This thesis discusses how to use topology and shape optimization, specifically the level set method, for innovative design. The level set method is a numerical algorithm that simulates the expansion of dynamic implicit surfaces. In this research, the equations for manufacturability are generated and solved through use of the level set method joined with the COMSOL multi-physics package. Specific constraints are added to make the optimization practical for engineering design. The resulting method was applied to design the best underlying support structure, conforming to both curvature and manufacturability constraints, for the longerons used with the International Space Station solar panels.

An interface-preserving level set method is incorporated into the Reynolds-Averaged Navier-Stokes (RANS) numerical method to simulate the application of the green water phenomena around a platform and the breaking wave above the deck. In the present study, this method is used to evaluate the laminar in two dimension plane with fixed orthogonal grids. In this method, it is assumed that the free surface is modeled as immiscible two-phase flow (air and water). A level set function can present the individual fluids, and the interface between two-phase is represented by the zero level set. In addition, the level set evolution equation is coupled with the conservation equations for mass and momentum, which will be solved in the transformed plane. For different purposes, there are several block domains in the application grid. Chimera domain decomposition technique is employed to handle such embedding, overlapping, or matching grids. Several simple test cases were performed to demonstrate the feasibility of this method. The comparisons between the ENO scheme and the WENO scheme will be illustrated in the Zalesak's disk case and will further prove that the WENO scheme is superior to the ENO scheme. The propagation of continuous wave case will validate some properties of wave and determine the importance of some parameters in code. Moreover, the method will be applied in simulation of green water around a two dimensional platform. By configuring different deck heights, some distinct phenomena can be represented. Lastly, it is crucial to observe the green water phenomena around the platform deck by applying the velocity-extrapolation routine.

Pore-scale simulation has become increasingly important in recent years as a tool to understand multiphase flow behavior. Wettability affects aspects of flow such as capillary-pressure saturation curves, residual saturation of each phase, and relative permeability. Simulation of wettability at the pore-scale is still a non-trivial problem, and many different approaches exist to model it. In this work, we implement a variational level set formulation to impose different contact angles at the solid-fluid-fluid contact line for two-phase flow in simple rhomboidal pore geometries, and calculate the maximum mean curvature (equivalently capillary pressure) for each case. We compare our results with a detailed set of analytical and experimental results in a range of pore geometries of varying wettability from Mason and Morrow (1994), and demonstrate the accuracy of this method. While the simulations shown are for relatively simple geometries, the method has the ability to handle arbitrarily complex geometry (such as input from X-ray microtomography imaging). / text

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18781号 / 理博第4039号 / 新制||理||1581(附属図書館) / 31732 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 藤 定義, 教授 佐々 真一, 教授 早川 尚男 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Numerical simulation of cell motility is one of the difficult problems in computational science. It belongs to a class of problems which involve moving interfaces between flowing or deforming media. Different numerical techniques are being developed for different application areas and in this work an attempt is made to apply two popular numerical techniques used in the field of computational multiphase flows to a cell motility problem. An unsteady cell motility problem is considered to simulate numerically based on a two-dimensional mathematical model. Two important numerical methods, the Level set method and the Front tracking methods are applied to the cell motility problem to study several cases and to verify the convergence of the solution. With the assumption of no mechanical or physical obstructions to the cell, the results of the numerical simulations show that the domain shapes converge to a circular shape as they reach the steady state condition. The final steady state velocities with which the domains move and the final steady state area to which they converge are observed to be independent of domain shapes. Moreover all shapes converge to exactly same radius of circle and move with same velocity after reaching steady state condition.

In this dissertation, novel variational optical-flow and active-contour methods are investigated to address challenging problems in computer vision and shape-based imaging. Starting from traditional applications of these methods in computer vision, such as object segmentation, tracking, and detection, this research subsequently applies similar active contour techniques to the realm of shape-based imaging, which is an image reconstruction technique estimating object shapes directly from physical wave measurements. In particular, the first and second part of this thesis deal with the following two physically inspired computer vision applications. Optical Flow for Vision-Based Flame Detection: Fire motion is estimated using optimal mass transport optical flow, whose motion model is inspired by the physical law of mass conservation, a governing equation for fire dynamics. The estimated motion fields are used to first detect candidate regions characterized by high motion activity, which are then tracked over time using active contours. To classify candidate regions, a neural net is trained on a set of novel motion features, which are extracted from optical flow fields of candidate regions. Coupled Photo-Geometric Object Features: Active contour models for segmentation in thermal videos are presented, which generalize the well-known Mumford-Shah functional. The diffusive nature of heat processes in thermal imagery motivates the use of Mumford-Shah-type smooth approximations for the image radiance. Mumford-Shah's isotropic smoothness constraint is generalized to anisotropic diffusion in this dissertation, where the image gradient is decomposed into components parallel and perpendicular to level set curves describing the object's boundary contour. In a limiting case, this anisotropic Mumford-Shah segmentation energy yields a one-dimensional ``photo-geometric'' representation of an object which is invariant to translation, rotation and scale. These properties allow the photo-geometric object representation to be efficiently used as a radiance feature; a recognition-segmentation active contour energy, whose shape and radiance follow a training model obtained by principal component analysis of a training set's shape and radiance features, is finally applied to tracking problems in thermal imagery. The third part of this thesis investigates a physics-driven active contour approach for shape-based imaging. Adjoint Active Contours for Shape-Based Imaging: The goal of this research is to estimate both location and shape of buried objects from surface measurements of waves scattered from the object. These objects' shapes are described by active contours: A misfit energy quantifying the discrepancy between measured and simulated wave amplitudes is minimized with respect to object shape using the adjoint state method. The minimizing active contour evolution requires numerical forward scattering solutions, which are obtained by way of the method of fundamental solutions, a meshfree collocation method. In combination with active contours being implemented as level sets, one obtains a completely meshfree algorithm; a considerable advantage over previous work in this field. With future applications in medical and geophysical imaging in mind, the method is formulated for acoustic and elastodynamic wave processes in the frequency domain.

