundancy in a shape and propose shape representations that leverage this redundancy to achieve descriptive compactness. The first is a method for segmenting a surface into piece-wise ellipsoidal parts, motivated by the fact that most organic objects and many manufactured objects have large curved areas. The second is an algorithm for robustly detecting global and local planar-reflective symmetry and a hierarchical segmentation approach based on this detection method. We note within these approaches the variation in segmentations resulting from different criteria and propose a way to generalize the segmentation problem to heterogenous criteria. We introduce a framework and relevant algorithms for multi-objective segmentation of 3D shapes which allow for the incorporation of domain-specific knowledge through multiple objectives, each of which refers to one or more segmentation labels. They can assert properties of an individual part or they can refer to part interrelations. We thus cast the segmentation problem as an optimization minimizing an aggregate objective function which combines all objectives as a weighted sum. We conclude with a summary and discussion of the contributions presented, lessons learned, and a look at the open questions remaining and potential avenues of continued research.

Surfaces in 3D are often represented by polygonal meshes and point clouds obtained from 3D modeling tools or acquisition processes such as laser range scanning. While these formats are very flexible and allow the representation of a wide variety of shapes, they are rarely appropriate in their raw form for the range of applications that benefit from their use. Their decomposition into simpler constituting parts is referred to as shape segmentation, and its automation remains a challenging area within computer science. We will present and analyze different aspects of shape segmentation. We begin by looking at useful segmentation criteria and present a categorization of current methods according to which type of criteria they address, dividing them into affinity-based, model-fitting, and property-based approaches. We then present two algorithmic contributions in the form of a model-based and a property-based segmentation approaches. These share the goals of automatically finding redundancy in a shape and propose shape representations that leverage this redundancy to achieve descriptive compactness. The first is a method for segmenting a surface into piece-wise ellipsoidal parts, motivated by the fact that most organic objects and many manufactured objects have large curved areas. The second is an algorithm for robustly detecting global and local planar-reflective symmetry and a hierarchical segmentation approach based on this detection method. We note within these approaches the variation in segmentations resulting from different criteria and propose a way to generalize the segmentation problem to heterogenous criteria. We introduce a framework and relevant algorithms for multi-objective segmentation of 3D shapes which allow for the incorporation of domain-specific knowledge through multiple objectives, each of which refers to one or more segmentation labels. They can assert properties of an individual part or they can refer to part interrelations. We thus cast the segmentation problem as an optimization minimizing an aggregate objective function which combines all objectives as a weighted sum. We conclude with a summary and discussion of the contributions presented, lessons learned, and a look at the open questions remaining and potential avenues of continued research.

Turbulent flows present structures with a wide range of scales. The computation of the complete physics of a turbulent flow (termed DNS) is very expensive and is, for the time being, limited to low and medium Reynolds number flows. As a way to capture high Reynolds number flows, a part of the physics complexity has to be modeled. Large eddy simulation (LES) is a simulation strategy where the large turbulent eddies present on a given mesh are captured and the influence of the non-resolved scales onto the resolved ones is modeled. The present thesis reports on the development and validation of a methodology in order to apply LES for complex wall-bounded flows. Discretization methods and LES models, termed subgrid scale models (SGS), compatible with such a geometrical complexity are discussed. It is proved that discrete a kinetic energy conserving discretization of the convective term is an attractive solution to perform stable simulations without the use of an artificial dissipation, as upwinding. The dissipative effect of the SGS model is thus unaffected by any additional dissipation process. The methodology is first applied to a developed parallel fourth-order incompressible flow solver for cartesian non-uniform meshes. In order to solve the resulting Poisson equation, an efficient multigrid solver is also developed. The code is first validated using DNS (Taylor-Green vortex, channel flow, four-vortex system) and LES (channel flow), and finally applied to the investigation of an aircraft two-vortex system in ground effect. The methodology is then applied to improve a RANS-based industrial unstructured compressible flow solver, developed at CENAERO, to perform well for LES applications. The proposed modifications are tested successfully on the unsteady flow past a sphere at Reynolds of 300 and 10000, corresponding to the subcritical regime.

Turbulent flows present structures with a wide range of scales. The computation of the complete physics of a turbulent flow (termed DNS) is very expensive and is, for the time being, limited to low and medium Reynolds number flows. As a way to capture high Reynolds number flows, a part of the physics complexity has to be modeled. Large eddy simulation (LES) is a simulation strategy where the large turbulent eddies present on a given mesh are captured and the influence of the non-resolved scales onto the resolved ones is modeled. The present thesis reports on the development and validation of a methodology in order to apply LES for complex wall-bounded flows. Discretization methods and LES models, termed subgrid scale models (SGS), compatible with such a geometrical complexity are discussed. It is proved that discrete a kinetic energy conserving discretization of the convective term is an attractive solution to perform stable simulations without the use of an artificial dissipation, as upwinding. The dissipative effect of the SGS model is thus unaffected by any additional dissipation process. The methodology is first applied to a developed parallel fourth-order incompressible flow solver for cartesian non-uniform meshes. In order to solve the resulting Poisson equation, an efficient multigrid solver is also developed. The code is first validated using DNS (Taylor-Green vortex, channel flow, four-vortex system) and LES (channel flow), and finally applied to the investigation of an aircraft two-vortex system in ground effect. The methodology is then applied to improve a RANS-based industrial unstructured compressible flow solver, developed at CENAERO, to perform well for LES applications. The proposed modifications are tested successfully on the unsteady flow past a sphere at Reynolds of 300 and 10000, corresponding to the subcritical regime.

