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 for the time-domain simulation of green water effects. This generalized method can be used to evaluate two- and three-dimensional, laminar and turbulent, free surface flows in moving non-orthogonal grids. In the method, free surface flows are modeled as immiscible two-phase (air and water) flows. A level set function is used to mark the individual fluids and the free surface itself is represented by the zero level set function. The level set evolution equation is coupled with the conservation equations for mass and momentum, and solved in the transformed plane. Chimera domain decomposition technique is employed to handle embedding, overlapping, or matching grids. To demonstrate the feasibility of the method, calculations are performed in several bench mark free surface flows including dam break flows, free jets, solitary wave propagations and the impingement of dam break flow on a fixed structure. The comparisons between the simulations and the experimental data provide a thorough validation of the present method. The results also show the potential capability of level-set RANS method in much more complicated free surface flow simulations. After validations, the method is applied to simulate sloshing flows in LNG tank and green water over the platform. In sloshing flows, the level-set RANS method captures the large impact pressure accurately on LNG tank walls. It also generates a plunging breaker successfully in front of a platform in the numerical wave tank. The good agreements between numerical and experimental results prove the level set RANS method is a powerful and accurate CFD methodology in free surface flow simulations.

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.

An interface-preserving level set method is incorporated into the Reynolds- Averaged Navier-Stokes (RANS) numerical method for the time-domain simulation of green water effects. This generalized method can be used to evaluate two- and three-dimensional, laminar and turbulent, free surface flows in moving non-orthogonal grids. In the method, free surface flows are modeled as immiscible two-phase (air and water) flows. A level set function is used to mark the individual fluids and the free surface itself is represented by the zero level set function. The level set evolution equation is coupled with the conservation equations for mass and momentum, and solved in the transformed plane. Chimera domain decomposition technique is employed to handle embedding, overlapping, or matching grids. To demonstrate the feasibility of the method, calculations are performed in several bench mark free surface flows including dam break flows, free jets, solitary wave propagations and the impingement of dam break flow on a fixed structure. The comparisons between the simulations and the experimental data provide a thorough validation of the present method. The results also show the potential capability of level-set RANS method in much more complicated free surface flow simulations. After validations, the method is applied to simulate sloshing flows in LNG tank and green water over the platform. In sloshing flows, the level-set RANS method captures the large impact pressure accurately on LNG tank walls. It also generates a plunging breaker successfully in front of a platform in the numerical wave tank. The good agreements between numerical and experimental results prove the level set RANS method is a powerful and accurate CFD methodology in free surface flow simulations.

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

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 65-69). Also available in electronic version. Access restricted to campus users.

Thesis (Ph. D.)--University of Iowa, 2007. / Supervisors: Ching-Long Lin, Larry J. Weber. Includes bibliographical references (leaves 153-162).

We present a novel framework to exert a topology control over a level set evolution. Level set methods offer several advantages over parametric active contours, in particular automated topological changes. In some applications, where some a priori knowledge of the target topology is available, topological changes may not be desirable. A method, based on the concept of simple point borrowed from digital topology, was recently proposed to achieve a strict topology preservation during a level set evolution. However, topologically constrained evolutions often generate topological barriers that lead to large geometric inconsistencies. We introduce a topologically controlled level set framework that greatly alleviates this problem. Unlike existing work, our method allows connected components to merge, split or vanish under some specific conditions that ensure that no topological defects are generated. We demonstrate the strength of our method on a wide range of numerical experiments.

Second order level set projection method for incompressible Navier-Stokes equations is proposed to solve flow around arbitrary geometries. We used rectilinear grid with collocated cell centered velocity and pressure. An explicit Godunov procedure is used to address the nonlinear advection terms, and an implicit Crank-Nicholson method to update viscous effects. An approximate pressure projection is implemented at the end of the time stepping using multigrid as a conventional fast iterative method. The level set method developed by Osher and Sethian [17] is implemented to address real momentum and pressure boundary conditions by the advection of a distance function, as proposed by Aslam [3]. Numerical results for the Strouhal number and drag coefficients validated the model with good accuracy for flow over a cylinder in the parallel shedding regime (47 < Re < 180). Simulations for an array of cylinders and an oscillating cylinder were performed, with the latter demonstrating our methods ability to handle dynamic boundary conditions.

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