A Level-Set Method for Computing the Eigenvalues of Elliptic Operators Defined on Compact Hypersurfaces

We demonstrate, through separation of variables and estimates from the semi-classical analysis of the Schrödinger operator, that the eigenvalues of an elliptic operator defined on a compact hypersurface in ? ⁿ can be found by solving an elliptic eigenvalue problem in a bounded domain Ω?? ⁿ . The latter problem is solved using standard finite element methods on the Cartesian grid. We also discuss the application of these ideas to solving evolution equations on surfaces, including a new proof of a result due to Greer (J. Sci. Comput. 29(3):321–351, 2006).     

A spatial warping method for freeform modeling based on a level-set method

Providing an intuitive and effective tool for freeform geometric modeling is important for product design. We introduce in this paper a level-set based spatial warping method for freeform modeling, allowing shape deformation to be initialed by rigid body transformations of volumetric tools. Intuitive user operations including imprinting, deformation and smoothing are developed to shield the user from the underlying geometric complexity. Unlike mesh-based spatial warping methods, the developed method represents a digital model by implicit distance field data and describes its change of geometry by the level-set method. This guarantees the generation of topologically correct triangular mesh models and circumvents the error-prone remeshing and mesh-repairing processes, thus preventing topological errors such as self-intersections. We present this method with algorithm details, numerical experiments and modeling examples.     

Fracture resistance via topology optimization

The fracture resistance of structures is optimized using the level-set method. Fracture resistance is assumed to be related to the elastic energy released by a crack propagating in a normal direction from parts of the boundary that are in tension, and is calculated using the virtual crack extension technique. The shape derivative of the fracture-resistance objective function is derived. Two illustrative two-dimensional case studies are presented: a hole in a plate subjected to biaxial strain; and a bridge fixed at both ends subjected to a single load in which the compliance and fracture resistance are jointly optimized. The structures obtained have rounded corners and more material at places where they are in tension. Based on the results, we propose that fracture resistance may be modeled more easily but less directly by including a term proportional to surface area in the objective function, in conjunction with nonlinear elasticity where the Young’s modulus in tension is lower than in compression.     

Support structure constrained topology optimization for additive manufacturing

There is significant interest today in integrating additive manufacturing (AM) and topology optimization (TO). However, TO often leads to designs that are not AM friendly. For example, topologically optimized designs may require significant amount of support structures before they can be additively manufactured, resulting in increased fabrication and clean-up costs.In this paper, we propose a TO methodology that will lead to designs requiring significantly reduced support structures. Towards this end, the concept of ‘support structure topological sensitivity’ is introduced. This is combined with performance sensitivity to result in a TO framework that maximizes performance, subject to support structure constraints. The robustness and efficiency of the proposed method is demonstrated through numerical experiments, and validated through fused deposition modeling, a popular AM process.     

Computation of feed-paths for casting solidification using level-set-method

The aim of the present work is to compute feed-paths and hot-spots by combining level-set-method based sharp interface and feed-path model. The model is based on the solution of energy and level-set equations in solid and liquid, with Stefan condition on the interface. The energy and level-set equation are discretized using finite-volume and finite-difference method, respectively. Feed-path is computed by tracking mass-less particles along the liquid-solid interface during solidification using combined Eulerian-Lagrangian framework. The proposed model is benchmarked on six test cases, where temperature contours and solidification time are compared with a finite-element-method based commercial software. The capability to predict the temporal evolution of interface and to identify multiple hot-spots is validated with an industrial aluminum-alloy lug casting. The numerical as well as experimental validations demonstrate the effectiveness of level-set-method for feed-path calculation.     

Bubble modulation using acoustic standing waves in a bubbling system

The behavior of a 6 mm mesobubble in an acoustic standing wave field is examined both experimentally and numerically in this study. The acoustic standing waves at 16 and 20 kHz are generated using two Nickel magnetostrictive transducers located at the top and bottom of the column. Experimental studies of the rise velocity of a mesobubble in the acoustic field indicate an axial wavy rising pattern of the bubble synchronized with that of the standing wave. The bubble rise velocity is significantly lower than that in the absence of an acoustic field. The behavior of bubble volume contraction and expansion can be accounted for by a 3-D direct numerical simulation of the bubble dynamics and flow field based on the compressible N-S equations coupled with the level-set method. The experiments and simulation reveal a consistent value of the ratio of the Bjerknes force to the buoyancy force for a single mesobubble rising in the acoustic field to be at 20-25%.     

An efficient block parallel AMR method for two phase interfacial flow simulations

The direct numerical simulation of two phase interfacial flows can be computationally challenging, as the strong resolution needed to follow the deformations of the interface leads to a lot of time spent solving the whole computation domain. Efficient solution of such problems requires an adaptive mesh refinement capability to concentrate computational effort where it is most needed. In this paper a parallel adaptive algorithm to solve incompressible two-phase flows with surface tension is presented: the AMR is handled with the help of the PARAMESH package. The free interface between fluids is tracked via Level Set approach; the jump conditions at the interface for pressure and velocity are imposed by the Ghost Fluid method. A multigrid preconditioned BiCG-stab solver adapted to the AMR data structure has been developed to allow high density ratio computations (up to 1:1000). Special treatment has been done at the refinement jumps to maintain the fine mesh accuracy. Computational results are compared in different test cases with analytical solutions or literature, and show very good agreement with the references. The effectiveness of PARAMESH parallelization has been quite well maintained, as shown in the strong and weak scaling tests. Speed-up capabilities of the AMR are demonstrated.     

Numerical simulation of boiling enhancement on a microstructured surface

Significant efforts have been made to augment nucleate boiling by surface modification with micro-machined structures, but a general predictive approach for heat transfer enhancement has not yet been developed. In this work, complete numerical simulations are performed for boiling enhancement on a microstructured surface by employing the sharp-interface level-set method, which is modified to handle the contact angle and the evaporative heat flux from the liquid microlayer on an immersed solid surface. The effects of cavity diameter and surface modification such as concentric grooves and multi-step cavities on bubble growth and boiling heat transfer are investigated.     

Contour-Based Multi-Source Information Fusion for Motion Segmentation

A motion segmentation framework that effectively exploited the multiple sources of image information and fused these sources of the information synergisti-cally was proposed to serve the purpose of motion segmen- tation. A Markov process was formulated for motion seg- mentation in which two feature spaces were established to estimate the state transition Probability density function （PDF） and the initial state, respectively. An information fusion space was developed such that each motion struc-ture was described as a single distribution in this space. The proposed framework can naturally embed the evolution equations of the active contour methods into the seg-mentation to achieve contour-based segmentation results. Extensive empirical evaluations demonstrate the robust-ness and the promise of this framework.     

基于多目标优化技术的发动机罩加强筋布局设计研究

为了加强发动机罩壳的静态刚度特性和抑制振动能力,实现罩壳结构的轻量化,引入基于水平集法的拓扑优化技术和多目标理论,完成发动机罩加强筋布局的多目标优化设计。采用折衷规划法构建关于静刚度和一阶固有频率的多目标优化模型,运用水平集法求出罩壳加强筋的最佳分布形式。结果表明,该方法能大大地提高静动态结构性能,最大应力的下降说明罩壳应力集中现象得到有效的改善,缓解罩壳的疲劳现象。此外,基于层次分析法确定权重因子,避免了多目标优化模型构建中的主观能动性。采用平均频率法对动态目标函数的处理,有效地消除了动态优化过程中的收敛性。