No description available.

This work details a multigrid-accelerated cut-cell Cartesian mesh methodology for the solution of a single partial differential equation set that describes incompressible as well as compressible flow. The latter includes sub-, trans- and supersonic flows. Cut-cell technology is developed which furnishes body-fitted meshes with an overlapping Cartesian mesh as starting point, and in a manner which is insensitive to surface definition inconsistencies. An edge-based vertex-centred finite volume method is employed for the purpose of spatial discretisation. Further, an alternative dual-mesh construction strategy is developed and the standard discretisation scheme suitably enhanced. Incompressibility is dealt with via a locally preconditioned artificial compressibility algorithm, and stabilisation is in all cases achieved with scalar-valued artificial dissipation. In transonic flows, shocks are captured via pressure switch-activated upwinding. The solution process is accelerated by the use of a full approximation scheme (FAS) multigrid method where coarse meshes are generated automatically via a volume agglomeration methodology. The developed modelling technology is validated by application to the solution of a number of benchmark problems. The standard discretisation as well as the alternative method are found to be equivalent in terms of both accuracy and computational cost. Finally, the multigrid implementation is shown to achieve decreases in CPU time of between a factor two to one order of magnitude. In the context of cut-cell Cartesian meshes, the above work has resulted in the following novel contributions: the development of an alternative vertex-centred discretisation method; the use of volume agglomerated multigrid solution technology and the use of a single equation set for both incompressible and compressible flows. / Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2007. / Mechanical and Aeronautical Engineering / unrestricted

Spatial statistics methods are widely used since several areas of knowledge such as environmental sciences, geology, agronomy, among others, involve the understanding of the spatial distribution of processes from spatially referenced data. With the advancement of Geographic Information Systems and the Global Positioning Systems this use has been extended. Many methods used in spatial statistics are computationally demanding, and therefore, the development of more computationally efficient methods has received a lot of attention in recent years. One such important development is the introduction of the integrated nested Laplace approximation method which is able to carry out Bayesian analysis in a more efficient way. The use of this method for geostatistical data is commonly done considering the stochastic partial differential equation approach that requires the creation of a mesh overlying the study area. This is the first and an important step since all results will depend on the choice of this mesh. As there is no formal and close way to specify the mesh, we investigate possible guidelines on how a suitable mesh is chosen for a specific problem. Through simulations studies, we tried to create guidelines for the construction of the mesh for random, regular and cluster data set and we aplly this guidelines in real data set. / Métodos de estatística espacial são amplamente utilizados, uma vez que várias áreas do conhecimento, como ciências ambientais, geologia, agronomia, entre outros, envolvem a compreensão da distribuição espacial de processos a partir de dados referenciados espacialmente. Com o avanço dos Sistemas de Informação Geográfica e dos Sistemas de Posicionamento Global, esse uso foi ampliado. Muitos métodos utilizados na estatística espacial são computacionalmente exigentes e, portanto, o desenvolvimento de métodos mais eficientes recebeu muita atenção nos últimos anos. Um desenvolvimento importante foi a introdução do método de aproximação de Laplace aninhado integrado, capaz de realizar análises Bayesianas de forma mais eficiente. O uso deste método para dados geoestatísticos é comumente feito considerando a abordagem de equações diferenciais parciais estocásticas que requer a criação de uma malha que cobre a área de estudo. Este é o primeiro e um importante passo, pois todos os resultados dependerão da escolha desta malha. Como não existe uma maneira formal e direta de especificar a malha, investigamos possíveis diretrizes sobre como uma malha adequada é escolhida para um problema específico. Através de estudos de simulações, tentamos criar diretrizes para a construção da malha para conjunto de dados aleatórios, regulares e de cluster e aplicamos essas diretrizes em conjunto de dados reais.

This thesis considers one-dimensional moving mesh (MM) methods coupled with semi-Lagrangian (SL) discretisations of partial differential equations (PDEs) for meteorological applications. We analyse a semi-Lagrangian numerical solution to the viscous Burgers’ equation when using linear interpolation. This gives expressions for the phase and shape errors of travelling wave solutions which decay slowly with increasing spatial and temporal resolution. These results are verified numerically and demonstrate qualitative agreement for high order interpolants. The semi-Lagrangian discretisation is coupled with a 1D moving mesh, resulting in a moving mesh semi-Lagrangian (MMSL) method. This is compared against two moving mesh Eulerian methods, a two-step remeshing approach, solved with the theta-method, and a coupled moving mesh PDE approach, which is solved using the MATLAB solver ODE45. At each time step of the SL method, the mesh is updated using a curvature based monitor function in order to reduce the interpolation error, and hence numerical viscosity. This MMSL method exhibits good stability properties, and captures the shape and speed of the travelling wave well. A meteorologically based 1D vertical column model is described with its SL solution procedure. Some potential benefits of adaptivity are demonstrated, with static meshes adapted to initial conditions. A moisture species is introduced into the model, although the effects are limited.