Pas de résumé / The level set method was introduced by Osher & Sethian (1988) as a general technique to capture moving interfaces. It has been used to study crystal growth, to simulate water and fire for computer graphics applications, to study two-phase flows and in many other fields. The wellknown problem of the level set method is the following: if the flow velocity is not constant, the level set scalar may become strongly distorted. Thus, the numerical integration may suffer from loss of accuracy. In level set methods, this problem is remedied by the reinitialization procedure, i.e. by reconstruction of the level set function in a way to satisfy the eikonal equation. We propose an alternative approach. We modify directly the level set equation by embedding a source term. The exact expression of this term is such that the eikonal equation is automatically satisfied. Furthermore on the interface, this term is equal to zero. In the meantime, the advantage of our approach is this: the exact expression of the source term allows for the possibility of derivation of its local approximate forms, of first-and-higher order accuracy. Compared to the extension velocity method, this may open the simplifications in realization of level set methods. Compared to the standard approach with the reinitialization procedure, this may give the economies in the number of level set re-initializations, and also, due to reduced number of reinitializations, one may expect an improvement in resolution of zero-set level. Hence, the objective of the present dissertation is to describe and to assess this approach in different test cases.

No description available.

A general framework is described for the solution of two-phase fluid-object interaction problems on the basis of coupling a distributed-Lagrange-multiplier fictitious domain method and a level-set method, intended for application to the problem of seabed scour by ice ridges. The resulting equations are discretized in space using stabilized finite-element methods and integrated in time using the generalized-α method. This approach is simple to implement and applicable to both structured and unstructured meshes in two and three dimensions. By means of examples, it is shown that despite the simplicity of the approach, good results are obtained in comparison with other more computationally demanding methods. A robust approach is utilized for constructing signed-distance functions on arbitrary meshes by introducing artificial numerical diffusivity to improve the robustness of classical signed-distance construction approaches without resorting to common pseudo-time relaxation. Under this approach, signed-distance functions can be rapidly constructed while preserving the numerical convergence properties and, generally, having minimal interfacial perturbation. The method is then applied with a modified deformation procedure for fast and efficient mesh adaptivity, including a discussion how it may be used in computational fluid dynamics. The two-phase fluid-object interaction approach is then customized for modeling of the seabed scour and soil-pipe interaction. In this approach, complex history-dependent soil constitutive models are replaced with a simple strain-rate dependent model. Utilization of this constitutive model along with the framework developed earlier leads to the treatment of seabed scour as a two-phase fluid-object interaction, and the soil-pipe interaction as a fluid-structure interaction problem without the need for remeshing. Good agreement with past experimental and numerical studies are obtained using our approach. The dissertation is concluded by conducting a parametric study of seabed scour in two- and three-dimensions. / text

The purpose of this thesis is to further develop numerical methods for solving surface problems by utilizing tangential calculus and the trace finite element method. Direct computation on the surface is possible by the use of tangential calculus, in contrast to the classical approach of mapping 2D parametric surfaces to 3D surfaces by means of differential geometry operators. Using tangential calculus, the problem formulation is only dependent on the position and normal vectors of the 3D surface. Tangential calculus thus enables a clean, simple and inexpensive formulation and implementation of finite element methods for surface problems. Meshing techniques are greatly simplified from the end-user perspective by utilizing an unfitted finite element method called the Trace Finite Element Method, in which the basic idea is to embed the surface in a higher dimensional mesh and use the shape functions of this background mesh for the discretization of the partial differential equation. This method makes it possible to model surfaces implicitly and solve surface problems without the need for expensive meshing/re-meshing techniques especially for moving surfaces or surfaces embedded in 3D solids, so called embedded interface problems. Using these two approaches, numerical methods for solving three surface problems are proposed: 1) minimal surface problems, in which the form that minimizes the mean curvature was computed by iterative update of a level-set function discretized using TraceFEM and driven by advection, for which the velocity field was given by the mean curvature flow, 2) elastic membrane problems discretized using linear and higher order TraceFEM, which makes it straightforward to embed complex geometries of membrane models into an elastic bulk for reinforcement and 3) stabilized, accurate vertex normal and mean curvature estimation with local refinement on triangulated surfaces. In this thesis the basics of the two main approaches are presented, some aspects such as stabilization and surface reconstruction are further developed, evaluated and numerically analyzed, details on implementations are provided and the current state of work is presented.